MATHEMATICS TEST 30 Minutes — 30 Questions pps

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MATHEMATICS TEST
30 Minutes — 30 Questions
Directions: Solve each problem, choose the correct answer,
and then fill in the corresponding space on your answer sheet.
Do not linger over problems that take too much time. Solve as
many as you can; then return to the others in the time you have
left for this test.
Note: Unless otherwise stated, all of the following should be
assumed.
1.
2.
3.
4.

1.

What is the value of 2x2 + 3x – 4 when x = –1?
A.
B.
C.
D.
E.

2.

Illustrative figures are NOT necessarily drawn to scale.
Geometric figures lie in a plane.
The word line indicates a straight line.
The word average indicates arithmetic mean.

D.
E.

–5rs2
5r2s2

–7
–5
–3
–1
1

Denise has tossed a fair coin 100 times. It has landed
heads up 51 times and tails up 49 times. What is the
probability that it will land heads up the next time

Denise tosses it?
1
100
1
G.
10
49
H.
100
1
J.
2
51
K.
100
F.

3.

If r ≠ 0 and s ≠ 0,
A.
B.
C.

15r 3s 4
=?
−3r 4s 2

–5r –1s2
5r –1s2

5rs2

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2
4.

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–1
–2
–3

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2

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In the figure below, PQ is parallel to the y-axis.
What is the value of a ?
y
3
2
1

v

Q (a, 2)

1

2

x
3

P (3,–1)

F. –3
G. –1
H. 1
J.
2
K. 3

5.

In ∆ABC below, AB is 4 units long and BC is 3
units long. What is the value of sin ?
A

4

B
A.
B.
C.

D.
E.

3

C

3
5
2
3
3
4
4
5
5
6

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6.

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J.

K.

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2

y
4x – 3y

50
85
110
145
175

In the figure below, AC and BD are parallel and EF
and GH are parallel; they intersect at points M, N, P,
and Q. If the measure of ∠AME is 57°, what is the
measure of ∠NQH ?
A

E

B

57°

M

G

N

P

A.
B.
C.
D.
E.

F

H

Q

C

8.

v

Randy has a collection of comic books. If you add 15
to the number of comic books in her collection and
multiply the sum by three, the result will be 65 less
than four times the number of comic books in her
collection. How many comic books are in her

collection?
F.
G.
H.
J.
K.

7.

v

D

57°
93°
114°
123°
153°

The area of a rectangular plot of land is equal to
(28x2 – 21xy) square feet. If the width of the
rectangular plot is 7x feet, what is the length, in feet?
F.
G.
H.

7(x – y)
21x – 14y
4x2 – 3xy

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9.

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2

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What is the greatest common factor of (32 × 5 3) and
(3 × 5 2)?
F.
G.
H.
J.
K.

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5
52
3 × 52
32 × 52
32 × 53

10. In triangle ABC below, ∠ACB is a right angle. If
AB is 8 units long and BC is 6 units long, how
many units long is AC ?
A

8

C
F.
G.
H.
J.
K.

6

B

2
2 3
2 7
10
4 7

11. Joan has 5% more money in the bank today than she
had one year ago. If she has $2,520 in the bank now,
how much did she have in the bank one year ago?
A.
B.

C.
D.
E.

$2,000
$2,250
$2,300
$2,315
$2,400

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12. What is the sum of the solutions of the equation
x2 + 4x – 2 = 0?
F.
G.
H.
J.
K.

v

–4 – 2 2
–4
–2
–4 + 2 2
8

13. The equation y = 10x + 3 can be graphed in the
standard (x, y) coordinate plane. What is the value of
1
the x-coordinate at the point where y =
?
2
A.
B.
C.
D.
E.

–4

5
–
2
1
–
4
1
4
8

14. The expression

p2 – 2 p is equal to which of the

following when p = 9 ?
F.
G.
H.
J.
K.

3
2
3
5
5

3
5
2

3

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15. Which of the following is a solution for the equation
2x2 + 5x + 1 = 0?
−5
+ 25 – 8
4

5 + 25 –8
=
4
−5 + 25– 8
=
4
= –5 + 25 – 8
2
= –5 + 25 – 8
4

A.

x =

B.

x

C.

x

D.

x

E.

x

16. A certain galaxy contains 27 × 3 8 stars. How many
stars is this in terms of a power of 3?
F.
G.
H.
J.
K.

310
311
316
324
327

17. Maria has a collection of valuable old baseball cards.
1
She has decided to sell of them. Jack offers to buy
3
1
of the ones Maria is selling for $40.00. At this
4
rate, how much would her entire collection be worth?
A.
B.
C.
D.
E.

$ 160.00

$ 300.00
$ 380.00
$ 480.00
$1,200.00

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18. A train travels 50 miles in 1 hour and then r miles in
s hours. Which expression represents the train's
average rate of speed, in miles per hour, for the entire
distance?
F.

v

50 + r
1+s
50 + r
s
50s + r
s
50s + r
1+s
50r
s

19. Which of the following expressions describes all of
the values of r that are solutions of the inequality
9 – 3r > 12 ?
A.
B.
C.
D.
E.

–1 < r < 7

r > –1
r >7
r < –7
r < –1

20. The area of a circle is 64π square centimeters. What
is the diameter, in centimeters?
F.
G.
H.
J.
K.

4
8
12
16
24

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21. What is the area, in square units, of the square whose
vertices are located at the coordinate points indicated
in the figure?
y
(2, 7)

(–1, 4)

(5, 4)

(2, 1)

x

(0, 0)

A.
B.

C.
D.
E.

9
12
16
18
24

22. What is the equation of the parabola graphed in the
(x, y) coordinate plane below?
y
6
5
4
3
2
1
–4 –3 –2 –1
–1
–2
–3
F.
G.
H.
J.
K.

x

1 2 3

4

y = x2 + 1
y = x2
1
y = x2
2
y = –x2 –1
y = x2 –1

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23. Which of the following best describes cos x as x
increases from π to π?
2
A.
B.
C.
D.
E.

v

It decreases from 0 to –1.
It increases from 0 to 1.
It decreases from 1 to 0.
It increases from –1 to 1.
It decreases from 1 to –1.

24. In the figure below, S is the center of the square
WXYZ, and ST is perpendicular to XY . If the
perimeter of WXYZ is a, what is the length of ST in
terms of a ?
W

Z

S

X
F.
G.
H.
J.
K.

T

Y

a
16
a
8
a
5
a
4
a
2

25. (3 5 – 2 3 )(3 5 + 2 3 ) = ?
A.
B.
C.
D.
E.

6 5 –4 3

9
9 5 –4 3
33
9 15

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25

15
F.
G.
H.
J.
K.

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H. 80°
J. 90°
K. 100°

26. Rob is experimenting with kites of various shapes,
such as the one shown in the illustration. If all the
dimensions are given in inches, what is the area of
the kite in square inches?

25

v

15

475
525
575
600
625

27. When positive integer n is divided by 8, the
remainder is 7. What is the remainder when 5n is
divided by 8 ?
A.
B.
C.

D.
E.

3
4
5
6
7

28. In ∆ABC below, the sum of the measures of
∠ABC and ∠BAC is 100°. What is the measure of
∠ACB ?
A

B
F.
G.

C

20°
50°

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29. A rectangular concrete pavilion with dimensions 20
feet by 25 feet is to be covered by a tarp in case of
rain. If the tarp is made large enough to extend 3
feet beyond the edge of the pavilion on all sides, by
how many square feet is the area of the tarp greater
than the area of the pavilion?
A.
B.
C.
D.
E.

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144
206
244
294
306

30. A recipe calls for sugar, water, and flour in the
volume ratio 1 : 3 : 4, respectively. If 1 cup of
water is used, how many cups of flour are required?

F.
G.
H.
J.
K.

1
4
1
1
3
1
1
2
3
4
1

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THERE IS NO TEST MATERIAL ON THIS PAGE

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