United Arab Emirates University
University Foundation Program
Math Program
Placement Tutoiral Sample Questions
Spring 2013
College Algebra, Trigonometry &
Algebra
Building the Concepts
1
College Algebra Sample Test
1. If f (x) = 2x3 − 7x2 + 4, then f (−2) =?
A. 16
B. −48
C. −32
D. −36
E. −40
2. If f (x) = −3x + 7, then f (1) =?
A. 7
B. 4
C. −3
D. 10
E. −21
3. If f (x) = x2 − 4 and g(x) = 1 − 3x, then f [g(−1)] =?
A. 12
B. 4
C. −21
D. −1
E. 20
2
4. If (4)3x · (2)x =
1
, then x =?
32
2
A. 1 or 5
B. 1 or 3
C. 6 or 5
D. −1 or −5
E. 2 or 4
5. What is the sixth term of an arithmetic progression whose first term is 1 and second term is 5?
A. 225
B. 16
C. 626
D. 10
E. 21
6. What is the minimum value of y = x2 − 3x + 1?
A. 1
B. −
5
4
C. −3
D.
3
2
E. 2
7. If the point (−3, 5) is on the graph of the function f (x), which of the following points will be
on the graph of f −1 (x)?
A. (3, −5)
3
B. (3, 5)
C. (5, −3)
D. (−3, −5)
1 1
E. − ,
3 5
8. log2 (8−3 ) =?
A. −9
B. −3
C. 2
D. 8
E. 4
9. If f (x) = x2 − 5x + 3, then f (2a − 1) =?
A. 4a2 − 10a + 9
B. 4a2 − 10a + 3
C. 4a2 + 14a − 9
D. 4a2 + 10a + 9
E. 4a2 − 14a + 9
10. If i2 = −1, then i212 =?
A. 1
B. i
C. −1
4
D. −i
E. 0
√
11. For what values of x is the y = −x 2x − 6 defined?
A. x ≥ −6
B. x ≥ 3
C. x ≥ −1
D. x ≥ 0
E. x ≥ 4
12. If f (x) =
f (1)
8
and
g(x)
=
x
−
9,
then
=?
x2
g(1)
A. −9
B. 1
C. 9
D. −
8
9
E. −1
5
A B
13. If C D
= AD − BC, then a 1
−7 2a
−3a 0
−
12 1
=?
A. 2a2 + 7
B. 2a2 − 3a
C. 2a2 + 3a + 7
D. 2a2 + 3a − 7
E. 2a2
14. What is the √
sum of the first 8 terms of a geometric sequence whose first, second and third
terms are 3, 3 and 1, respectively?
240
A. √
3−1
80
B. √
3
C. −240
√
D. −
3
80
240
E. √
3+1
15. The point P (2, −3) is on the graph of the function f (x). What will be the coordinates of the
point P if the graph of the function f (x) is shifted 2 units to the right then 1 unit downward?
A. (4, −4)
B. (0, −4)
C. (1, −1)
D. (0, −2)
E. (0, 0)
6
Answers
1. E
2. B
3. A
4. D
5. E
6. B
7. C
8. A
9. E
10. A
11. B
12. E
13. C
14. A
15. B
7
Trigonometry Sample Test
2
1. If 0◦ ≤ θ ≤ 90◦ and cos θ = , then sin θ =?
5
A.
3
5
1
7
√
21
C.
5
B.
D.
E.
5
2
√
5
5
2. Which of the following expressions is equivalent to 1 − sec2 θ?
A. − tan2 θ
B. csc2 θ
C. − sin2 θ
D. cos2 θ
E. sin2 θ + cos2 θ − 1
4
and A is a fourth quadrant angle, what is cot A?
5
3. If cos A =
A. −
B.
3
4
3
5
C. −
3
9
D. −
1
4
E. −
4
3
1
4. If sin x = , then cos x =?
3
8
3
4
√
2 2
B.
3
√
2
C.
3
√
2
D.
4
A.
E. 1
5
5. In 4LM N , ∠LM N is a right angle and tan ∠LN M = . What is the value of sin ∠N LM ?
3
√
3 34
A.
34
N
√
8 34
B.
34
√
5 34
C.
34
√
15 34
D.
34
L
M
√
2 34
E.
34
√
π
3
6. If < θ < π and sin θ =
, then tan θ =?
2
4
√
13
A. −
4
7
B. √
13
1
C.- √
10
4
D. √
10
√
3
E. − √
13
7. Kaila is flying a kite whose string is making a 70◦ angle with the ground. The kite string is 65
meters long. How far is the kite above the ground?
9
A. 22 meters
B. 61 meters
C. 179 meters
D. 455 meters
E. 5 meters
√
8. If cos x =
A.
B.
1
2
√
3
, then sin 2x =? (Note: sin 2x = 2 sin x cos x)
2
3
1
C. √
3
√
3
D.
2
2
E. √
3
9. What is the value of y = 3 − 4 cos x when x = 7π
A. 3
B. −12
C. −1
D. −4
E. 7
10. Which of the following is equivalent to sin2 x sec2 x + 1
A. sec2 x
10
B. sin2 x
C. cos2 x
D. tan2 x
E. 0
11. A homeowner is to construct a ramp to his front door to make it wheelchair accessible. How
long is the ramp if the door is 4 ft above the ground and the ramp is inclined at an angle of
20◦ ?
A. 80 ft
B. 11.7 ft
C. 10.9 ft
D. 4.3 ft
E. 1.4 ft
12. If f (x) = sin πx, then its successive maxima are separated by
A. π
B. 2π
C. 1
D. 2
E. 4π
11
Answers
1. C
2. A
3. E
4. B
5. A
6. E
7. B
8. D
9. E
10. A
11. B
12. D
12
Algebra Sample Questions
Algebra Sample Test (1)
1
1. If r = 3 and h = 8, which of the following is equal to πr2 + πr2 h?
3
A. 81π
B. 22π
C. 33π
D. 20π
E.
35
π
3
2. Which of the following expressions is equivalent to (5x − 1)(2x + 7)?
A. 10x2 − 7
B. 10x2 + 35x − 7
C. 10x2 − 2x − 7
D. 10x2 − 33x + 7
E. 10x2 + 33x − 7
√
√
3. What is the value of 5x − 4 x3 + x 75x2 when x = 3?
√
A. 15 + 33 3
√
B. 15 + 43 3
√
C. 15 + 57 3
√
D. 3 + 45 3
13
√
E. 48 3
4. What are the solutions of the equation 28x2 − 11x − 30 = 0?
A. −
6
5
and −
4
7
B.
6
5
and
4
7
C.
5
6
and −
4
7
D. −
E.
6
5
and
4
7
7
5
and −
4
7
1
5. If 3x − 20 = , then x =?
2
A. −6
5
6
B. 6
C. 13
D. 3
E. 8
1
2
1
3
1
2
1
5
6. In 2010, 15% of the women who went to maternity leave returned to full-time work. If 12
women returned to work in that year, how many left to have babies?
A. 20
B. 400
C. 180
D. 27
E. 80
14
7. For all x 6= 0,
6x5 + 15x4 − 9x3
=?
3x3
A. 6x5 + 15x4 − 3
B. 2x5 + 15x4 − 9
C. 2x2 + 15x − 9
D. 2x2 + 15x4 − 9x3
E. 2x2 + 5x − 3
8. If 8x7 +14x4 −3Cx2 +23x−4 = 2x4 (4x3 +7)+(6x−1)(x+4), what is the value of the constant C?
A. 6
B. 8
C. −2
D. −4
E. 7
9. In the standard coordinate plane, what is the distance between the the x and y intercepts of
the line given by the equation 3y + 4x = 12?
A. 5
B. 4
C. 3
D. 12
E. 7
10. Which of the following equations represents a line that passes through the point (−1, 5) and is
perpendicular to the line 7y − x = 2
36
1
A. y = − x +
7
7
15
B. y = 7x + 12
1
C. y = x + 2
7
D. y = x −
2
7
E. y = −7x − 2
11. Which of the following is the complete factorization of 10x3 y 2 + 35x2 y 3 − 20xy 4 ?
A. 5x2 y(4x − y)(x + 2y)
B. 5xy 2 (2x − y)(x + 4y)
C. 5y 2 (2x + y)(x − 4y)
D. 5xy 2 (x − y)(x + 4y)
E. 5y 2 (2x − y)(x + y)
12. If the radius of the circle in the figure below is a, what are the coordinates of the point P ?
A. (3a, a)
B. (3a, 3a)
P
C. (6a, 2a)
D. (3a, 2a)
a
−a
E. (2a, 2a)
16
2a
3a
4a
5a
13. For all x 6= 0 and 5,
4x2
2x
x−5
=?
A. 2x2 − 10x
B. 4x3 − 20x
C. 2x2 − 5
D. 4x3 − 5x
E. 2x2 − 5x
14. Michael can pain a room in 5 hours while John can paint the same room in 3 hours. How long
does it take if Michael and John work together to paint the room?
A. 8 hours
B. 15 hours
C. 2 hours
D. 4 hours
E. 1.875 hours
17
Answers
1. C
2. E
3. A
4. C
5. B
6. E
7. E
8. C
9. A
10. E
11. B
12. D
13. A
14. D
18