University of Massachusetts Lowell. Department of Mathematical Sciences.
Calculus Readiness Test. (Sample Exam). Directions: You should plan on
finishing ...
University of Massachusetts Lowell Department of Mathematical Sciences Calculus Readiness Test (Sample Exam)
Directions: You should plan on finishing the exam in under 1 hour. Part of the needs of Calculus 1 are not only to know certain algebra and trigonometry topics, but be able to fairly quickly have them at your fingertips. The thread of calculus can easily be lost if you are struggling with the necessary background mathematics. Once you have taken your practice test, check your answers with the correct ones given on the reverse side of this sheet. Once you have taken your practice test, check your answers with the correct ones given below, and then check the topical list to determine your deficiencies.
1.
If 0o ≤ x < 90o , then tan x cos x simplifies to: A) sin x
2.
4.
5.
x3 y6
x5 y11
C)
f (a) f (b ) 1 The domain of g ( x) = is: 3− x B)
A) [ 3, ∞ )
B) ( 3, ∞ )
E) csc x
x2 y16
D) x 9 y −6
E) None of these.
C) f (a b )
C) (−∞ , 3 ]
D) f (a ) + f (b)
E) None of these.
D) (−∞ , 3 )
E) None of these.
5π 6
E) None of these.
D) x = 1.1
E) None of these.
The angle 150o in radian measure is given by: 5π 12
Solve for x:
B)
6 5π
C) 75 π
D)
6.4 x − 3.2 = 4.4 x + 1.2 C) x = − 1
B) x = 2
One solution to the equation 3 x 2 + x − 5 = 0 is: A)
8.
B)
A) f (a ) ⋅ f (b)
A) x = − 2.2 7.
D) sec x
If f ( x) = 2 x , and a and b are any positive numbers, then f (a + b) is equivalent to:
A) 6.
C) cot x
( x 4 y −3 ) 2 The expression simplifies to: x3y5 A)
3.
B) cos x
− 1 + i 61 6
B)
1 + i 61 6
What is the number ( .01 ) A) .01
−1
B) 10
2
C)
−1+ 61 6
D)
1 − 61 6
E) None of these.
equal to? C) 1000
D) .1
E) 100
9.
If f ( x ) = x 2 and g ( x ) = x 3 + 2 x , what is the compostion ( f o g ) ( x) ? A) x 5 + 2x 3
10.
(
B) x 3 + 2x
)
2
x3 + 2 x x4
C) x 6 + 4 x 2
D)
C) 101
D) 99
E) None of these.
Solve log10 ( x − 1 ) = 2 for x. A) 1025
B) 21
The function f ( x) = cot x is not defined for: π π C) x = A) x = 0 B) x = 4 2 12. In the right triangle shown, a = 8 and c = 10, find tan A
E) None of these.
11.
5 A) 3 4 D) 3 13.
The expression
15.
E) None of these.
(Ignore the domain change when simplified.)
b2 + a 2 B) 2 2 a b
b2 C) 2 a
a2 D) 2 b
E) None of these.
Find the equation of the line through the two points (5,3) and (−1,6). 1 11 B) y = − x + 2 2 E) None of these.
C) y = 2 x + 8
If f ( x) = 5 x − 2 , the inverse function is: 1 x+2 5 E) None of these. A) f −1 ( x ) =
B) f −1 ( x ) =
x+2 5
C) f −1 ( x ) =
1 1 x− 5 2
D) f −1 ( x) = 2 x − 5
x − 3 − y − 3 is equivalent to: A) ( x − y ) −3
18.
a
D) 2 5 + 2
simplifies to:
1 11 x+ 2 2 D) y = − 2 x + 4
17.
B
C) − 3
A) y =
16.
A
b
x − 4 1 is: = 5x + 15 x + 3
B) 1
1 + a4 A) 1 + b4
E) None of these.
c
E) None of these.
1 + a2 2 b 1 + b2 2 a
π 3
3 C) 4
One solution to the equation A) 3
14.
3 B) 5
D) x =
B)
x3 y 3 x3 − y 3
C)
1 ( x − y )3
D)
y 3 − x3 x3 y 3
E) None of these.
The expression x 4 y − xy 4 may be factored as: A) ( x − y ) ( x 2 − y 2 ) ( x 2 + y 2 )
B) x y ( x − y ) 3 (Sample)
C) x y ( x − y )( x 2 + xy + y 2 )
D) ( x 2 y − x y 2 ) 2 19.
4π is 3 3 B) − 2
The exact value of cos A)
20.
E) None of these.
3 2
C)
1 2
D) −
1 2
E) None of these.
The expression log 2 2 x − 2 log 2 y + log 2 z is equivalent to: 2xz A) log 2 2 y E) None of these.
xz B) log 2 y
(
C) log 2 2 x − y 2 + z
)
D)
log 2 2 x log 2 z 2 log 2 y
Scroll Down for Correct Answers
Correct Solutions: 1) A 11) A Question 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20)
2) B 12) D
3) A 13) E
4) D 14) D
5) D 15) B
6) E 16) B
7) C 17) D
8) B 18) C
9) B 19) D
10) C 20) A
Related Topics Basic definitions of trigonometric functions Laws of exponents Exponential functions, laws of exponents Functions, solution of inequalities Relationship between radians and degrees Linear Equations Quadratic Equations Exponents, roots Composition of functions Converting logarithmic equations to exponential equations Basic definitions of trigonometric functions and their domains Triangle trigonometry, Pythagorean Theorem Solutions of Rational Equations Simplifying compound fractions Slope, Equations of a line Finding inverses of functions. Exponents, Adding fractions Factoring, Difference of cubes,( should also know difference of squares and sum of cubes) Evaluation of trigonometric functions. Laws of logarithms
(Sample)
