PRETEST

Mathematical Reasoning

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This Mathematical Reasoning Pretest is designed to introduce you to this section of the GED^® test and to give you a good idea of your current skill level in this subject area.

This test has 46 questions. The questions are in the same formats as the ones on the real exam and are designed to measure the same skills. Some of the questions simply ask you to make calculations. Others describe real-life situations that you must decide how to solve using mathematics. Many of the questions on this test are based on graphs or diagrams. Most of the questions are in multiple-choice format, but you will also see questions that ask you to indicate a point on a graph, write your answer in a box, select an answer from a drop-down menu, or “drag” an answer into the correct position in a math expression or equation. On the real GED^® test, you will indicate your answers by clicking on the computer screen. For this paper-and-pencil practice test, mark your answers directly on the page.

To get a good idea of how you will do on the real exam, take this test under actual exam conditions. Complete the test in one session and follow the given time limit. If you do not complete the test in the time allowed, you will know that you need to work on improving your pacing. Do not use a calculator on the first section of 5 questions, but you may use a calculator on the rest of the test.

Try to answer as many questions as you can. There is no penalty for wrong answers, so guess if you have to. In multiple-choice questions, if you can eliminate one or more answer choices, you can increase your chances of guessing correctly.

After you have finished the test, check your answers in the Answers and Explanations section that follows the pretest. Then use the Evaluation Chart at the end of the Answers and Explanations section to determine the skills and content areas in which you need more practice.

Now turn the page and begin the Mathematical Reasoning Pretest.

Mathematics Formula Sheet

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Perimeter

Area

Surface Area and Volume

Algebra

Data

Mean	The total of the values of a data set, divided by the number of elements in the data set
Median	The middle value in an odd number of ordered values of a data set, or the mean of the two middle values in an even number of ordered values in a data set

PRETEST

Mathematical Reasoning

46 questions      115 minutes

Part 1, Questions 1–5: No calculator allowed.

1.  A storage room contains a table, two bookshelves, and a large mirror. If the table weighs 37 pounds, each of the bookshelves weighs 42 pounds, and the mirror weighs 18 pounds, how much, in total, do the items in the storage room weigh? Indicate your answer in the box.

2.  If a number x has an absolute value of 4, then how many units away from 0 is x on the number line? Indicate your answer in the box.

3.  What is the sum of

A.  

B.  

C.  

D.  

4.  Bella wants to give each of her four friends a piece of ribbon for a craft project. If she has 162.8 inches of ribbon and wants to cut it into four equal pieces, how long will each piece be?

A.  40.7 inches

B.  65.12 inches

C.  325.6 inches

D.  407 inches

5.  What is the greatest common factor of 32 and 68?

A.  2

B.  4

C.  8

D.  16

END OF PART 1. YOU MAY TAKE A 3-MINUTE BREAK.

Part 2: Calculator allowed

6.  A line k passes through point (−2, 5) and has the same y-intercept as the line y = – 3x – 4. What is the equation for the line k?

A.  

B.  

C.  

D.  

7.  If 2(x − 8) = −4x + 2, then x =

A.  −7

B.  −5

C.  3

D.  9

8.  Which of the following is equivalent to the expression 5x – 20?

A.  5(x – 20)

B.  4(x – 5)

C.  5(x – 4)

D.  5(x – 15)

9.  Which of the following is a factor of x⁴ – 5x²?

A.  x²

B.  x⁴

C.  5x²

D.  –x³

10.  If a line is perpendicular to line m in the figure above, and it passes through point P, which of the following points must it also pass through?

A.  Point A

B.  Point B

C.  Point C

D.  Point D

Item 11 contains two numbered blanks, each marked “Select. . . .” Following are two choices for each blank. Indicate the choice that is correct and belongs in each blank. (Note: On the real GED^® test, the choices will appear as a “drop-down” menu. When you click on a choice, it will appear in the blank.)

11.  The figure above shows the graph of a function f. For this function, the value of y is positive when x is than .

12.  A gallon of paint will cover about 400 square feet in a single coat. To the nearest tenth, how many gallons will be required to cover a circular region with a radius of 40 feet? Indicate your answer in the box.

13.  The following chart represents the number of a company’s full-time and part-time employees in four states. Complete a bar graph that represents the total number of employees in each state. (Note: On the real GED^® test, you will click on each bar and “drag” it to its proper location on the graph.)

14.  Machine part A must always be four inches smaller in diameter than machine part B’s diameter. If machine part A’s diameter is 16 inches and machine part B’s diameter is x inches, which of the following can be used to solve for x?

A.  16 = 4 x

B.  16 = x − 4

C.  16 = x + 4

D.  

15.  If 2x – 2 < 8 + x, then x <

A.  2

B.  4

C.  9

D.  10

16.  The number of fans produced by a manufacturer in a week can be no more than five times the number of lamps produced by the same manufacturer during the same week. If the number of fans produced this week by the manufacturer was 20, what is the minimum number of lamps produced by the manufacturer this week?

A.  4

B.  5

C.  15

D.  20

17.  To the nearest tenth of a cubic meter, what is the volume of a cylinder with a height of 4 meters and a radius of 6 meters? Indicate your answer in the box.

18.  What is the completely simplified form of the expression 2(1 − 3x) − (5x + 1)?

A.  -11x + 1

B.  -8 x + 1

C.  -11x + 3

D.  -8 x + 3

19.  If x is a positive rational number, which two of the following numbers or expressions can be added together to equal the area of the given rectangular region? (Note: On the real GED^® test, you will click on the expressions you choose and “drag” each one into a box below.)

20.  What is the value of −2x + 5 when x = −3?

A.  −6

B.  −1

C.  0

D.  11

21.  Which of the following represents the product of 3x + 1 and x² – 1?

A.  3x² – 1

B.  x² – 1

C.  4x² – 3x – 1

D.  3x³ + x² – 1

22.  Five students took the same mathematics course last semester. Their scores on the first exam and the final exam are listed in the following table. If these points are plotted on the coordinate grid that follows, what would be their locations? (Note: On the real GED^® test, you will click on the grid to plot the points.)

Item 23 contains a blank marked “Select. . . .” Beneath it are three choices. Indicate the choice that is correct and belongs in the blank. (Note: On the real GED^® test, the choices will appear as a “drop-down” menu. When you click on a choice, it will appear in the blank.)

23.  In the figures shown, shows a graph that represents y as a function of x.

24.  Which of the following is equivalent to ?

A.  2²

B.  2⁴

C.  2⁸

D.  2¹¹

25.  A shipping box measures 14 inches wide, 10 inches tall, and 18 inches long. In cubic inches, what is the volume of this box?

A.  42

B.  54

C.  2520

D.  2744

26.  Which of the following is a solution to the equation x² − 6x + 1 = 0 ?

A.  −6

B.  

C.  3

D.  

27.  Four data entry specialists—Tom, Jason, Henrietta, and Alton—are observed for a two-hour testing period. During this period, Tom completed 28 forms, while Jason completed 31. Further, if h represents the number of hours, f = 13.1h represents the number of forms Henrietta completed during the testing period and f = 17h represents the number of forms Alton completed during the testing period.

Which specialist completed the forms at the fastest average rate?

A.  Tom

B.  Jason

C.  Henrietta

D.  Alton

28.  Which of the following inequalities is represented by the graph?

A.  2x < −6

B.  2x ≤ −6

C.  3x ≥ −9

D.  3x > −9

29.  The figure represents the property line of a piece of land that is being prepared for sale. If the property is to be completely fenced in prior to the sale, how many feet of fencing will be required?

A.  1600 feet

B.  2400 feet

C.  2800 feet

D.  3200 feet

30.  The mean of the data set 5, 10, 2, 1, and x is 5. What is the value of x?

A.  5

B.  7

C.  13

D.  18

31.  In a group of 20 students, 40% scored 85 on a recent exam while the remaining students scored 90. To the nearest tenth, what was the average score for all 20 students?

A.  87.5

B.  88.0

C.  88.5

D.  89.0

32.  The map shows a hiking trail through a city park. On the map, the distance along the trail between points A and B is 2.5 units. To the nearest tenth of a mile, what is the true distance between the two points?

A.  1.7

B.  2.1

C.  3.8

D.  5.0

33.  What is the value of g(h) = −2h² − h + 5 when h = −3?

A.  −7

B.  −10

C.  38

D.  44

34.  On the following grid, plot the point indicated by the ordered pair (−5, 5). (Note: On the real GED^® test, you will click on the grid to plot the point.)

35.  If two coins are flipped, what is the probability that both coins will land on tails?

A.  0.05

B.  0.25

C.  0.30

D.  0.50

36.  Airfare for a plane ticket varies based on the time purchased, among other factors. On a particular flight from Chicago O’Hare Airport to Atlanta Hartsfield Airport, 65 passengers each paid $127.99, 24 passengers each paid $198.50, and 4 each paid $301.70.

What was the total fare paid by all passengers on this flight?

A.  $14,290.15

B.  $17,224.75

C.  $18,129.85

D.  $58,421.67

37.  The figure shows a line graphed in the x-y coordinate plane and indicates two points through which it passes. What is the equation of this line?

A.  y = −3

B.  x = −3

C.  y = −3 x

D.  x = −3 y

38.  In a survey, participants were asked how many televisions they currently own. The results of this survey are shown in the following table. What is the median of this data set?

A.  0

B.  1

C.  2

D.  3

39.  Ten employees took part in a raffle to determine who gets a new workstation. There are two new workstations available, and two employees’ names will be randomly chosen, one at a time, without replacement.

How many possible ways are there to choose the two employees?

A.  20

B.  45

C.  90

D.  100

40.  The distance between Earth and the moon is 2.4 × 10⁸ miles. A rocket has been sent to explore the moon. If the rocket has currently covered of this distance, how many miles has it traveled?

A.  2.4 × 10^-2

B.  2.4 × 10^-1

C.  2.4 × 10⁶

D.  2.4 × 10⁷

41.  Assuming x is nonzero, which of the following is equivalent to (x ² − 5x) ÷ x ?

A.  x − 5

B.  

C.   −4 x

D.  x² − 4x

42.  In a company with 26 offices, 10 of the offices are located in the Southeast, 8 in the Midwest, 6 in the West, and 2 in the Northeast. If an office is randomly selected, then to the nearest ten thousandth, what is the probability it is located in the Southeast or the West?

A.  0.0769

B.  0.0888

C.  0.3846

D.  0.6154

43.  The volume of a perfectly spherical weather balloon is approximately 381.7 cubic feet. To the nearest tenth of a foot, what is the approximate radius of this weather balloon?

A.  4.5

B.  5.1

C.  7.2

D.  9.4

44.  A placekicker kicks a football from the ground (y = 0). The vertical path of the football follows a parabolic path described by the equation: y = 5t − 4.4t² where t is the time in seconds. After how much time will the football hit the ground?

A.  0 s

B.  0.88 s

C.  1.14 s

D.  2.0 s

45.  Mrs. Barnes wants to wrap a cylindrical container with a radius of 4 inches and a height of 12 inches. To wrap the container, she has only whole sheets of 8.5 inch by 11 inch paper. How many whole sheets will she need?

A.  2

B.  3

C.  4

D.  5

46.  A wind-up toy car can travel 5 yards in about 3 minutes. If the car travels at a constant speed, then how many minutes will it take to travel 40 meters? State your answer to the nearest minute. (1 yard = 0.92 meters)

A.  20

B.  22

C.  24

D.  26

THIS IS THE END OF THE MATHEMATICAL REASONING PRETEST.

Answers and Explanations

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1.  Correct answer: 139 pounds. The total weight is 37 + 2(42) + 18 = 139.

2.  Correct answer: 4. The absolute value of a number can be viewed as its distance from zero on the number line. If the absolute value of a number is 4, then the number is 4 units from zero.

3.  Correct answer: D. A common denominator must be found before adding:

4.  Correct answer: A. Divide 162.8 inches by 4 to get 40.7 inches.

5.  Correct answer: B. The factors of 32 are 1, 2, 4, 8, 16, and 32. The factors of 68 are 1, 2, 4, 17, 34, and 68. The greatest common factor is 4.

6.  Correct answer: A. The line y = 3x − 4 is in y = mx + b form where b is the y-intercept. If line l shares the same y-intercept, then it must pass through the point (0, −4) and have an equation of the form y = mx − 4 for some m. Given that l also passes through (−2, 5),

7.  Correct answer: C. On the left side of the equation, the 2 must be distributed over (x − 8). This yields the equation 2x − 16 = −4x + 2. After adding 4x and 16 to both sides, 6 x = 18 and x = 3.

8.  Correct answer: C. Both 5x and 20 contain a common factor of 5. After factoring out the 5, the remaining factor is x − 4.

9.  Correct answer: A. The first term can be written as x⁴ = x² (x²) to show that both terms share a factor of x ².

10.  Correct answer: A. In the figure, line m passes through the points (0, 4) and (−4, 0) indicating it has a slope of 1. Any line perpendicular to m will therefore have a slope of −1 (the negative reciprocal of 1). If a line passes through point P(0, −2) with a slope of −1, it must pass through point A (−2, 0).

11.  Correct answer: for this function, the value of y is positive when x is less than 4.

When the graph of any function is above the x-axis, it indicates the values of y are positive. Similarly, when the graph is below the x-axis, the y values are negative. The graph of this function is above the x-axis at all x-values less than 4.

12.  Correct answer: 12.6. The area of the circular region is 40²π ≈ 5026.55 square feet. This will require gallons of paint.

13.  Correct answer:

The total number of workers for each state can be found by adding the number of part-time and full-time workers in those states. For Alabama, Georgia, Florida, and Mississippi, those totals are 400, 300, 210, and 450, respectively. These totals are represented in the chart as the height of the bars.

14.  Correct answer: B. If the diameter of machine part A must be 4 smaller, or 4 fewer than machine part B’s diameter, then it must have a diameter of x − 4.

15.  Correct answer: D. Subtracting x and adding 2 to both sides, x < 10.

16.  Correct answer: A. Letting F represent the number of fans and L the number of lamps, you are given that F ≤ 5L. Substituting in 20 fans, 20 ≤ 5L or 4 ≤ L. Thus, 4 or more lamps are produced.

17.  Correct answer: 452.2. Using the formula, the volume is πr²h where r represents radius and h represents height. Using the given values, the volume is π(6²)(4) ≈ 452.2.

18.  Correct answer: A. 2(1 − 3x) − (5x + 1) = 2 − 6x − 5x − 1 = −11x + 1

19.  Correct answer: 2x² + 3x. The area of a rectangular region is always the product of the width and the height. In this case that product is x(2x + 3) = 2x ² + 3x.

20.  Correct answer: D. Replacing x with −3, the expression becomes −2(−3) + 5 = 6 + 5 = 11.

21.  Correct answer: D. Using the FOIL method, (3x + 1)(x ² − 1) = 3x ³ − 3x + x ² − 1 = 3x ³+ x ² − 3x − 1.

22.  Correct answer:

Each point represents the two scores for a single student where the exam 1 score acts as the x-coordinate and the final exam score acts as the y-coordinate.

23.  Correct answer: B. In the figures, B shows a graph that represents y as a function of x. When y is shown as a function of x, there is only one possible y value for each possible x value. In figures A and C, one x value had many possible y values (plot A) or two possible y values (plot C).

24.  Correct answer: B. Using the rules of exponents, .

25.  Correct answer: C. The volume is found using the formula l × w × h where l is the length, w is the width, and h is the height. In this case the volume is 14 × 10 × 18 = 2520 cubic inches.

26.  Correct answer: B. Using the quadratic formula, the solutions are:

.

27.  Correct answer: D. Finding the average rate for each person, Tom completed forms per hour, Jason completed forms per hour, Henrietta completed 13.1 forms per hour, and Alton completed 17 forms per hour.

28.  Correct answer: D. The open circle indicates the point is not included in the solution, so the graph shows the solution set x > −3 which is equivalent to 3x > −9 if both sides are multiplied by 3.

29.  Correct answer: C. Starting from the bottom, moving counterclockwise, and including the missing side lengths, the individual side lengths are 400, 300, 400, 100, 200, 200, 600, and then finally on the left 600. The total amount of fencing needed would therefore be 400 + 300 + 400 + 100 + 200 + 200 + 600 + 600 = 2800 feet.

30.  Correct answer: B. Using the general formula for the mean, it must be that . Cross multiplying and adding terms results in the equation 25 = 18 + x which has a solution of x = 7.

31.  Correct answer: B. Forty percent of 20 is 8 students. Therefore, 8 students scored an 85 while 12 scored a 90. The mean score is then .

32.  Correct answer: C. According to the map, 1 unit of the given length represents 1.5 miles. For each of the 2.5 units, there are 1.5 miles for a total of 2.5 × 1.5 = 3.75 miles between the two points.

33.  Correct answer: B. g(− 3) = −2(−3)² − (−3) + 5 = −2(9) + 3 + 5 = −18 + 8 = −10

34.  Correct answer:

The ordered pair is of the form (x, y). Since the x value is −5 and the y value is 5, the point will be located 5 units to the left of 0 on the x-axis and 5 units above 0 on the y-axis.

35.  Correct answer: B. The sample space for this experiment S = {HH, TT, HT, TH}. One of the four outcomes consists of two tails.

36.  Correct answer: A. The total fare paid by passengers on this flight is (65 × 127.99) + (24 × 198.5) + (4 × 301.7) = 14,290.15.

37.  Correct answer: B. Any vertical line will have an equation of the form x = c for some constant c. In this case, the x value is always −3, so the equation is x = −3.

38.  Correct answer: B. There are 20 total data values, so the median will be the average of the 10th and 11th data values on the list if they are placed in order. The first 5 data values are 0 while the next 8 are 1. The 10th and 11th data values therefore must be 1, and the average of 1 and 1 is 1.

39.  Correct answer: C. When choosing the first employee, there are 10 possibilities. This employee cannot be chosen again, so for the second choice there are only 9 possibilities. By the multiplication rule, there are 10 × 9 = 90 possible ways to choose the two employees.

40.  Correct answer: D.

41.  Correct answer: A.

42.  Correct answer: D.

43.  Correct answer: A. Using the formula for the volume of a sphere, where r is the radius. Solving this equation for r:

44.  Correct answer: C. The left side of the equation should be set to zero (the height of the ground). The right side can be factored into the terms t(5 – 4.4t). By the zero product rule, the solutions are then t = 0 and t = 1.14 s. The solution t = 0 represents when the ball was kicked, so t = 1.14 s is when the ball hits the ground.

45.  Correct answer: D. The surface area of the cylindrical container can be calculated as:

A = 2πr² + 2πrh

A = 2π(4)² + 2π(4)(12)

A = 2π(16) + 2π(48)

A = 2π(64)

A = 128π = (128)(3.14)

A = 401.92

The area of a sheet of 8.5 inch by 11 inch paper is: A = (8.5)(11) = 93.5. So the number of whole sheets required is:

. Therefore,

5 whole sheets will be necessary to wrap the container.

46.  Correct answer: D. At the given speed, the car can travel 1 yard (or 0.92 meter) in minutes. Therefore, the car can travel 40 meters in (40 m) = 26 min.

Evaluation Chart

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Check the Answers and Explanations section of the Mathematical Reasoning Pretest to see which answers you got correct and which ones you missed. For each question that you missed, find the item number in the chart below. Check the column on the left to see the test content area for that item. If you missed questions in a particular content area, you need to pay particular attention to that area as you study for the GED^® test. The pages of this book that cover that content area are listed in the column on the right. Content