Department of Mathematics

For All Students

Mathematics Sample Placement Test

1.   25.01 + 36.5 + 200.35 =

(a)  81.545    (b)  228.91     (c)  229.01     (d)  261.41    (e)  261.86

2.   -5[4 - (-3)(2)] =

(a)  -70       (b)  -50       (c)  -10       (d)  5      (e)  10

3.   If \( \frac 43x - \frac 12 = {}\)0 , then \(x =\)

(a)  3/8    (b)  2/3     (c)  3/2     (d)  11/6    (e)  8/3

4.  \( (-8p^2q)(-4p^4q^5) = \)

(a)  32p⁵q⁶       (b)  4p^-4q^-2       (c)  32p⁶q⁶       (d)  4p⁵q⁸        (e)  -2p⁵q⁸

5.   If  x² + 2x = 3, then x could equal

(a)    -3       (b)  -2       (c)  -1       (d)  0       (e)  3

6.   The polynomial equation   x(x² + 4)(x² - x - 6) = 0  has how many real roots?

7.   If  f(a) = 2a -1 and g(a) = a²,    then g(f(a)) =

8.   If  7^x = 3,   then x =

(a)  3/7      (b)  7/3      (c)   log₃(7)      (d)   log₇(3)      (e)   log₁₀(7/3)

9.   If  t = e^{x + 2} ,   then x =

(a)  2 + ln(t)       (b)  (t + 2)/e       (c)  t/e       (d)  ln(t - 2)       (e)  ln(t) - 2

10.   The inequality x² - 14x > 15   is equivalent to

11.   The two parallel lines represent the graph of which of the following pair of equations?

(a)    x - 2y = 3 and    x - 2y = 7
(b)    x + y = 1  and    x + y = -2
(c)    x + y = 3  and  2x + 2y = 6
(d)    x + y = 3  and    x - y   = 5
(e)    x - y = 7   and    x - y   = 14

12.   Of the following numbers, which is largest?

13.   Triangle ABC is an equilateral triangle. The height  h   is:

(a)  -8        (b)  -(1/8)        (c)   0        (d)   (1/8)        (e)   8

15.   For all real numbers x ,   cos²(x) - sin²(x) =

(a)  0      (b)  1      (c)  sin(2x)      (d)  cos(2x)      (e)  cos(x/2)

16.   If  f  is a function whose graph is sketched below,

         then f(x) < 0 whenever