Advanced
Academic Placement Testing Program
Box 355837
Seattle, Washington 98195-5837
(206) 543-1790 telephone
(206) 543-3961 facsimile
aptp@u.washington.edu
www.washington.edu/oea/aptp.htm
APTP
Practice Problems for the
Advanced
Mathematics Placement Test
The following practice problems do not constitute a sample test.
The Advanced Mathematics Placement Test covers the following topics:
Trigonometry
Linear Functions
Graph Interpretation
Quadratic Functions
Proportions
Central
Washington
University
Eastern
Washington
University
Exponents and Logs
Equations
Simplifying
Functional Notation
Absolute Value
University
of
Washington
Washington
State
University
Western
Washington
University
1
Advanced
1.
3  27  5 12 
(A)  5 12
(B) 12 3
31 x 2 y 1

9x
27 y
(A)
x
(C) 18 3
(D) 15 2  2 3
(D)
x
3y
(E)
x
6y
(E) 8 3
2.
3 5


a ab
3a  5
(A)
ab
(B)
x
27 y
(C) 1/3xy
(B)
8
ab
(C)
25
a 2b
(D)
3b  5
ab
(E)
8
a  ab
(B)
b 3c 3
27a 6
(C)
9a 6 c 3
b3
(D)
9b 3 c 3
a6
(E)
a 6b 3
27c 3
(C)
5x 2
(D)
(C)
ab
ab
3.
 3a 2 b 1 


4.
 c

6 3
 27 a b
(A)
c3
5.
(A)
6.
(A)
7.
3

For x  0, 9 x 3  4 x 
x 3x  2
(B)
x
3x  4
(E) x 9 x  4
1 1

a b 
1 1

a b
ba
ba
(B)
1
a  b2
2
(D) 0
(E)
ab
ab
x 3a 1

x a2
(A) 2a  3
(B) x 4 a 1
(C) 4a + 1
(D)
x 2 a 3
(E) 12 a 1
2
Advanced
8.
Hook's law states that the force required to stretch a spring x units beyond its natural length is directly
proportional to x. If a weight of 4 pounds stretches a spring from its natural length of 10 inches to a length of
10.3 inches, what weight will stretch it to a length of 11.5 inches?
(A) 2.5lbs
(B) 46lbs
3x  1
x


x 1 x 1
3x 2  x
4 x 2  3x  1
(A) 2
(B)
x 1
x 2
(C) 3.75lbs
(D) 1.5lbs
(E) 20lbs
2 x 2  5x  1
(C)
x2 1
3( x  1) 2
(D)
 x( x  1)
(E)
3x
x 1
(D) 2a 2 b
(E)
2b
a2
9.
16a b 
8
10.
(A)
2a
b
4
1
4
2

2
(B)
a2
2b
(C)
4a 2
b
11.
Density is the mass of a substance divided by its volume. What is the volume in cubic centimeters of a
mass of 300 grams having a density of 60 grams per cubic centimeter?
(A) .20
(B) 5
(C) 1,800
(D) 50
(E) 18,000
(D) – 1
(E) 6
When 3 x 2  5 x  4 is divided by x – 2 the remainder is
12.
(A) -3
(B) 1
(C) 0
13.
In a room with 90 students, there are 4 times as many women as men. How many women are in the
room?
(A) 18
14.
(A)
15.
(A)
(B) 72
For what value of t does
4
3
(B) 
If x 
ac
bc
2
3
(C) 56
2t  1
 1?
t 3
(C)
2
9
bx
 a, and b  c, then x =
c
a
ac
1
(B)
(C)
bc
b
(D) 30
(E) 75
(D)
4
3
(E) none of the above
(D)
a
bc
(E)
ac
1
b
3
Advanced
16.
If x  2 and  x  2  x  1  3 x  2 x  1   x  2 P, then P =
2
(A) x  1x  2
17.
(A)
18.
(C) x 2  2
(B) ( x  1)( x  5)
(D) ( x  1) 2
(E) x +1
One of the roots of x 2  3x  1  0 is
1 5
2
(B)
 3  13
2
In the system of equations
(A) x = 7
(B) x = 0
(C)
3 5
2
x + 3y = 17
4x - y = 3
(D)
 3  13
2
(E)
1 5
2
the value of x is
(C) x = 3
(D) x = 5
(E) x = 2
19.
Suppose that you have 12 coins, all nickels (5 cents apiece) and dimes (10 cents apiece) with a total
value of $1.00. If x is the number of nickels in your pocket and y is the number of dimes, then which of the
following systems of equations can be used to determine x and y?
(A)
(D)
20.
10x +5y = 12
x + y = 100
x + y = 100
5x + 10y = 12
(B)
x + y = 15
10x + 5y = 100
(E)
10x + 5y = 100
x + y = 12
x + y = 12
5x + 10y = 100
1
1
1



a  1a  2 a  2a  3 a  1a  3
(A)
1
(a  1) 2
(B)
a4
a  1a  2a  3
(D)
a6
a  1(a  2)a  3
(E)
1
a  1(a  2)a  3
21.
(C)
(C)
(a  1)( a  2)( a  3)
a3  6
If f x   2 x 2  x  5 then f a 1 
(A) 4a 2  3a  6
(D) 2a 2  3a  8
(B) 2a 2  3a  6
(E) a + 6
(C) 2a 2  5a  8
4
Advanced
If f  x  
22.
(A)
2
5
23.
(A)
3
, for what value of x does f x   6
x2
(B)
4
3
(C)
1
6
(D)
5
2
(E)
3
4
In the figure to the right x =
3
2
(B)
2
3
10
3
(C)
5
7
(D)
7
5
(E)
15
7
x
24.
The inequality x  5  3 is equivalent to
(A) x > -2
(B) x > 8 and x < -8
(D) x < -8 or x > 2
(E) 3 < x < 5
25.
(A) 3
5
(C) –8 < x < -5
If the radius of a circle is tripled then the area is increased by a factor of
(B) 3
(C) 9
(D) 6
(E) 9
26.
5
Advanced
27.
28.
The graphs of the equations 3x + 4y = -2 and 3x + 2y = -4 are
(A) not linear
(B) two parallel lines
(C) the same line
(D) two intersecting lines which are not parallel
(E) are two perpendicular lines
29.
(A) 8
What number must be added to x2 + 8x to form a perfect square?
(B) 4
(C) 2
(D) 32
(E) 16
6
Advanced
30.
31.
cos (- ) =
(A) sin(- )
32.
(C) - cos
(D) sin
(E) - sin
(D) x > 7/4
(E) x < 8/5
The inequality 5 - 4x > 2 is equivalent to
(A) x < 3/4
33.
(B) cos
(B) x > 3/4
(C) x < 7/4
In the figure to the right sin  tan  =
c
b

b2
(A)
ca
a2
(D)
cb
a
(B)
c
b
(E)
c
ab
(C) 2
c
a
7
Advanced
In the figure to the right, tan  =
34.
(A) 
(D)
3
4
4
3
(B) 
(E) 
3
5
y
(C)
3
4

4
3
x

(3, -4)
35.
If sin   0 then csc  - cos  cot  =
(A) 0
36.
(B) 
(C) sin 
(D) cos 
(E) 1
(B) sin2
(C) -sin
(D) sin
(E) cos
sin (  - ) =
(A) -cos
Please continue to next page.
8
Advanced
37.
38.
(A) 27
log381
(B) 243
(C) 381
(D) 9
(E) 4
9
Advanced
39.
(A)


log 5 25  5 3 
2
3
(B) -1
(C) 5
(D) -5
(E) 1
40.
41.
The chart below shows Martha’s distance as a function of time as she drives between two points. Based
on the information in the graph, which of the following is true:
(A) Martha increases her speed during the entire time
(B) Martha decreases her speed during the entire time.
(C) Martha at first increases her speed and then decreases it.
(D) Martha at first decreases her speed and then increases it
(E) Cannot tell from the chart.
10
Advanced
42. Tom wishes to estimate the height of a telephone pole. He waits until late afternoon on a sunny day. He
then places the bottom end of a 10 foot pole on the shadow of the telephone pole just so both shadows terminate
at the same point when he holds his pole straight up. If the distance from the end of the shadow to the end of
the 10 foot pole is x, and the distance between the two poles is y, how high is the long pole?
(A) (10x + y)/(x + y) (B) 10(y – x)/y
(D) 10y/x
(E) (x + y)/10x
(C) ab(a + b)
(D) (a – b)/(b – a)
(E) b – a
(a2 – b2) / [(a/b) – (b/a)] =
43.
(B) (a2 – b2)/(a + b)
(A) ab
44.
(C) 10(x+y)/x
A rectangle has an area of 48 square inches. Its base is 6 inches. What is the length of diagonal?
(A) 8 inches
(B) 10 inches
(C) ( 48 )/6 inches
(D) 14 inches
(E) 20 inches
45.
The wedding photographer for the Smith/Jones wedding charges $1,000 for her preparation and first 60
prints. The cost is $2.00 per photo for photos beyond the first 60. Which formula should be used to determine
the total cost, C, as a function of the number of photos, p, that are purchased, assuming at least 60 are
purchased?
(A)
(B)
(C)
(D)
(E)
46.
C = 1000p + 2
C = 1000(p – 60)
C = 1000(p + 2) – 60
C = 1000p + 2(60)
C = 1000 = 2(p-60)
If f(0) = -2 and f(x+2) – f(x) = 5, and f(x) is linear, which of the following is the equation for f(x)
(A) f(x) = -2x + (5/2)
(B) f(x) = (2/5)x +5
(D) f(x) = (5/2)x – 2
(E) f(x) = 5x + 2
47.
(C) f(x) =2x + 5
Given the table below, choose the correct linear function for f(x)
x
-2
-1
0
+1
+2
f(x)
13
1/f(x)
2f(x)
20
1/7
4
(A) f(x) = -7x + 13
(B) f(x) = (1/7)x + 1 (C) f(x) = 20x – 1
(D) f(x) = -3x + 7
(E) f(x) = x + 1/7
11
Advanced
48.
A mathematical model for the Future Value of a savings account earning interest that is compounded
continuously is given by the equation FV = Pert, where FV is the amount after t years. P is the principal amount
invested at t = 0, and the principal is assumed to grow continuously at a rate, r. How many years will it take the
principal to triple at an annual rate of 12%.
(A) FV/Pe.12
49.
(B) ln 3/.12
(C) .12 log10e
Select the largest set of criteria that are met by f(x ) =
(D) log103/.12
(E)log10e/-.12
( x  2)
I. f(x) is continuous for -2≤ x < 7
II. f(x) is increasing for 3 ≤ x< 5,
III. the domain of f(x) is -2 ≤ x < ∞
IV. the range of f(x) is -2 < f(x) < ∞
(A) I, II, and IV
(B) II, III, IV
(C) II, III
(D) II
(E) all of the above
12
Advanced
Correct responses:
1 - 'E'
2 – A or'B'
3 - 'D'
4 - 'B'
5 - 'A'
6 - 'A'
7 - 'D'
8 - 'E'
9 - 'C'
10 - 'A'
11 - 'B'
12 - 'E'
13 - 'B'
14 - 'E'
15 - 'A'
16 - 'B'
17 - 'C'
18 - 'E'
19 - 'C'
20 - 'B'
21 - 'B'
22 - 'D'
23 - 'E'
24 - 'D'
25 - 'E'
26 - 'C'
27 - 'C'
28 - 'D'
29 - 'E'
30 - 'E'
31 - 'B'
32 - 'A'
33 - 'A'
34 - 'E'
35 - 'C'
36 - 'C'
37 - 'A'
38 - 'E'
39 - 'B'
40 - 'E'
41 - 'C'
42 - 'C'
43 - 'A'
44 - 'B'
45 - 'E'
46 - 'D'
47 - 'D'
48 - 'B'
49 - 'A'
13