POSTTEST

Mathematical Reasoning

46 questions 115 minutes

!is posttest is intended to give you an idea of how ready you are to take the real GED® Mathematical
Reasoning test. Try to work every problem, in a quiet area and with enough time so that you are free
from distractions. !e usual time allotted for the test is 115 minutes, but it is more important to be sure
you get a chance to think about every problem than it is to "nish ahead of time.
Answers and solutions for every problem can be found at the end of the posttest.

PART I: NO CALCULATOR
7
1. Circle all values that are solutions to C.
8
4 x 2 – 36 = 0 . 7
D.
–36 –9 –3 3 9 36 80
PART II: CALCULATOR ALLOWED
136
2. Write as a mixed number in lowest terms.
32 6. If the table represents a function, !ll in the two
17 missing numbers.
A. Write your answers in the shaded boxes.
4
1 x –2 –1 0 1 2 1 5 –2
B. 4
4
8 f(x) 3 0 2 6 7 5
C. 4
32
4 7. Circle any pair of points on the graph that
D. 4 show why it is not the graph of a function.
16
y
3 2
3. Add 7 + 4 .
8 5 10
Write your answer in the blank. 8

4
4. Add 13.50 + 17.995 + 6.008.
2
Write your answer in the box.
x
–10 –8 –6 –4 –2 2 4 6 8 10
–2

–4
5. What fraction equals 0.875? –6

–8
87.5
A.
100 –10
151
B.
200
151
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POSTTEST

x –2 y 5
8. If f ( x ) = 2 x 2 + 7 x + 3 , what is f (5)? 14. Divide .
x –3 y 2
A. 88
y3
B. 63 A.
C. 138 x5
D. 85 B. xy 3
x5
9. Circle two points on the number line that are C.
y3
separated by a distance of 23 units.
D. x –5 y 7
–18 –12 –8 –1 4 8 15
15. Solve for x: 4 x 2 – 7 x = 15.
–20 –15 –10 –5 0 5 10 15 20

⎛ −1 ⎞ ⎛ 1 ⎞
10. Multiply ⎜ x 3 ⎟ ⎜ x 3 ⎟ .
⎝ ⎠⎝ ⎠
A.
{ }
5
− ,3
4

A. 1
–
1
B. { }
5
4
,−3

B. x 9

C. x 3
2

2
C.
{− 45 , −3}
{ }
–
D. x 3
D. 5
,3
4
11. Factor 8 x 2 + 24 x + 18 .
A. ( 4 x + 3)2 x 2 y 4 z −3
16. Divide .
B. 2(2 x + 3)2 xyz 3
C. ( 4 x + 3)(2 x + 6) x2y 4
A.
D. (2 x + 3)2 xyz 6
B. 3x 6
x 2 – 9 x + 20 y z
12. Divide .
x –5 xy 3
C.
A. x – 4 z6
x –5 xy 3
B. 1 D. 9
z
x –5
C.
x–4
D. x – 4

13. Solve for x: 3 x – 11 < 5 x – 7 .

A. x > –2
B. x < –2
C. x >2
D. x <2
 POSTTEST: Mathematical Reasoning 153

POSTTEST

17. Andy rides his bike from his house to the 21. 7 : 4 :: 49 : .
library, a distance of 4 miles. After that, he Fill in the blank.
rides 3 miles from the library to the store. If
he follows the path shown below, how far is it
22. The ratio of the sides of two squares is 1:2.
from the store back to Andy’s house?
What is the ratio of their areas?
Home
A. 1:1
B. 1:2
C. 1:4
D. 2:1
Library Store
23. Circle the number of the straight line that has
A. 5 miles slope 4 and that passes through the point (5, 3).
B. 7 miles y
C. 9 miles
D. 12 miles 12
2
10
1
18. Wendy has taken !ve tests and has an average 8
of 84. What must she make on the next test to 6
3
raise her average to an 85? 4

A. 84 2 4

B. 85 –12 –10 –8 –6 –4 –2 2 4 6 8 10 12
x

C. 86 –2
D. 90 –4

–6
19. Solve for x: 4 x 2 – 9 = 0. –8

–10
9
A. ±
4 –12

3
B. ±
2
24. What does f ( x ) approach as x becomes larger
2 and larger but negative, if
C. ±
3
f ( x ) = x 3 – 2 x 2 + 12 x + 5?
3
D. ± Circle the correct answer.
2
+∞
2x − 7 7y + 3
20. Subtract − .
4x 6y
0
9 xy – 4
A.
24 xy
6 x + 8 xy + 21y –∞
B. –
12 xy
–8 xy – 21y + 6 x 25. Write 0.0095 as a reduced fraction.
C.
12 xy Write your answer in the box.
2 x – 7 y – 10 xy
D.
24 xy
154 POSTTEST: Mathematical Reasoning

POSTTEST

The following question contains a blank marked 29. What is the area of this triangle?
Select . . . ▾ . Beneath the blank is a set of choices.
Indicate the choice that is correct and belongs in the
blank. (Note: On the real GED® test, the choices will
5 10
appear as a “drop-down” menu. When you click on a
5
choice, it will appear in the blank.)

26. Erlene and Bob have a bet to see who makes

10
the higher score on their !nal exam in biology.
After the exam they compare papers. Erlene’s A. 50
teacher has written 86% at the top of her B. 25
paper. Bob’s teacher has written 42/50 on C. 10
the top of his paper. After Erlene and Bob D. 5
convert their scores to be on the same scale,
it is clear"that made the 30. What is the length of a side of a right triangle
higher"score. if the other side measures 12 centimeters and
the hypotenuse measures 20 centimeters?
Select . . . �
A. 8 centimeters
Erlene B. 16 centimeters
Bob C. 23.32 centimeters
D. 256 centimeters
27. What is the average of the data set below?
Write your answer in the box. 31. Which of the following has a larger area?
Place an X on the correct blank.
{0.0012, 0.00067, 0.0023, 0.01, 0.009}
a circle with a diameter of
30"centimeters

a square that measures

30"centimeters on a side
28. What is the perimeter of a hexagon that is
17"inches on a side? 32. Gerald uses 4 cups of #our and 1 cup of sugar
A. 51 inches in his famous cookie recipe. If he needs to
B. 102 inches make !ve batches, how much #our and sugar
C. 112 inches must he have on hand?
D. 119 inches A. 4 cups #our, 1 cup sugar
1
B. 10 cups #our, 2 cups sugar
2
C. 5 cups #our, 20 cups sugar
D. 20 cups #our, 5 cups sugar
 POSTTEST: Mathematical Reasoning 155

POSTTEST

5
33. Evaluate 4 2 . 38. What is the smallest integer value that makes
x ≥ −10 true?
A. 32
Write your answer in the box.
B. 1.74
C. 512
D. 1,048,567

Use the following for questions 34–35. 39. Arrange in order from smallest to greatest:
4 3 1
0.47, 21%, 0.06, , , 33 %
Only 9% of the residents in a county live on farms. 5 8 3
The population of the county is 127,000 people.
< < < <
34. How many people do NOT live on farms?
<
A. 11,430
B. 14,111 40. A line has the equation 3 x − 5 y = 15 . What is
C. 114,300 its slope?
D. 115,570
5
A. −
35. 17% of the people in the county are above 3
the average age. How many people are 3
B. −
above the average age? 5
A. 21,590 3
C.
5
B. 74,700
C. 90,170 5
D.
D. 105,050 3

36. A bowl is !lled with 5 red, 6 yellow, and 41. What is the sum of 2 x + 13 and 6 x + 3?
4 white balls. What is the probability of
drawing a red ball and then a white ball at A. 8x + 16
random? B. 8x2 + 16
C. 4x $ 10
9 D. x+2
A.
21
9 42. Given a group of 12 women and six men, how
B. many distinct groups of three women and
29
2 three men can be formed?
C.
21 A. 120
1 B. 1320
D.
3 C. 4400
D. 158,400
37. Expand ( 2 x + 5) .
2

A. 4 x 2 + 25
B. 2 x 2 + 10 x + 5
C. 4 x + 10
D. 4 x 2 + 20 x + 25
156 POSTTEST: Mathematical Reasoning

POSTTEST

43. Graph y = – x 2 + 2 x + 8 . 45. Build the equation of the line passing between
y the points ( 2, 7 ) and ( 4 ," –7 ) by !lling in the
blanks with the correct numbers. Choose from
10 –21, –14, –7, 7, 14, 21. (Note: On the real GED®
8 test, you will click on the numbers you choose
6 and “drag” them into position.)
4 y = _____x + _____
2

–10 –8 –6 –4 –2 2 4 6 8 10
x 46. Where does the graph of y = 6 x 2 + 5 x − 6
–2 intersect the y-axis?
–4 A. 1
–6 B. 6
C. –6
–8
D. –1
–10

44. If the enrollment at a school was 1250 last

year and is 1500 this year, what is the percent
increase from last year to this year?
A. 20%
B. 17%
C. 9%
D. –20%

THIS IS THE END OF THE MATHEMATICAL REASONING POSTTEST.

ANSWERS AND SOLUTIONS BEGIN ON THE NEXT PAGE.