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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 0 , then simplifies to:
o o ≤ x < 90 tan x cos x
A) sin x B) cos x C) cot x D) sec x E) csc x
2. The expression 3 5
4 3 2 )
x y
y
− ( x simplifies to:
A)
6
3
y
x B) 11
5
y
x C) 16
2
y
x D)
− x y E) None of these.
9 6
3. If f ( , and a and b are any positive numbers, then is equivalent to:
x x ) = 2 f ( a + b )
A) f ( a ) ⋅ f ( b ) B) ( )
f b
f ( a C) f ( ) D) f ( + E) None of these.
b a a ) f ( b )
4. The domain of x
g x −
( ) is:
A) [ 3 , ∞ ) B) ( 3 , ∞ ) C) ( −∞ , 3 ] D) ( −∞, 3 ) E) None of these.
5. The angle 150 in radian measure is given by:
o
A)
5 π B) 5 π
C) 75 π D) 6
5 π E) None of these.
6. Solve for x : 6. 4 x − 3. 2 = 4. 4 x + 1. 2
A) x = − 2.2 B) x = 2 C) x = − 1 D) x = 1.1 E) None of these.
7. One solution to the equation 3 5 0 is:
2 x + x − =
A)
− 1 + i 61 B) 6
1 + i 61 C) 6
D)
E) None of these.
8. What is the number 2
1
. 01 )
− ( equal to?
A) .01 B) 10 C) 1000 D) .1 E) 100
9. If f ( and , what is the compostion?
2 x ) = x g ( x ) x 2 x
3 = + ( f o g )( x )
A) x + B) ( C) x + D)
5 3 2 x )
3 2 x + 2 x
6 2 4 x 4
3
x
x + 2 x E) None of these.
10. Solve log 10 ( x − 1 )= 2 for x.
A) 1025 B) 21 C) 101 D) 99 E) None of these.
11. The function f ( x )=cot x is not defined for:
A) x = 0 B) x = 4
C)
π x = 2
D)
π x = 3
E) None of these.
π
12. In the right triangle shown, a = 8 and c = 10, find tan A
A
A)
B)
C)
c
b
D)
E) None of these.
B
a
13. One solution to the equation
3
x x
x is:
A) 3 B) 1 C) − 3 D) 2 5 + 2 E) None of these.
14. The expression
2 2
2 2
b a
a b
simplifies to: (Ignore the domain change when simplified.)
A)
4
4
1 + b
1 + a B) 2 2
2 2
a b
b + a C) 2
2
a
b D) 2
2
b
a E) None of these.
15. Find the equation of the line through the two points (5,3) and (−1,6).
A)
x +
y = B) 2
y = − x + C) y = 2 x + 8
D) y =− 2 x + 4 E) None of these.
16. If f ( x )= 5 x − 2 , the inverse function is:
A) 2
1 ( x = x +
− f B) 5
x ( x
− f C) 2
1 ( x = x −
− f D)
− f ( ) 2 5
1 x = x −
E) None of these.
17. x is equivalent to:
− 3 − 3 − y
A) ( x − B)
3 )
− y 3 3
3 3
x − y
x y C) 3 ( x − y )
D)
3 3
3 3
x y
y − x E) None of these.
18. The expression x may be factored as:
4 4 y − xy
A) ( − y ) ( )( ) B) x y ( x C) xy (
2 2 2 2 x x − y x + y
3 − y ) )( )
2 2 x − y x + xy + y
(Sample)
Correct Solutions:
1) A 2) B 3) A 4) D 5) D 6) E 7) C 8) B 9) B 10) C
11) A 12) D 13) E 14) D 15) B 16) B 17) D 18) C 19) D 20) A
Question 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)
