Certificate SAM Level 1 & Level 2 Mathematics Booklet 2011.indd

Edexcel Level 1/Level 2 Certificate Mathematics

Sample Assessment Material (SAMs)

Edexcel Level 1/Level 2 Certificate in Mathematics (KMA0) First teaching from September 2011

Contents General marking guidance

2

Paper 1F

3

Sample Assessment Material

3

Sample Mark Scheme

21

Paper 2F

31


31

Sample Mark Scheme

51

Paper 3H

59


59

Sample Mark Scheme

79

Paper 4H

89


89

Sample Mark Scheme

UG025980 Edexcel Level 1/Level 2 Certificate in Mathematics

109

SAMs

© Edexcel Limited 2011

1

General Marking Guidance x

All candidates must receive the same treatment. Examiners must mark the first candidate in exactly the same way as they mark the last.

x

Mark schemes should be applied positively. Candidates must be rewarded for what they have shown they can do rather than penalised for omissions.

x

All the marks on the mark scheme are designed to be awarded. Examiners should always award full marks if deserved, ie if the answer matches the mark scheme. Examiners should also be prepared to award zero marks if the candidate’s response is not worthy of credit according to the mark scheme.

x

Where some judgement is required, mark schemes will provide the principles by which marks will be awarded and exemplification may be limited.

x

Crossed out work should be marked UNLESS the candidate has replaced it with an alternative response.

Guidance on the use of codes within this mark scheme M1 – method mark A1 – accuracy mark B1 – working mark oe – or equivalent cao – correct answer only ft – follow through sc - special case

2


SAMs


Write your name here Surname

Other names

Edexcel Certificate L1/L2

Centre Number

Candidate Number

Mathematics Paper 1F Foundation Tier Paper Reference

Sample Assessment Material Time: 2 hours

KMA0/1F

You must have:

Total Marks

Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser, calculator. Tracing paper may be used.

Instructions

black ink or ball-point pen. • Use in the boxes at the top of this page with your name, • Fill centre number and candidate number. all questions. • Answer sufficient working, correct answers may be awarded no marks. • Without the questions in the spaces provided • Answer – there may be more space than you need. may be used. • Calculators You must NOT write anything on the formulae page. • Anything you write on the formulae page will gain NO credit.

Information

total mark for this paper is 100. • The for each question are shown in brackets • –Theusemarks this as a guide as to how much time to spend on each question.

Advice

Read each question carefully before you start to answer it. • Write answers neatly and in good English. • Checkyour • your answers if you have time at the end.

Turn over

S39742A ©2010 Edexcel Limited.

*S39742A0118*


SAMs


3

FORMULA – FOUNDATION IGCSESHEET MATHEMATICS 4400 TIER You must not writeFORMULAE on the fomulae page.–Anything you do write SHEET FOUNDATION TIERwill gain no credit. Area of a trapezium = 12 (a + b)h

Pythagoras’ Theorem a2 + b2 = c2

c

a

b

h

a

b

hyp

opp

adj = hyp u cos T opp = hyp u sin T opp = adj u tan T

Volume of prism = area of cross section ulength

T adj

or

sin T

opp hyp

cosT

adj hyp

tan T

opp adj

cross section

lengt

h

Circumference of circle = 2S r Area of circle = S r2 r r

Volume of cylinder = S r2h h

4

Curved surface area of cylinder = 2S rh


SAMs


Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working. 1 15

21

23

24

25

27

33

35

39

From the numbers in the box, write down (5) (i)

an even number .................................... . . . . . . . . . . . . . . . . . . .

(ii) a factor of 60 .................................... . . . . . . . . . . . . . . . . . . .

(iii) a multiple of 9 .................................... . . . . . . . . . . . . . . . . . . .

(iv) a square number .................................... . . . . . . . . . . . . . . . . . . .

(v) a prime number. .................................... . . . . . . . . . . . . . . . . . . .

(Total for Question 1 = 5 marks)


SAMs


5

2 The diagram shows a triangle ABC on a centimetre grid. y 6 5

A

C

4 3 2 1 B O

1

2

3

4

5

6

7

8

9

10 x

(a) Write down the coordinates of the point (2) (i) A,

(..................... , ..................... )

(ii) B.

(..................... , ..................... )

(b) Measure the length of the line AB. Give your answer in millimetres. (1) ................................................ . . . . . . .

mm

(c) Find the perimeter of triangle ABC. (2) ................................................ . . . . . . .

mm

(d) Write down the special name for triangle ABC. (1)

.................................... . . . . . . . . . . . . . . . . . . .

(e) (i) Measure the size of angle B. (1) ° ....................................... . . . . . . . . . . . . . . . .

(ii) Write down the special name for this type of angle. (1)

.................................... . . . . . . . . . . . . . . . . . . .

(Total for Question 2 = 8 marks) 6


SAMs


3 (a) Write down the number which is exactly halfway between 0.3 and 0.4 ........................................... . . . . . . . . . . . . . . . . . . .

(1)

3.7

3.8

(b) What is the reading on the scale? ........................................... . . . . . . . . . . . . . . . . . . .

(1) (c) Write down the value of the 4 in the number 0.746 ........................................... . . . . . . . . . . . . . . . . . . .

(1) (d) Here is a list of numbers. 0.3

0.32

0.02

0.23

0.03

Write these numbers in order of size. Start with the smallest number. ........................................... . . . . . . . . . . . . . . . . . . .

(1) (e) Write

3 as a decimal. 4 ........................................... . . . . . . . . . . . . . . . . . . .

(1) (f) Write 0.7 as a percentage. ........................................... . . . . . . . . . . . .

%

(1) (g) Round 6.84 to the nearest whole number. ........................................... . . . . . . . . . . . . . . . . . . .

(1) (Total for Question 3 = 7 marks)


SAMs


7

4 Here are the first five terms of a number sequence. 1

7

13

19

25

(a) Write down the next term in the sequence. (1) .................................... . . . . . . . . . . . . . . . . . . .

(b) Explain how you worked out your answer. (1) . . . . . . . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . . . . . . . . . . . . . .

(c) Find the 11th term of the sequence. (1)

.................................... . . . . . . . . . . . . . . . . . . .

(d) The 50th term of the sequence is 295 Work out the 49th term of the sequence. (1) .................................... . . . . . . . . . . . . . . . . . . .

Tamsin says, “Any two terms of this sequence add up to an even number.” (e) Explain why Tamsin is right. (1) . . . . . . . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................. . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . . . . . . . . . . . . . .


8


SAMs


5 Here are 9 flags.

A

B

C

D

E

F

G

H

I

(a) Write down the letter of the flag which has: (4) (i) exactly one line of symmetry .................................... . . . . . . . . . . . . . . . . . . .

(ii) rotational symmetry of order 4 .................................... . . . . . . . . . . . . . . . . . . .

(iii) 2 lines of symmetry and rotational symmetry of order 2 .................................... . . . . . . . . . . . . . . . . . . .

(iv) no lines of symmetry and rotational symmetry of order 2 .................................... . . . . . . . . . . . . . . . . . . .

(b) Write down the letter of the flag which has a rhombus on it. (1) .................................... . . . . . . . . . . . . . . . . . . .

(Total for Question 5 = 5 marks) UG025980 Edexcel Level 1/Level 2 Certificate in Mathematics

SAMs


9

6 The bar chart shows information about the number of people, in millions, who speak each of 6 languages.

Number of people (million)

900 800 700 600 500 400 300 200 100 0 Mandarin Spanish English Chinese

Hindi

Arabic

Bengali Japanese

Language

(a) Write down the number of people who speak Hindi. (1)

.......................................................

million

(b) Write down the number of people who speak Mandarin Chinese. (1)

.......................................................

million

(c) Which language is spoken by 190 million people? (1)

.................................... . . . . . . . . . . . . . . . . . . .

125 million people speak Japanese. (d) Draw a bar on the bar chart to show this information. (1) (e) Find the ratio of the number of people who speak Hindi to the number of people who speak Japanese. Give your ratio in its simplest form. (2)

.................................... . . . . . . . . . . . . . . . . . . .

10


SAMs


330 million people speak English. 70% of these people live in the USA. (f) Work out 70% of 330 million. (2)

.......................................................

million

332 million people speak Spanish. 143 million of these people live in South America. (g) Work out 143 million as a percentage of 332 million. Give your answer correct to 1 decimal place. (2)

........................................... . . . . . . . . . . . .

%

(Total for Question 6 = 10 marks) 7 (a) Solve 2x + 9 = 1 (2)

x = .................................... . . . . . . . . . . . . . . . . . . . (b) Solve 5y – 4 = 2y + 7 (2)

y = .................................... . . . . . . . . . . . . . . . . . . . (Total for Question 7 = 4 marks) UG025980 Edexcel Level 1/Level 2 Certificate in Mathematics

SAMs


11

8 The table shows information about the time in each of five cities. For each city, it shows the number of hours time difference from the time in London. + shows that the time is ahead of the time in London. í shows that the time is behind the time in London.

City

Time difference from London (hours)

Cairo

+2

Montreal

−5

Bangkok

+7

Rio de Janeiro

−3

Los Angeles

−8

Mexico City (a) When the time in London is 6 a.m., what is the time in: (2) (i) Bangkok,

.................................... . . . . . . . . . . . . . . . . . . .

(ii) Los Angeles.

.................................... . . . . . . . . . . . . . . . . . . .

(b) The time in Mexico City is 2 hours ahead of the time in Los Angeles. Complete the table to show the time difference of Mexico City from London. (1) (c) Write down the name of the city in which the time is 10 hours behind Bangkok. (1) .................................... . . . . . . . . . . . . . . . . . . .

(d) Work out the time difference between (2) (i) Cairo and Montreal, .................................................... . . .

hours

.................................................... . . .

hours

(ii) Rio de Janeiro and Los Angeles.



SAMs


9

£1 = 72.5 Indian rupees (a) Change £86 to Indian rupees. .......................................................

Indian rupees (2)

(b) Change 8700 Indian rupees to pounds (£). £

.................................... . . . . . . . . . . . . . . . . . . .

(2) (Total for Question 9 = 4 marks)


SAMs


13

10 y 8

C

B

6 4 A 2 –2

O

2

4

6

8

x

–2 Write down the equation of (3) (i)

line A, .................................... . . . . . . . . . . . . . . . . . . .

(ii) line B, .................................... . . . . . . . . . . . . . . . . . . .

(iii) line C. .................................... . . . . . . . . . . . . . . . . . . .

(Total for Question 10 = 3 marks) 11 (a) Use your calculator to work out the value of (3.7 4.6) 2 2.8 6.3 Write down all the figures on your calculator display. (2)

.................................... . . . . . . . . . . . . . . . . . . .

(b) Give your answer to part (a) correct to 2 decimal places. (1) .................................... . . . . . . . . . . . . . . . . . . .



SAMs


12 Here are five shapes.

Four of the shapes are squares and one of the shapes is a circle. One square is black. Three squares are white. The circle is black. The five shapes are put in a bag. Alec takes at random a shape from the bag. (a) Find the probability that he will take the black square. (1)

.................................... . . . . . . . . . . . . . . . . . . .

(b) Find the probability that he will take a white square. (2)

.................................... . . . . . . . . . . . . . . . . . . .

Jasmine takes a shape at random from the bag 150 times. She replaces the shape each time. (c) Work out an estimate for the number of times she will take a white square. (2)

.................................... . . . . . . . . . . . . . . . . . . .



SAMs


15

13 A basketball court is a rectangle, 28 m long and 15 m wide. (a) Work out the area of the rectangle. (2)

............................................. . . . . . . . . . .

m2

(b) In the space below, make an accurate scale drawing of the rectangle. Use 1 cm to represent 5 m. (2)

(Total for Question 13 = 4 marks) 14 (a) Work out the value of x2 – 5x when x = –3 (2)

.................................... . . . . . . . . . . . . . . . . . . .

(b) Factorise x2 – 5x (2)

.................................... . . . . . . . . . . . . . . . . . . .



SAMs


15 Hajra counted the numbers of sweets in 20 packets. The table shows information about her results. Number of sweets

Frequency

46

3

47

6

48

3

49

5

50

2

51

1

(a) What is the mode number of sweets? (1)

.................................... . . . . . . . . . . . . . . . . . . .

(b) Work out the range of the number of sweets. (2)

.................................... . . . . . . . . . . . . . . . . . . .

(c) Work out the mean number of sweets in the 20 packets. (3)

.................................... . . . . . . . . . . . . . . . . . . .



SAMs


17

16

y 4 3 2 P

1

Q

-2

-1

0

1

2

3

4

-1

5

6

7

x

R

-2

(a) Describe fully the single transformation which maps triangle P onto triangle Q. (2) . . . . . . . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................. . . . . . . . . . . . . . . . . .

(b) Describe fully the single transformation which maps triangle P onto triangle R. (3) . . . . . . . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................. . . . . . . . . . . . . . . . . .


18


SAMs


17 (a) Simplify, leaving your answers in index form, (2) (i) 75 u

.................................... . . . . . . . . . . . . . . . . . . .

(ii) 59 y

.................................... . . . . . . . . . . . . . . . . . . .

(b) Solve

9

4

2 ×2 = 28 n 2

(2)

n = .................................... . . . . . . . . . . . . . . . . . . . (Total for Question 17 = 4 marks) 18 (a) Expand and simplify 3(4x – 5) – 4(2x + 1) (2)

.................................... . . . . . . . . . . . . . . . . . . .

(b) Expand and simplify (y + 8)(y + 3) (2)

.................................... . . . . . . . . . . . . . . . . . . .

(c) Expand p(5p2 + 4) (2)

.................................... . . . . . . . . . . . . . . . . . . .


SAMs


19

19 A tunnel is 38.5 km long. (a) A train travels the 38.5 km in 21 minutes. Work out the average speed of the train. Give your answer in km/h. (3)

................................................... . . . .

km/h

(b) To make the tunnel, a cylindrical hole 38.5 km long was drilled. The radius of the cylindrical hole was 4.19 m. Work out the volume of earth, in m3, which was removed to make the hole. Give your answer correct to 3 significant figures. (3)

............................................. . . . . . . . . . .

m3

(Total for Question 19 = 6 marks) TOTAL FOR PAPER = 100 MARKS

20


SAMs



SAMs


21

1 1 1 2 1 1 1

(1,5) (5,0) 64 204 – 212 inc isosceles 77 acute

8(0) + 2 x “64”

2(d) 2(e)(i) 2(e)(ii)

Mark

Answer

Working

1 1 1 1 1

24 15 27 25 23

Question Number 2(a)(i) 2(a)(ii) 2(b) 2(c)

Mark

Answer

Working

Question Number 1 (i) 1 (ii) 1 (iii) 1 (iv) 1 (v)

Paper 1F

Sample Mark Scheme

cao cao cao cao cao

B1 B1 B1 Allow +2mm M1 Also award for 20.4 – 21.2 A1 ft from “64” B1 B1 allow + 2 B1

Notes

B1 B1 B1 B1 B1

Notes

22


SAMs


Question Number 4(a) 4(b) 4(c) 4(d) 4(e)

Working

Mark 1 1 1 1 1

Answer 31 eg ‘Add 6’ 61 289 eg ‘Sum of two odd numbers is always even’

1 1 1 1

0.02 0.03 0.23 0.3 0.32 0.75 70 7

3 (d) 3 (e) 3 (f) 3 (g)

Mark 1 1 1

Answer 0.35 3.74 hundredths

Working

Question Number 3 (a) 3 (b) 3 (c) 1 100

B1 cao B1 B1 cao B1 ft from (b) B1 Accept if ‘odd’ used correctly

Notes

B1 cao B1 cao B1 cao B1 cao

B1 Also accept 4 hundredths,

B1 cao B1 cao

Notes

,

4 100

, 0.01, 0.04


SAMs


23

2

43.1

143 u 100 332

6(g)

2

231

300:125

70 u 330 100

1 1 1 1 2

300 855 - 875 Bengali 100 < bar < 150 12:5

6(f)

Mark

Answer

Working

1 1 1 1 1

B F I D H

Question Number 6(a) 6(b) 6(c) 6(d) 6(e)

Mark

Answer

Working

Question Number 5(a)(i) 5(a)(ii) 5(a)(iii) 5(a)(iv) 5(b) cao cao cao cao cao

B1 cao B1 B1 B1 M1 for 300:125, 60:25 also for 125:300, 25:60, 5:12 A1 70 M1 for u 330 100 A1 for 231 143 M1 for or 0.430722… 332 A1 for 43.1 or better

Notes

B1 B1 B1 B1 B1

Notes

24


SAMs


4 oe

2x = 1 9

5y 2y = 7 + 4

Working

7(b)

Mark 1 1 1 1 1 1

Answer 1 pm 10 pm

6 Rio de Janeiro 7 5

8(a)(ii)

8(b) 8(c)

8(d)(i)

8(d)(ii)

B1 for 1pm Accept 1300 B1 for 10pm Accept 2200 B1 cao B1 for Rio de Janeiro Accept Rio B1 for 7 Accept -7 B1 for 5 Accept -5

Notes

M1 for 2 x = 1 9 [separate evidence of M1 is required] A1 for 4 oe M1 for 5 y 2 y = 7 + 4 [separate evidence of M1 is required] 11 2 , 3 oe A1 for 3 3 Also accept 2 or more d.p. rounded or truncated e.g. 3.66, 3.67

2 2

Notes

Mark

Question Number 8(a)(i)

11 2 , 3 oe 3 3

Answer

Working

Question Number 7(a)


SAMs


25

7.57 1

2

7.5703…

68.89 9 .1

11(b)

Mark

Answer

Working

1 1 1

y=3 x =5 y x


Mark

Answer

2

120

8700 ÷ 72.5

9 (b)

Working

2

6235

86 × 72.5

Question Number 10(i) 10(ii) 10(iii)

Mark

Answer

Working

Question Number 9 (a)

519 6889 , 910 910

B1 ft from (a) if non-trivial ie (a) must have more than 2 d.p.

Also accept 7

M1 for 8.3, 68.89, 9.1 or 30.90… A1 Accept if first 5 figures correct

Notes

B1 cao B1 cao B1 cao

Notes

M1 for 86 × 72.5 A1 cao M1 for 8700 ÷ 72.5 A1 cao

Notes

26


SAMs


2

90

12(b)

12(c)

14(b)


13(b)


2

3 5

2

2

24

(-3)2 5 u 3

x( x 5)

Mark

2

Rectangle 5.6cm long and 3cm wide

Answer

2

420

28 × 15

Working

Mark

Answer

Working

3 5

1

1 5

150 x “ ”

Mark

Working

Answer

Question Number 12(a) 1 5

3 5

3 5

90 150

M1 for substn or 9 or 15 seen A1 cao B2 for x( x 5) B1 for factors which, when expanded and simplified, give two terms, one of which is correct SC B1 for x (5 - x ), x (x - 5x )

Notes

M1 for 28 × 15 A1 cao B2 for an accurate scale drawing of the rectangle/ Allow + 2mm B1 for either length or width.

Notes

Do not accept

A1 ft from “ ”

3 5

, Accept 0.6, 60%

M1 for 150 x “ ”

A1 for

Accept 0.2, 20% M1 for fraction with denominator 5

B1 for

Notes


SAMs


27

16(b)

Working

3

2

translation 3 squares to the right and 1 square down

rotation of 90° clockwise about (2, 1)

Mark

Answer

3

48


1 2

47 5

51 46

(46 u 3) (47 u 6) (48 u 3) (49 u 5) (50 u 2) (51 u 1) or 138 282 144 245 100 51 or 960 “960” y 20

Mark

Answer

Working

15(c)

Question Number 15(a) 15(b)

§ 3· ¨ 1¸ © ¹

but not

(3, 1) B3 for correct description of the transformation B1 for rotation Accept rotate, rotated etc B1 for 90° clockwise or 90° or 270° B1 for (2, 1)

B1 for 3 right and 1 down or

B2 for correct description of the transformation B1 for translation. Accept translate, translated etc Accept ‘across’ instead of ‘to the right’

Notes

These marks are independent but award no marks if answer is not a single transformation


B1 cao M1 for 51 46, 46 51 etc A1 cao M1 for finding at least 4 products and adding M1 (dep on 1st M1) for division by 20 A1 cao

Notes

28


SAMs


18(c)

18(b)


Question Number 17(a)(i) 17(a)(ii) 17(b)

y 2 3 y 8 y 24

2 2

5p 3 + 4 p

B2 cao B1 for either 5p3 or for + 4p

M1 for 3 terms correct or y 2 11 y seen A1

M1 for at least 3 terms correct inc signs A1

2

y 2 11 y 24

4 x 19

12 x 15 8 x 4

Notes

B1 cao B1 cao M1 for 9 4 n = 8 or better Also award for 2n = 25, 2n= 32 or 25 on answer line A1 cao

Notes

Mark

1 1 2

78 56 5

Answer

Mark

Answer

Working

9 4 n = 8 or 13 n = 8

Working


SAMs


29

19(b)


ʌ × 4.19² × 38500 = 2123433.419 m³

2 120 000 3

3

110

21 38.5 = 0.35 ; u 60 or 60 21

38.5 0.35

Mark

Answer

Working

21 or 0.35 60

A1 for 2 120 000 or for answer which rounds to 2 120 000

A1 cao M2 ʌ × 4.19² × 38500 [M1 for ʌ × (no with digits 419)2 × no with digits 385]

38.5 "0.35"

38.5 38.5 or 1.8333… or or 183.333… 21 0.35

M1 for “1.8333…” u 60 or

or

M1 for

Notes

30


SAMs



Other names


Centre Number

Candidate Number

Mathematics Paper 2F Foundation Tier Paper Reference


KMA0/2F

You must have:

Total Marks


Instructions


Information


Advice


Turn over


*S39745A0120*


SAMs


31

FORMULA SHEET – FOUNDATION TIER IGCSE MATHEMATICS 4400 You must not write on the fomulae page. Anything you do write will gain no credit. FORMULA SHEET – FOUNDATION TIER Area of a trapezium = 12 (a + b)h

Pythagoras’ Theorem a2 + b2 = c2

c

a

b

h

a

b

hyp

opp


Volume of prism = area of cross section ulength

T adj

or

sin T

opp hyp

cosT

adj hyp

tan T

opp adj

cross section

lengt

h

Circumference of circle = 2S r Area of circle = S r2 r r

Volume of cylinder = S r2h h

32



SAMs


Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1

(a) Here is a list of numbers. 999

1999

199

9000

1009

(i) Write these numbers in order of size. Start with the smallest. (3)

. . . . . . .................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . . . . . .

(ii) From the list, write down an even number.

..................................... . . . . . . . . . . . . . . . . . .

(iii) From the list, write down a number that is a multiple of 9

..................................... . . . . . . . . . . . . . . . . . .

(b) Here are four cards. Each card has a number on it.

3

4

1

2

The four cards are arranged to make the number 3412 The cards can be re-arranged to make other numbers. (3) (i) Write down the largest number that can be made. ..................................... . . . . . . . . . . . . . . . . . .

(ii) Write down the smallest odd number that can be made. ..................................... . . . . . . . . . . . . . . . . . .



SAMs


33

2

On the probability scale, mark the following with a cross (x). (i) The probability that the next baby to be born will be a boy. Label this cross A. (ii) The probability that the day after Saturday will be Sunday. Label this cross B. (iii) The probability that a person chosen at random has a birthday in May. Label this cross C.

0

0.5

1 (Total for Question 2 = 3 marks)

3

O is the centre of the circle. A

T

C O

B

The line AB touches the circle at T. (a) Write down the mathematical name for the line (3) (i) OT, ..................................... . . . . . . . . . . . . . . . . . .

(ii) CT, ..................................... . . . . . . . . . . . . . . . . . .

(iii) AB. ..................................... . . . . . . . . . . . . . . . . . .

(b) Write down the mathematical name for the shaded region. (1) ..................................... . . . . . . . . . . . . . . . . . .



SAMs


4

(a) Write the number 3969 in words (1)

. . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . . . . . .

(b) Write a number in the box so that this is a correct calculation. (1)

189 u

= 3969

(c) Write down the value of the 3 in the number 3969 (1) .................................... . . . . . . . . . . . . . . . . . . .

(d) Write the number 3969 correct to the nearest 10 (1) .................................... . . . . . . . . . . . . . . . . . . .

(e) Write the number 3969 correct to the nearest 100 (1) .................................... . . . . . . . . . . . . . . . . . . .

(f) Find the cube root of 3969 (i) Write down all the figures on your calculator display. (2) .................................... . . . . . . . . . . . . . . . . . . .

(ii) Give your answer correct to 3 significant figures.

.................................... . . . . . . . . . . . . . . . . . . .



SAMs


35

5

This formula gives the cost of hiring a bike for a number of days.

cost in pounds = 4 × number of days + 2 (a) Angus hired a bike for 5 days. Calculate the cost. (2)

£ ..................................... . . . . . . . . . . . . . . . . . . (b) Jeevan hired a bike. The cost was £30 Calculate the number of days for which Jeevan hired the bike. (2)

.................................... . . . . . . . . . . . . . . . . . . .


36


SAMs


6

(a) What fraction of this shape is shaded? (1)

.................................... . . . . . . . . . . . . . . . . . . .

(b) Find a fraction that is equivalent to

4 9

(1)

.................................... . . . . . . . . . . . . . . . . . . .

(c) Here is a list of fractions. 7 20

3 10

9 25

12 36

Which fraction in the list is the greatest fraction? (3)

.................................... . . . . . . . . . . . . . . . . . . .



SAMs


37

7

Chocolate bars cost £1.10 each. Cakes cost £1.25 each. Joshi buys 2 chocolate bars and 3 cakes. He pays with a £10 note. Work out how much change he should receive.

£ ..................................... . . . . . . . . . . . . . . . . . . (Total for Question 7 = 3 marks)

38


SAMs


8

Here are the numbers of points scored by 8 teams in a season. 5

3

14

12

4

3

6

9

(a) Find the mode. (1)

.................................... . . . . . . . . . . . . . . . . . . .

(b) Work out the mean. (3)

.................................... . . . . . . . . . . . . . . . . . . .

(c) Find the median. (2)

.................................... . . . . . . . . . . . . . . . . . . .

(d) The team that scored 4 points was The Cheetahs. Later, The Cheetahs had points taken away because of foul play. (2) (i) Will the median increase or decrease or stay the same? .................................... . . . . . . . . . . . . . . . . . . .

(ii) Give your reason. . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . . . . . .

. . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . . . . . .

. . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . . . . . .

(e) A team is chosen at random from these 8 teams. Find the probability that this team scored more than 10 points. (2)

.................................... . . . . . . . . . . . . . . . . . . .



SAMs


39

9

The diagram shows a triangle drawn on a centimeter squared grid.

(a) Work out the area of the triangle. State the units of your answer. (3)

.................................... . . . . . . . . . . . . . . . . . . .

(b) (2)

On the grid, reflect the triangle in the dotted line. (Total for Question 9 = 5 marks)

40


SAMs


10 Here is a number machine. Input

Add 3

Multiply by 5

Output

(a) Work out the output when the input is 6 (2) ..................................... . . . . . . . . . . . . . . . . . .

(b) Work out the input when the output is 70 (2)

..................................... . . . . . . . . . . . . . . . . . .

(c) Work out the input when the output is –85 (2)

..................................... . . . . . . . . . . . . . . . . . .

(d) Find an expression, in terms of x, for the output when the input is x. (2)

..................................... . . . . . . . . . . . . . . . . . .



SAMs


41

11

A y

Diagram NOT accurately drawn x

50° B

C

D

In the diagram BCD is a straight line. (a) Work out the size of angle x. (1)

° ....................................... . . . . . . . . . . . . . . . .

(b) (i) Work out the size of angle y.

° ....................................... . . . . . . . . . . . . . . . .

(ii) Give a reason for your answer to part (b)(i). (2) . . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . . . . . .

. . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . . . . . .


42


SAMs


12 Michelle has £4800 She gives

2 of the £4800 to a charity. 5

(a) How much money does Michelle give to the charity? (2)

£ ..................................... . . . . . . . . . . . . . . . . . . (b) The charity spends 85% of this money on medicines. How much money does the charity spend on medicines? (2)

£ ..................................... . . . . . . . . . . . . . . . . . . (Total for Question 12 = 4 marks) 13 The diagram shows the lengths, in cm, of the sides of a triangle. (3x – 5)

x

(2x + 1) The perimeter of the triangle is 17 cm. (i) Use this information to write an equation in x.

.................................... . . . . . . . . . . . . . . . . . . .

(ii) Solve your equation.

x = .................................... . . . . . . . . . . . . . . . . . . . (Total for Question 13 = 3 marks)


SAMs


43

14 Anji mixes sand and cement in the ratio 7 : 2 by weight. The total weight of the mixture is 27 kg. Calculate the weight of sand in the mixture.

............................................. . . . . . . . . . .

kg

(Total for Question 14 = 3 marks) 15 Solve 5(x – 4) = 35

x = ..................................... . . . . . . . . . . . . . . . . . . (Total for Question 15 = 3 marks)

44


SAMs


16 Julian has to work out

6.8 u 47.6 without using a calculator. 2.09

(a) Round each number in Julian’s calculation to one significant figure. (2)

.................................... . . . . . . . . . . . . . . . . . . .

(b) Use your rounded numbers to work out an estimate for

6.8 u 47.6 2.09

Give your answer correct to one significant figure. (2)

.................................... . . . . . . . . . . . . . . . . . . .

(c) Without using your calculator, explain why your answer to part (b) should be greater than the exact answer. (2) . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . . . . . .

. . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . . . . . .

. . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . . . . . .



SAMs


45

17 The diagram shows a wall.

3m

2m

Diagram NOT accurately drawn

6m (a) Calculate the area of the wall. (2)

.............................................. . . . . . . . . .

m2

(b) 1 litre of paint covers an area of 20 m2. Work out the volume of paint needed to cover the wall. Give your answer in cm3. (3)

................................................. . . . . . .

cm3


46


SAMs


18 Solve the simultaneous equations y=x+3 y = 7x

x = ..................................... . . . . . . . . . . . . . . . . . . y = ..................................... . . . . . . . . . . . . . . . . . . (Total for Question 18 = 3 marks)


SAMs


47

19 (a)

4.2 cm x°

5.1 cm


Calculate the value of x. Give your answer correct to 3 significant figures. (3)

x = .................................... . . . . . . . . . . . . . . . . . . . (b)

A 5 cm


29° B

C

Calculate the length of AB. Give your answer correct to 3 significant figures. (3)

............................................... . . . . . . . .

cm


48


SAMs


20 A bag contains some marbles. The colour of each marble is red or blue or green or yellow.

A marble is taken at random from the bag. The table shows the probability that the marble is red or blue or green. Colour

Probability

Red

0.1

Blue

0.2

Green

0.1

Yellow (a) Work out the probability that the marble is yellow. (2)

.................................... . . . . . . . . . . . . . . . . . . .

(b) Work out the probability that the marble is blue or green. (2)

.................................... . . . . . . . . . . . . . . . . . . .

The probability that the marble is made of glass is 0.8 (c) Beryl says “The probability that the marble is green or made of glass is 0.1 + 0.8 = 0.9” (2) Is Beryl correct?

................................................ . . . . . . .

Give a reason for your answer. . . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . . . . . .

. . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . . . . . .

(Total for Question 20 = 6 marks) PLEASE TURN OVER FOR QUESTION 21 UG025980 Edexcel Level 1/Level 2 Certificate in Mathematics

SAMs


49

21 Diagram NOT accurately drawn

h cm

4 cm

6 cm Calculate the value of h. Give your answer correct to 3 significant figures.

h = ..................................... . . . . . . . . . . . . . . . . . . (Total for Question 21 = 3 marks) TOTAL FOR PAPER = 100 MARKS

50


SAMs



SAMs


51

Working

Working

Question Number 3(a)(i) 3(a)(ii) 3(a)(iii) 3(b)

Working

Question Number 2(i) 2(ii) 2(iii)

1(a)(ii) 1(a)(iii) 1(b)(i) 1(b)(ii)


Paper 2F

Sample Mark Scheme

1

199, 999, 1009, 1999, 9000 9000 999 or 9000 4321 1243

Radius Chord Tangent Sector 1 1 1 1

Mark

1 1 1

A at 0.5 ± 2mm B at 1 C at 2 d d d 25mm from 0 Answer

Mark

Answer

1 1 1 2

Mark

Answer

B1 B1 B1 B1

allow allow allow allow

Notes misspellings misspellings misspellings misspellings

B1 B1 B1 ie between 0 and 0.25 exclusive

Notes

B1 B1 B1 B2 B1 for begin with 1 or end with 1 or 3

B1

Notes

52


SAMs


6(c)

9 25

8 12 12 15 , , , ,... 18 27 4 50

Answers from

5 12

Answer

3

M1 for attempt to convert all to dec or % or c.d. Eg 0.35, 0.3, 0.36, 0.333… M1 for all correctly converted A1

B1 cao

B1 cao

1 1

Notes

M1 for 4 u 5 2 A1 cao 30 or ans 7.25 oe M1 Allow 4 A1 cao

Notes

B1 B1 cao B1 for thousands or 3000 or 3 thousand B1 cao B1 cao B1 B1 ft from (f)(i)

Notes

Mark

2

7

Working

2

22

4u52


Mark

Answer

1 1 1 1 1 1 1

Mark

Working

28 4

6(b)

Answer

Three thousand, nine hundred and sixty nine 21 thousands 3970 4000 15.83289… 15.8

Working

5(b)


Question Number 4(a) 4(b) 4(c) 4(d) 4(e) 4(f)(i) 4(f)(ii)


SAMs


53

9(b)


8(d)(i) 8(d)(ii) 8(e)

8(c)


Question Number 7

Working

Arrange in order

56 6 x attempted or 8

Triangle correctly drawn

2

B2 for 6 B1 (independent) for cm2 oe (B1 for 5 to 7 incl) B2 for correct triangle drawn r 2mm or B1 for two vertices correct

3

6cm2

1 1 2

Same Middle unchanged 2 oe 8

Notes

2

5.5 oe

B1 cao M1 eg 48.125 M1 dep A1 cao M1 for arrangement in order A1 for 5.5 oe B1 indep B1 or still 5.5 B1 for denominator of 8 B1 for numerator of 2 (SC B1 for 2:8)

Mark

1 3

3 7

Notes

M1 for 2 × 1.10 + 3 × 1.25 or 5.95 M1 dep on 1st M1 A1

Notes

Answer

Mark

Answer

3

4.05

2 × 1.10 + 3 × 1.25 or 5.95 10.00 – “5.95”

Working

Mark

Answer

Working

54


SAMs


12(b)

2

2

1920

1632

2 x 4800 5

0.85 × “1920” oe

Mark

Answer

Working

1 1 1

130 40 angle sum of triangle


Mark

Answer

Working

Question Number 11(a) 11(b)(i) 11(b)(ii)

2

2

5( x 3) or ( x 3) u 5 or 5 x 15 oe

20

10(d)

- 85 3 or 17 3 5

2

11

10(c)

2

45

(6 3) u 5 oe

70 or 14 3 5

Mark

Answer

Working

10(b)


- 85 3 or 17 3 5

2 x 4800 5 A1 cao M1 0.85 × “1920” oe A1 cao

M1 for

Notes

B1 cao B1 cao B1 for correct reason Do not accept 180 (90 + 50)

Notes

A1 cao B2 for 5( x 3) or ( x 3) u 5 or 5 x 15 oe B1 for answer x 3 u 5 B0 for answer 5 x 3 or x 15 ‘ x =’ subtract B1

M1 for

M1 Bracket essential unless answer is correct A1 for 45 67 M1 allow or 13.2 5 A1 cao

Notes


SAMs


55

5 x – 20 35 5 x = 55

Working 11

Answer

3

21

9 seen 7 27 u 27 or 7 u oe 9 9

Question Number 15

Mark

Answer

Working

3

Mark

35

M1 dep on 1st M1 or M2 for x 4 A1 (dependent on both M marks)

M1 for 5 x – 20

Notes

A1 cao

M1 (dep B1) for

B1 for 9 seen

Notes

21 6

17

7

7 27 u 27 or 7 u oe 9 9

c

A1 for 3.5 oe, eg

M1 ft (i) if 6 x

Question Number 14

2

3.5 oe

0

6x etc

13(ii)

21 or 6 x 21

B1 oe eg 6 x 4

1

x 2x 13x5 17

Notes

Mark

Answer

Working

Question Number 13(i)

56


SAMs


15 u 1000 oe 20

750 3

2

15

(2 + 3) × 6 or 2 1 u 6 u 1 oe 2u6 2

17(b)

Mark

Answer

Working


2

2

(6 or 7) u (48 or 50) , correctly 2 or 3

(2 + 3) × 6 or 2 1 u 6 u 1 oe 2u6 2 A1 cao 15 ’ oe M1 for ‘ 20 15 ’ u 1000 oe M1 for ‘ 20 A1 cao M1 for

Notes

evaluated) A1 for 200 or 100 (if no working out use ft from (a)) B2 any two of these B1 any one of these Ignore other

M1 ft from (a), (175 seen, using

B1 for 7 and 2 B1 for 50

2

7 × 50 or 7, 50, 2 2 200 or 100

Numerator increasing or 6.8 and 47.6 increasing denominator decreasing or 2.09 decreasing (b) rounded up (not rounded to 1 sf) or ‘175’ rounded to 200

175

16(b)

Notes

Mark

Answer

16(c)

Working



SAMs


57

19(b)


Question Number 18

5.1 or 4.2 tan x º 1.214285…. oe sin29 AB/5 or AB/sin29 5/sin90 AB 5sin29 2.42 3

3

50.5

(tan used)

tan x º

2

(5 2 (5cos29)2) or 5cos29 u tan29

A1 for answers which round to 2.42

OR M2 for AB

M1 sin29 = AB/5 or AB/sin29 = 5/sin90 M1 AB 5sin29

M1 (sin or cos) and ( (4.2 2 + 5.1 2 ) or 6.6 used M1 sin x = 5.1/( (4.2 2 + 5.1 2 ) or cos x = 4.2/( (4.2 2 + 5.1 2 ) A1 for answers which round to 50.5

Notes

2

A1 for y = 3 1

M1 for x 3 = 7 x oe or 7(y – 3) oe or 0 = 6x – 3 oe 6 x = 3 oe [separate evidence for M1 is required] A1 for x = 1

3

Mark

1 1 , y=3 2 2

Notes

Mark

Answer

x =

Answer

Working

x 3 = 7x (6 x = 3 oe)

Working

58


SAMs


Mark 3

Answer 7.21

Working

42 + 62 (= 52) ¥(42 + 62) or ¥“52” or 213

Question Number 21

2

0.3 oe

2

2

0.6

1 (0.1 + 0.2 + 0.1) or 1 0.4 oe 0.2 + 0.1 or 1 (‘0.6’ + 0.1) (Poss) overlap or mut excl or doesn’t wk for B or Y {No or poss or poss yes}

Mark

Answer

Working

20(c)

20(b)


M1 for 42 + 62 (= 52) M1 dep on 1st M1 ¥ (42 + 62) or ¥“52” or 2¥13 A1 for answers which rounds to 7.21

Notes

M1 or 0.6 in table A1 allow in table if not contrad on line M1 0.2 + 0.1 or 1 (‘0.6’ + 0.1) A1 B2 B1 Can’t tell and (No or poss) B1 Correct reason only B0 Incorrect reason B0 Unqualified Yes

Notes


Other names


Centre Number

Candidate Number

Mathematics Paper 3H Higher Tier Paper Reference


KMA0/3H

You must have:

Total Marks


Instructions


Information

total mark for this paper is 100. • The marks for each question are shown in brackets • The – use this as a guide as to how much time to spend on each question.

Advice


Turn over


*S39743A0120*


SAMs


59

FORMULA SHEET – HIGHER TIER MATHEMATICS 4400do write will gain no credit. You must not write on theIGCSE fomulae page. Anything you FORMULA SHEET – HIGHER TIER Pythagoras’ Theorem c

b

Volume of cone = 13 Sr2h

Volume of sphere = 43 Sr3

Curved surface area of cone = Srl

Surface area of sphere = 4Sr2 r

l

a a + b2 = c2

h

2

hyp

r

opp


In any triangle ABC

T adj

or

sin T

opp hyp

cosT

adj hyp

tan T

opp adj

C b

a

A Sine rule:

B

c a sin A

b sin B

c sin C

Cosine rule: a2 = b2 + c2 – 2bc cos A Area of triangle =

1 2

ab sin C

cross section lengt

h

Volume of prism = area of cross section ulength Area of a trapezium = 12 (a + b)h r

a

Circumference of circle = 2S r Area of circle = S r2

h b

r 2

Volume of cylinder = S r h h

60



The Quadratic Equation The solutions of ax2 + bx + c = 0, where a z 0, are given by x

b r b 2 4ac 2a

SAMs


Answer ALL questions. Write your answers in the spaces provided. You must write down all stages in your working. 1

(a) Use your calculator to work out the value of (3.7 4.6) 2 2.8 6.3 Write down all the figures on your calculator display. (2)

..................................... . . . . . . . . . . . . . . . . . .

(b) Give your answer to part (a) correct to 2 decimal places. (1)

..................................... . . . . . . . . . . . . . . . . . .


(a) Work out the value of x2 – 5x when x = –3 (2)

..................................... . . . . . . . . . . . . . . . . . .

(b) Factorise x2 – 5x (2)

..................................... . . . . . . . . . . . . . . . . . .



SAMs


61

3

Hajra counted the numbers of sweets in 20 packets. The table shows information about her results. Number of sweets

Frequency

46

3

47

6

48

3

49

5

50

2

51

1

Work out the mean number of sweets in the 20 packets.

..................................... . . . . . . . . . . . . . . . . . .


62


SAMs


4

y 5 4 3 P 2 Q

1 –2

–1

O

1

2

–1

3

4

5

6

7

8 x

R

–2 –3 (a) Describe fully the single transformation which maps triangle P onto triangle Q. (2) . . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . .

. . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . .

(b) Describe fully the single transformation which maps triangle P onto triangle R. (3) . . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . .

. . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . .



SAMs


63

5

(a) Simplify, leaving your answers in index form, (2) (i) 75 u

..................................... . . . . . . . . . . . . . . . . . .

(ii) 59 y

..................................... . . . . . . . . . . . . . . . . . .

(b) Solve

29 × 2 4 = 28 2n

(2)

n = ..................................... . . . . . . . . . . . . . . . . . . (Total for Question 5 = 4 marks) 6

(a) Expand and simplify 3(4x – 5) – 4(2x + 1) (2)

..................................... . . . . . . . . . . . . . . . . . .

(b) Expand and simplify (y + 8)(y + 3) (2)

..................................... . . . . . . . . . . . . . . . . . .

(c) Expand p(5p2 + 4) (2)

..................................... . . . . . . . . . . . . . . . . . .


64


SAMs


7

A tunnel is 38.5 km long. (a) A train travels the 38.5 km in 21 minutes. Work out the average speed of the train. Give your answer in km/h. (3)

.................................................... . . .

km/h

(b) To make the tunnel, a cylindrical hole 38.5 km long was drilled. The radius of the cylindrical hole was 4.19 m. Work out the volume of earth, in m3, which was removed to make the hole. Give your answer correct to 3 significant figures. (3)

.............................................. . . . . . . . . .

m3



SAMs


65

8

(a) Shri invested 4500 dollars. After one year, he received 270 dollars interest. Work out 270 as a percentage of 4500. (2)

............................................ . . . . . . . . . . .

%

(b) Kareena invested an amount of money at an interest rate of 4.5% per year. After one year, she received 117 dollars interest. Work out the amount of money Kareena invested. (2)

.......................................................

dollars

(c) Ravi invested an amount of money at an interest rate of 4% per year. At the end of one year, interest was added to his account and the total amount in his account was then 3328 dollars. Work out the amount of money Ravi invested. (3)

.......................................................

dollars


66


SAMs


9

(a) Solve 5x – 4 = 2x + 7 (2)

x = ..................................... . . . . . . . . . . . . . . . . . . (b) Solve

7 2y 4

2y 3 (4)

y = ..................................... . . . . . . . . . . . . . . . . . . (Total for Question 9 = 6 marks)


SAMs


67

10 Here are five shapes.

Four of the shapes are squares and one of the shapes is a circle. One square is black. Three squares are white. The circle is black. The five shapes are put in a bag. (a) Jasmine takes a shape at random from the bag 150 times. She replaces the shape each time. Work out an estimate for the number of times she will take a white square. (3)

..................................... . . . . . . . . . . . . . . . . . .

(b) Alec takes a shape at random from the bag and does not replace it. Bashir then takes a shape at random from the bag. Work out the probability that (i) they both take a square, (2)

..................................... . . . . . . . . . . . . . . . . . .

(ii) they take shapes of the same colour. (3)

..................................... . . . . . . . . . . . . . . . . . .


68


SAMs


11

B

O


6.9 cm C

5.7 cm

A

A and B are points on a circle, centre O. The lines CA and CB are tangents to the circle. CA = 5.7 cm. CO = 6.9 cm. (a) Give a reason why angle CAO = 90°. (1) . . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . .

. . . . . .................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . .

(b) Calculate the perimeter of the kite CAOB. Give your answer correct to 3 significant figures. (5)

............................................... . . . . . . . .

cm



SAMs


69

12 The grouped frequency table gives information about the weights of 60 cows. Weight (w kg)

Frequency

100 < w - 200

10

200 < w - 300

16

300 < w - 400

15

400 < w - 500

9

500 < w - 600

6

600 < w - 700

4

(a) Complete the cumulative frequency table. (1) Weight (w kg)

Cumulative frequency

100 < w - 200 100 < w - 300 100 < w - 400 100 < w - 500 100 < w - 600 100 < w - 700

70


SAMs


(b) On the grid, draw the cumulative frequency graph for your table. (2)

(c) Use your graph to find an estimate for the number of cows that weighed more than 430 kg. Show your method clearly. (2)

..................................... . . . . . . . . . . . . . . . . . .



SAMs


71

13 Show, by shading on the grid, the region which satisfies all three of these inequalities. y-5

y - 2x

y.x+1

Label your region R. y

6

4

2

–2

O

2

4

6

x

–2


72


SAMs


14 (a) Make r the subject of the formula A = ʌr2, where r is positive. (2)

r = ..................................... . . . . . . . . . . . . . . . . . . The area of a circle is 14 cm2, correct to 2 significant figures. (b) (i) Work out the lower bound for the radius of the circle. Write down all the figures on your calculator display. (2)

............................................... . . . . . . . .

cm

(ii) Give the radius of the circle to an appropriate degree of accuracy. You must show working to explain how you obtained your answer. (2)

............................................... . . . . . . . .

cm



SAMs


73

15 The frequency, f kilohertz, of a radio wave is inversely proportional to its wavelength, w metres. When w = 200, f = 1500 (a) (i) Express f in terms of w. (3)

f = ..................................... . . . . . . . . . . . . . . . . . . (ii) On the axes, sketch the graph of f against w. f

(1)

O

w

(b) The wavelength of a radio wave is 1250 m. Calculate its frequency. (2)

.......................................................

kilohertz


74


SAMs


16 PQR is a triangle. E is the point on PR such that PR = 3PE. F is the point on QR such that QR = 3QF. R Diagram NOT accurately drawn

F

E b P

o PQ = a,

Q

a

o PE = b.

(a) Find, in terms of a and b, o (i) PR (1)

..................................... . . . . . . . . . . . . . . . . . .

o (ii) QR (1)

..................................... . . . . . . . . . . . . . . . . . .

o (iii) PF (1)

..................................... . . . . . . . . . . . . . . . . . .

o o (b) Show that EF = kPQ where k is a number. (2)



SAMs


75

17 A curve has equation y

x2

16 x

The curve has one turning point. Find dy and use your answer to find the coordinates of this turning point. dx

..................................... . . . . . . . . . . . . . . . . . .


76


SAMs


18 A

Diagram NOT accurately drawn 2.8 cm

A solid hemisphere A has a radius of 2.8 cm. (a) Calculate the total surface area of hemisphere A. Give your answer correct to 3 significant figures. (3)

................................................. . . . . . .

cm2

A larger solid hemisphere B has a volume which is 125 times the volume of hemisphere A. (b) Calculate the total surface area of hemisphere B. Give your answer correct to 3 significant figures. (3)

................................................. . . . . . .

cm2


PLEASE TURN OVER FOR QUESTION 19


SAMs


77

19 Solve the simultaneous equations y = 3x – 1 x2 + y2 = 5

..................................... . . . . . . . . . . . . . . . . . .


78


SAMs



SAMs


79

Mark 3

Answer 48

Working

46 u 3 47 u 6 48 u 3 49 u 5 50 u 2 51 u 1 or 138 282 144 245 100 51 or 960 “960” y 20

2

24

(-3)2 5 u -3

Question Number 3

Mark

Answer

Working

Question Number 2(a) 2

1

7.57

1(b)

x( x 5)

2

7.5703…

68.89 9.1

2(b)

Mark

Answer

Working


Paper 3H

Sample Mark Scheme

519 6889 , 910 910

M1 for finding at least 4 products and adding M1 (dep on 1st M1) for division by 20 A1 cao

Notes

M1 for substn or 9 or 15 seen A1 cao M1A1 for x( x 5) B1 for factors which, when expanded and simplified, give two terms, one of which is correct SC B1 for x (5 - x ), x (x - 5x )

Notes

B1 ft from (a) if non-trivial ie (a) must have more than 2 d.p.

Also accept 7

M1 for 8.3, 68.89, 9.1 or 30.90… A1 Accept if first 5 figures correct

Notes

80


SAMs


2

3

Mark 1 1 2

translation 3 squares to the right and 1 square down

rotation of 90° clockwise about (2, 1)

Answer 78 56 5

4(b)

Question Number 5(a)(i) 5(a)(ii) 5(b)

9 4 n = 8 or 13 n = 8

Working

Mark

Working

Answer


§ 3· ¨ 1¸ © ¹

but not These marks are independent but award no marks if answer is not a single transformation


B1 cao B1 cao M1 for 9 4 n = 8 or 13 n = 8 , Also award for 2n = 25, 2n= 32 or 25 on answer line A1 cao

Notes

B1 for rotation Accept rotate, rotated etc B1 for 90° clockwise or 90° or 270° B1 for (2, 1)

(3, -1) B3 for for correct description of transformation

B1 for 3 right and 1 down or

B2 for correct description of transformation B1 for translation. Accept translate, translated etc Accept ‘across’ instead of ‘to the right’

Notes


SAMs


81

4 x 19

12 x 15 8 x 4

S u 4.19 u 38500 = 2123433.419 m³

2

2 120 000 3

3

110

21 38.5 = 0.35 ; u 60 or 60 21

7(b)

Mark

Answer

Working


38.5 0.35

2

5p3 + 4p

6(c)

M1 for at least 3 terms correct inc signs A1 cao

2

21 or 0.35 60

A1 cao M2 ʌ × 4.19² × 38500 = 2123433.419 m³ M1 for ʌ × (no with digits 419)2 × no with digits 385 A1 for 2 120 000 or for answer which rounds to 2 120 000

38.5 "0.35"

38.5 38.5 or 1.8333… or or 183.333… 21 0.35

M1 for “1.8333…” u 60 or

or

M1 for

Notes

B2 cao B1 for either 5p3 or for + 4p

M1 for 3 terms correct or y 2 11 y seen A1 cao

Notes

Mark

2

y 2 3 y 8 y 24

Answer

Working

y 2 11y 24

6(b)


82


SAMs


2

3

2600

3200

117 or 26 seen 4 .5

270 4770 or 0.06 or or 1.06 4500 4500

9(b)

10 y - 5

simpler

7 2 y 8 y 12 or

72y or 7 2 y 4 = 4(2 y 3)

4u

-

1 oe 2

4

7 2y or 7 2 y 4 4 × 2 y 3 or 8 y 3 or 2 y 3 u 4 or 2 y 12 M1 for correct expansion of brackets (usually 8 y 12 ) or for correct rearrangement of correct terms eg 8 y 2 y 7 12 A1 for reduction to correct equation of form ay = b (dependent on both M marks) 1 A1 for oe (dependent on all previous marks) 2

For example, award for 4 u

M1 for correct rearrangement [separate evidence for M1 is required] A1 also accept 2 or more d.p. rounded or truncated eg 3.66, 3.67 M1 for clear intention to multiply both sides by 4 or a multiple of 4.

2

11 2 , 3 oe 3 3

5x 2x

74

Notes

Mark

Answer

Working

Question Number 9 (a)

3328 100 or 3328 u 1.04 104 3328 M1 for , 104% = 3328 or 32 seen 104 A1 cao

M2 for

A1 cao

M1 for

A1 cao

M1 for

Notes

3328 100 or 3328 u 1.04 104

100 4.5

2

6

270 u 100 4500

117 u

Mark

Answer

Working

8(c)

8(b)



SAMs


83

2 1 3 2 × + × 5 4 5 4

10(b)(ii)

3 5

4 3 × 5 4

150 x

Working

10(b)(i)


8 2 or oe 5 20

3

2

3

90

3 12 or oe 20 5

Mark

Answer

A1 for

8 2 or oe 5 20

M1 (dep) for adding both above products

Accept decimals 2 1 3 2 M1 for × or × 5 4 5 4

Accept decimals 3 seen B1 for 5 3 M1 for 150 x 5 A1 cao 90 Do not accept 150 Accept decimals 4 3 M1 for × 5 4 3 12 or oe A1 for 20 5

Notes

2 2 3 3 × or × 5 5 5 5 SC M1 (dep) for adding both above products

SC M1 for

84


SAMs


6.92 5.72 or 47.61 32.49 or 15.12 (6.92 5.72)

11(b)

1

tangent at any point of a circle and the radius at that point are perpendicular 19.2

Working

Approx 16

Curve or line segments Use of w = 430 on graph

12(c)

Question Number 13

1 2

10, 26, 41, 50, 56, 60 Correct graph drawn

Points correct

Mark 4

Answer Lines drawn correctly Correct region labelled

2

Mark

Answer

Working

5

Mark

Answer


3.88844… 2 u 5.7 + 2 u “3.88844…”

Working


B3 for Lines drawn correctly [B1 for each correct line - ignore additional lines] B1 for Correct region labelled R

Notes

B1 cao B1 + ½ sq ft from sensible table B1 ft if 4 or 5 points correct or if points are plotted consistently within each interval (inc end points) at the correct height M1 may be shown on graph or implied by 43, 44 or 45 stated A1 if M1 scored, ft from cumulative frequency graph

Notes

M1 for squaring and subtracting M1 (dependent on 1st M1) for square root A1 for 3.89 or better M1 for 2 u 5.7 + 2 u “3.888..” only A1 for 19.2 or answer which rounds to 19.2 (19.176888…)

B1 for mention of tangent and radius or line from centre

Notes


SAMs


85

15(b)

15(a)(ii)


f=

f=

300000 1250

k w

Working

14.5 or 2.14836…

14(b)(ii)

S

A

13.5

r2 =

Working

14(b)(i)


240

f

f=

300000 w

w

2

1

3

Mark

2

2.1

Answer

2

2

Mark

2.07296…

A

Answer

S

A

A1 ft from k

M1 for substitution in f =

300 000 in (a) or (b) B1 for correct graph

k w

A1 Also award if answer is f =

k 200

k but k is evaluated as w

k k , (may be implied by 1500 = ) 200 w

M1 for 1500 =

M1 for f =

Notes

14.5 or value which rounds to 2.148 or 2.149 cao A1 dep on previous 3 marks in (b)

M1 for

A1 Ignore ± M1 for 13.5 seen A1 for answer which rounds to 2.073

or r2 = A y S

M1 for r2 =

Notes

86


SAMs


Question Number 17

16(b)

2 3

2 3

or

or k

“2 x ±

16 ” x2

0

16 § dy · ¨ ¸ 2x 2 x © dx ¹

Working

PQ

a

2 3

Question Working Number 16(a)(i) 16(a)(ii) 16(a)(iii)

4

2

(2, 12)

(3b a) oe

a)

Mark

a

2 3

1 (3b 3

Answer

2 3

or 3b

a + b or a +

1 1 1

3b 3b a 2 3

Mark

Answer

2 3

a or

2 3

PQ or k

2 3

unless clearly obtained by non-vector

b + EF FQ

A1 cao For answer (2, 12) with no preceding marks scored, award B0 B0 M1 A1

B1 for ±

16 or ± 16 x î2 2 x 16 M1 for “2 x ± 2 ” 0 x

B1 for 2 x

a

PE EF FQ

PE EF

Notes

PF

eg PQ

B1 for correct vector statement with at least 3 terms which includes EF (or FE) in terms of capital letters and/or a, b

method

B2 for

B1 B1 B1

Notes


SAMs


87

18(b)


1 × 4 × 2.8 2 2

125 or 5 seen 25 u 73.89…

3

× 2.8 2 +

Working

Mark 3

3

Answer 73.9

1850

1 × 4 × 2.8 2 2

M1 for finding the linear scale factor 3 125 or 5 M1 for 25 u (a) or for S u (2.8 × 5)2 2S u (2.8 u 5)2 or for substituting r = 2.8 u 5 in the expression used in (a) A1 for 1850 or for any value in range 1846.3 847.5 ft from 25 u (a)

M1 for each item Also award for values rounding to 24.6 and to 49.2 or 49.3 A1 for 73.9 or answer which rounds to 73.9

M2 for × 2.8 2 +

Notes

88


SAMs


Question Number 19

x -

2 1 , y -2 5 5 x 1, y 2

3 49 r or 10 10

6 r 196 3 r 49 or or 20 10

or 10 x 4 x 1 0

or 5 x 2 x 1 0

10 x 2 6 x 4 0 5 x 2 2 x 2 0

or x 2 9 x 2 6 x 1 5

A1 for complete, correct solutions

A1 for both values of x

or for using square completion correctly as far as is indicated

or for correct substitution into the quadratic formula and correct evaluation of ‘b2 4ac’

B1 for correct factorisation

B1 for correct simplification

B1 (independent) for correct expansion or (3 x 1)2 even if unsimplified

M1 for correct substitution

6

2 1 , y -2 5 5 x 1, y 2

x 2 (3 x 1) 2 5 x 2 9 x 2 3x 3x 1 5 x -

Notes

Mark

Answer

Working


Other names


Centre Number

Candidate Number

Mathematics Paper 4H Higher Tier Paper Reference

Sample Assessement Material Time: 2 hours

KMA0/4H

You must have:

Total Marks


Instructions


Information


Advice

each question carefully before you start to answer it. • Read Write answers neatly and in good English. • Checkyour • your answers if you have time at the end.

Turn over


*S39744A0120*


SAMs


89

FORMULA SHEET – HIGHER TIER IGCSE MATHEMATICS 4400 You must not write on the fomulae page. Anything you do write will gain no credit. FORMULA SHEET – HIGHER TIER Pythagoras’ Theorem c

b

Volume of cone = 13 Sr2h

Volume of sphere = 43 Sr3

Curved surface area of cone = Srl

Surface area of sphere = 4Sr2 r

l

a a + b2 = c2

h

2

hyp

r

opp


In any triangle ABC

T adj

or

sin T

opp hyp

cosT

adj hyp

tan T

opp adj

C b

a

A Sine rule:

B

c a sin A

b sin B

c sin C

Cosine rule: a2 = b2 + c2 – 2bc cos A Area of triangle =

1 2

ab sin C

cross section lengt

h

Volume of prism = area of cross section ulength Area of a trapezium = r

1 2

(a + b)h

a

Circumference of circle = 2S r Area of circle = S r2

h b

r

h

Volume of cylinder = S r2h Curved surface area of cylinder = 2S rh

90


The Quadratic Equation The solutions of ax2 + bx + c = 0, where a z 0, are given by x

b r b 2 4ac 2a

SAMs


Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1

The diagram shows the lengths, in cm, of the sides of a triangle. (3x – 5)

x

(2x + 1) The perimeter of the triangle is 17 cm. (i) Use this information to write an equation in x. (1)

..................................... . . . . . . . . . . . . . . . . . .

(ii) Solve your equation. (2)

x = ..................................... . . . . . . . . . . . . . . . . . . (Total for Question 1 = 3 marks) 2

Anji mixes sand and cement in the ratio 7 : 2 by weight. The total weight of the mixture is 27 kg. Calculate the weight of sand in the mixture.

............................................. . . . . . . . . . .

kg


SAMs


91

3

Solve 5(x – 4) = 35

x = .................................... . . . . . . . . . . . . . . . . . . . (Total for Question 3 = 3 marks) 4

Julian has to work out

6.8 × 47.6 without using a calculator. 2.09

(a) Round each number in Julian’s calculation to one significant figure. (2)

.................................... . . . . . . . . . . . . . . . . . . .

(b) Use your rounded numbers to work out an estimate for

6.8 × 47.6 2.09

Give your answer correct to one significant figure. (2)

.................................... . . . . . . . . . . . . . . . . . . .

(c) Without using your calculator, explain why your answer to part (b) should be larger than the exact answer. (2) . . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . .

. . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . .

. . . . . ................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . .


92


SAMs


5

The diagram shows a wall.

3m

2m


6m (a) Calculate the area of the wall. (2)

.............................................. . . . . . . . . .

m2

(b) 1 litre of paint covers an area of 20 m2. Work out the volume of paint needed to cover the wall. Give your answer in cm3. (3)

................................................. . . . . . .

cm3



SAMs


93

6

Solve the simultaneous equations y=x+3 y = 7x

x = .................................... . . . . . . . . . . . . . . . . . . . y = .................................... . . . . . . . . . . . . . . . . . . . (Total for Question 6 = 3 marks)

94


SAMs


7

(a)

4.2 cm x°

5.1 cm


Calculate the value of x. Give your answer correct to 3 significant figures. (3)

x = ..................................... . . . . . . . . . . . . . . . . . . (b) A


5 cm 29° B

C

Calculate the length of AB. Give your answer correct to 3 significant figures. (3)

............................................... . . . . . . . .

cm



SAMs


95

8

A bag contains some marbles. The colour of each marble is red or blue or green or yellow.

A marble is taken at random from the bag. The table shows the probability that the marble is red or blue or green. Colour

Probability

Red

0.1

Blue

0.2

Green

0.1

Yellow (a) Work out the probability that the marble is yellow. (2)

..................................... . . . . . . . . . . . . . . . . . .

(b) Work out the probability that the marble is blue or green. (2)

..................................... . . . . . . . . . . . . . . . . . .

The probability that the marble is made of glass is 0.8 (c) Beryl says “The probability that the marble is green or made of glass is 0.1 + 0.8 = 0.9” Is Beryl correct?

.......................................................

(2) Give a reason for your answer. . . . . . . .................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . .

. . . . . . .................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . .



SAMs


9 Diagram NOT accurately drawn

h cm

4 cm

6 cm Calculate the value of h. Give your answer correct to 3 significant figures.

h = ....................................................... (Total for Question 9 = 3 marks)


SAMs


97

10 (a)

y 7 6 5 4 3 2 1 –2

–1 O

1

2

3

x

–1 –2 Find the equation of the straight line that passes through the points (0, 1) and (1, 3). (4)

..................................... . . . . . . . . . . . . . . . . . .

(b) Write down the equation of a line parallel to the line whose equation is y = –2x + 5 (1)

..................................... . . . . . . . . . . . . . . . . . .

(c) Write down the coordinates of the point of intersection of the two lines whose equations are y = 3x – 4 and y = –2x – 4 (1)

(......................... , ......... . . . . . . . . . . . . . . . . ) (Total for Question 10 = 6 marks) 98


SAMs


11 Here are three similar triangles.

56° 12 cm

Diagrams NOT accurately drawn

6 cm 30°

94° 10 cm

20 cm

y cm

4 cm w°

56° x cm

8 cm Find the value of (a) w,

(1)

w = ..................................... . . . . . . . . . . . . . . . . . . (b) x, (2)

x = ..................................... . . . . . . . . . . . . . . . . . . (c) y. (2)

y = ..................................... . . . . . . . . . . . . . . . . . . (Total for Question 11 = 5 marks) UG025980 Edexcel Level 1/Level 2 Certificate in Mathematics

SAMs


99

12 Simplify (a)

a3 × a 4 a2

(2)

..................................... . . . . . . . . . . . . . . . . . .

(b) ( x )6

(1)

..................................... . . . . . . . . . . . . . . . . . .

(c)

3( x + 1) 2 6( x + 1)

(2)

..................................... . . . . . . . . . . . . . . . . . .


100


SAMs


13 Here are the marks scored in a maths test by the students in two classes. Class A

2

13

15

16

4

6

19

10

11

4

5

Class B

12

11

2

5

19

14

6

6

10

14

9

15

4

16

6

(a) Work out the interquartile range of the marks for each class. (4)

Class A ..................................... . . . . . . . . . . . . . . . . . . Class B ..................................... . . . . . . . . . . . . . . . . . . (b) Use your answers to give one comparison between the marks of Class A and the marks of Class B. (1) . . . . . . .................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................................................................................................................ . . . . .. . . . . . .

. . . . . . .................................. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........................................................................................................................................... . . . . .. . . . . . .

(Total for Question 13 = 5 marks) 14 Solve

5x 7 x 1

x 1

..................................... . . . . . . . . . . . . . . . . . .



SAMs


101

15 There are 35 students in a group. 18 students play hockey. 12 students play both hockey and tennis. 15 students play neither hockey nor tennis. Find the number of students who play tennis.

.................................... . . . . . . . . . . . . . . . . . . .

(Total for Question 15 = 4 marks) 16 A triangle has sides of length 5 cm, 6 cm and 9 cm. 5 cm

6 cm


x° 9 cm Calculate the value of x. Give your answer correct to 3 significant figures.

x .................................... . . . . . . . . . . . . . . . . . . . (Total for Question 16 = 3 marks) 102


SAMs


17 The functions f and g are defined as follows. f ( x) g( x)

1 x2 x 1

(a) (i) State which value of x cannot be included in the domain of f. (1)

.................................... . . . . . . . . . . . . . . . . . . .

(ii) State which values of x cannot be included in the domain of g. (2)

.................................... . . . . . . . . . . . . . . . . . . .

(b) Calculate fg(10) (3)

.................................... . . . . . . . . . . . . . . . . . . .

(c) Express the inverse function g–1 in the form g–1(x) = ...... (4)

g–1(x) = .................................... . . . . . . . . . . . . . . . . . . . (Total for Question 17 = 10 marks) UG025980 Edexcel Level 1/Level 2 Certificate in Mathematics

SAMs


103

18 A fair, 6-sided dice has faces numbered 1, 2, 3, 4, 5 and 6 When the dice is thrown, the number facing up is the score. The dice is thrown three times. (a) Calculate the probability that the total score is 18 (2)

..................................... . . . . . . . . . . . . . . . . . .

(b) Calculate the probability that the score on the third throw is exactly double the total of the scores on the first two throws. (4)

..................................... . . . . . . . . . . . . . . . . . .


104


SAMs


19 (a) Calculate the area of an equilateral triangle of side 5 cm. Give your answer correct to 3 significant figures. (2) Diagram NOT accurately drawn 5 cm

5 cm

5 cm

................................................. . . . . . .

cm2

(b) The diagram shows two overlapping circles. The centre of each circle lies on the circumference of the other circle. The radius of each circle is 5 cm. The distance between the centres is 5 cm. Diagram NOT accurately drawn 5 cm

5 cm

5 cm

Calculate the area of the shaded region. Give your answer correct to 3 significant figures. (3)

................................................. . . . . . .

cm2


SAMs


105

20 The histogram shows information about the heights, h metres, of some trees.

Frequency density

O

1

2

3

4

5

6

7

8

9

Height (m) The number of trees with heights in the class 2 < h -3 is 20 Find the number of trees with heights in the class (a) (i) 4 < h -8 (2) .................................... . . . . . . . . . . . . . . . . . . .

(ii) 3 < h -4 .................................... . . . . . . . . . . . . . . . . . . .

(b) Find an estimate for the number of trees with heights in the interval 2.5 < h -3.5 (1)

.................................... . . . . . . . . . . . . . . . . . . .


106


SAMs


21 (a) Factorise 16x2 – 1 (1)

..................................... . . . . . . . . . . . . . . . . . .

(b) Hence express as the product of its prime factors (i) 1599 (3)

..................................... . . . . . . . . . . . . . . . . . .

(ii) 1.599 u 106 (2)

..................................... . . . . . . . . . . . . . . . . . .



SAMs


107

BLANK PAGE

108


SAMs



SAMs


109

Question Number 3

3

21

9 seen 7 27 u 27 or 7 u oe 9 9

Mark 3

Answer 11

Working

5 x – 20 35 5 x = 55

2

Mark

21 6

Answer

x = 3.5 oe eg

Working

0

Question Number 2

21 or 6 x 21

6x etc

1(ii)

M1 dep on 1st M1 or M2 for x 4 A1 cao

35 7

7 27 u 27 or 7 u oe 9 9

c

17

3 B1M1AO)

M1 for 5 x 20

Notes

A1 cao (for answer

M1 (dep B1) for

B1 for 9 seen

Notes

M1 ft (i) if 6 x A1

ISW not ‘=p’

B1 oe eg 6 x 4

1

x 2x 13x5 17

Notes

Mark

Answer

Working

Question Number 1(i)

Paper 4H

Sample Mark Scheme

110


SAMs


15 u 1000 20 1000 u 15 20 15 1000 u 20

750 3

2

15

(2 + 3) × 6 or 2 1 u 6 u 1 oe 2u6 2

5(b)

Mark

Answer

Working


2

2

(6 or 7) u (48 or 50) 2 or 3

(2 + 3) × 6 or 2 1 u 6 u 1 oe 2u6 2 A1 cao 15 M1 for u 1000 oe 20 or 0.75 or ¾ litre M1 ft ‘15’ for M1M1 only A1 cao M1 for

Notes

evaluated A1 for 200 or 100 (if no working out, use ft from (a)) B2 any two of these B1 any one of these Ignore other

M1 ft from (a), (175 seen, using

B1 for 7 and 2 B1 for 50

2

7 × 50 or 7, 50, 2 2 200 or 100

Number incr or 6.8 and 47.6 incr denom decr or 2.09 decr (b) rnded up (not rnd to 1 sf) or ‘175’ rnded to 200

175

4(b)

Notes

Mark

Answer

4(c)

Working

Question Number 4(a) correctly


SAMs


111

7(b)


Question Number 6

tan x

5.1 or 4.2 tan x 1.214285…. oe sin29 AB/5 or C/sin29 5/sin90 AB 5sin29 AB 2.42…cm

3

M1 BC 5cos29 M1 AB (5 2 (5cos29)2) or 5cos29 u tan29 A1 for correct answer to 3 sf

M1 (sin or cos) and ( (4.2 2 + 5.1 2 ) or 6.6) used M1 sin x = 5.1/( (4.2 2 + 5.1 2 ) or cos x = 4.2/( (4.2 2 + 5.1 2 ) A1 for correct answer to 3 sf

3

x

tan used

50.5…

Notes

M1 for x 3 = 7 x 6 x = 3 oe 1 A1 for x = 2 1 A1 for y = 3 2 OR M1 for 7 y = 7 x 21 6 y = 21 oe 1 A1 for x = 2 1 A1 for y = 3 2

3

Mark

1 1 , y=3 2 2

Notes

Mark

Answer

x =

Answer

Working

OR 7 y = 7 x 21 (6 y = 21)

x 3 = 7x (6 x = 3 oe)

Working

112


SAMs


3

h = 7.21…

42 + 62 (= 52) ¥(42 + 62) or ¥“52” or 213

42 + 62 (= 52) ¥(42 + 62) or ¥“52” or 2¥13

Mark

Answer

Working

Question Number 9

2

0.3 2

2

0.6

1 – (0.1 + 0.2 + 0.1) or 1 0.4 oe 0.2 + 0.1 or 1 (‘0.6’ + 0.1) (Poss) overlap or mut excl or doesn’t wk for B or Y {No or poss or poss yes}

Mark

Answer

Working

8(c)

8(b)


M1 for 42 + 62 (= 52) M1 dep on 1st M1 ¥ (42 + 62) or ¥“52” or 2¥13 A1 for correct answer to 3 sf

Notes

M1 or 0.6 in table A1 allow in table if not contrad on line M1 or 0.3 seen A1 0.3 oe B2 B1 Can’t tell and (No or poss) B1 Correct reason only B0 Incorrect reason B0 Unqualified Yes

Notes


SAMs


113

y = 2x 1

V/H in any correct triangle attempted

11(c)

4 6 or oe 8 12

y 4 8 = or oe 10 6 12

x 20

Working

2

1 2

56 10 or 10.0… 6.6 to 6.7 incl oe

Mark

1

1

4

Mark

Answer

(0, 4)

10(c)


y = 2 x ± c

Grad = 2, may be embedded or implied

Answer

Working

10(b)


3 1 3 not 1 0 1

A1 (a)(b): ft (a) M-mks only

M1 or y = (4 2 82 2 u 4 u 8 u cos‘56’) or y /sin56 = 8/sin(180 30 56)

B1 M1 or x /sin30 = 20/sin(180 30 56) A1

Notes

B1

(No working, answer of 2 x 1: M1A1 B1) B1 y 2 x ± any no. (not 5) or letter or y

A1for 2 B2 ft for y = ‘2’ x 1 (B1ft for just ‘2’ x 1 or y = x 1 (m z 2))

M1 eg

Notes

2 x

114


SAMs


13(b)


12(b) 12(c)


Mark 4

1

Answer Class A:11 Class B:8

A more spread or greater dispersion or less consistent than B

Attempt arrange one set in order State or indicate correct 15 and 4 or 14 and 6

/2( x + 1) or 0.5( x + 1) x 1 x 1 or or equiv or 2 2 2

Working

Correctly cancel numbers or ( x + 1)

3( x 1) 3x 3 or or k ( x 1) k1 6 6

1 or 0.5 or denom = 2 2

B1 (B1 if consistent with (a). Ignore other.) Not: greater “range” or “difference” or “more constant” or “greater IQR” or “greater variance”

M1 M1 NB: IQR for B = 8, check working A1 A1

Notes

A1 Not ISW

or

M1 eg

B1

1 2

1

M1 A1

2

a5

a7 or a u a 4 or 2 a a3 u a2 x3

Notes

Mark

Answer

Working


SAMs


115

Question Number 16

Question Number 15

Question Number 14

Mark 3

Answer 38.9

92 + 5 2 2 × 5 × 9 × cos x 62 90cos x 70 or 90cos x 70 (cos x 70/90)

4

14

2 overlapping circles, 12 in overlap 6 in H only 2 in T only

Working

Mark

Answer

4

Mark

Working

5 r ( 5) 2 4 u 6 2

x = 2 or 3

5x 7 = x2 1 or 5 x 7 = ( x 1)( x 1) x2 5x 6 = 0 ( x 2)( x 3) (= 0)

or

Answer

Working

9 2 52 6 2 2u5u9

62 70, (cos x

A1 for answers which round to 38.9

OR M2 for cos x

M1 for 92 + 52 2 × 5 × 9 × cos x M1 for 90cos x 70 or 90cos x

Notes

M1 M1 or 6 play H only M2 M1 or 20 6, 6 12 x A1 ans 2: M3A0

/90)

70

20, 20 18, 35 33: M3

condone 5 x 7 = x 1 × x 1 allow different order with = 0 ( x 2.5)2 + 6 6.25 (dependent on all other M marks)

Notes

M1 M1 M1 A1

Notes

116


SAMs


17(c)

17(a)(ii) 17(b)


x

92

( x 1)

y2 1

y2 = x 1

y

fg ( x)

1

9 or (10 1)

Working

g x 1

1 or 0.2 5

( x 1) oe

2

4

-2

[SC g 1 x

2

(x=..)

(y= )

x 1 : B1]

x2

M1

y 1

x

M1dep

A1

x 1 y 1

y

M1

A1 ignore ans = -1

B2 B1 for x < 1 or 0, 1, 2, 3… M1 for 9 or (10 1) 1 M1 for x 1 2

B1 or x z - 2 or x

1

2 x