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Mathematical Reasoning

Practice Test • New York State Edition (Version 1)

24 MULTIPLE CHOICE + 1 CONSTRUCTED RESPONSE

Recommended time: 50 minutes

Student Copy • Write Answers by Hand

Arithmetic • Algebra • Geometry • Data Analysis & Probability

STUDENT NAME

________________________________

DATE

____________________

CLASS / PROGRAM

________________________________

📋 Directions for Students

This is a printable practice worksheet designed to mirror the official GED Mathematical Reasoning test. Write your answers clearly by hand in the spaces provided.

Read each problem, table, graph, or scenario carefully before answering.
For multiple-choice questions, write the letter of the best answer (A, B, C, or D) on the line provided.
For the Constructed Response, show all calculations and explain your reasoning in the lined space provided.
Work carefully. You have approximately 50 minutes for this practice test.
Calculators are allowed on the real GED Math test — use one here if you have it for practice.

Content areas: Arithmetic & Number Sense (~25%) • Algebra & Functions (~30%) • Geometry (~20%) • Data Analysis, Statistics & Probability (~25%)

STIMULUS 1 Data Table • Arithmetic & Data Analysis

Weekly Sales Data — Riverside Coffee Shop

Day	Coffee Sales ($)	Food Sales ($)	Customers
Monday	312	95	58
Tuesday	378	112	69
Wednesday	295	88	54
Thursday	425	135	82
Friday	510	168	105
Saturday	620	210	128
Sunday	480	155	92

Source: Practice data for GED preparation.

1. What was the total revenue from coffee sales for the entire week?

A. $3,020

B. $2,890

C. $3,150

D. $2,950

Answer:

2. Which day had the highest average revenue per customer (total sales divided by number of customers)?

A. Monday

B. Tuesday

C. Wednesday

D. Friday

Answer:

3. Food sales made up approximately what percent of the shop’s total weekly revenue?

A. 18%

B. 21%

C. 24%

D. 29%

Answer:

4. What is the range of the daily coffee sales amounts shown in the table?

A. $285

B. $310

C. $330

D. $325

Answer:

STIMULUS 2 Graph • Data Analysis & Algebra

Weekly Revenue for a Food Truck (First 5 Weeks of Operation)

Source: Practice data for GED preparation.

5. According to the graph, in which week did the food truck experience the largest increase in revenue from the previous week?

A. Week 2

B. Week 3

C. Week 4

D. Week 5

Answer:

6. What was the average (mean) weekly revenue over the five weeks shown?

A. $1,380

B. $1,476

C. $1,520

D. $1,550

Answer:

7. If the trend from Week 4 to Week 5 continued at the same rate of change, which is the best prediction for Week 6 revenue?

A. $1,750

B. $1,820

C. $1,900

D. $1,950

Answer:

8. The graph shows a generally increasing trend. Which statement best describes the relationship between week number and revenue?

A. Revenue decreased steadily each week.

B. Revenue increased overall, with one week showing a slight decrease.

C. Revenue remained constant after Week 2.

D. Revenue doubled every single week.

Answer:

STIMULUS 3 Geometry • Measurement & Pythagorean Theorem

Right Triangle Garden Bed

A community garden is planning a right triangular flower bed. The two legs of the right triangle measure 6 feet and 8 feet. A border will be placed around the entire perimeter of the bed, and the garden club wants to know the length of the border needed and the area that will be planted.

9. What is the length of the hypotenuse (the longest side) of the triangular garden bed?

A. 10 feet

B. 12 feet

C. 14 feet

D. 9 feet

Answer:

10. What is the perimeter of the triangular garden bed?

A. 18 feet

B. 20 feet

C. 24 feet

D. 28 feet

Answer:

11. What is the area of the triangular garden bed in square feet?

A. 24 square feet

B. 28 square feet

C. 32 square feet

D. 48 square feet

Answer:

12. If the garden club decides to double both leg lengths to make a larger similar triangle, what will be the new perimeter?

A. 36 feet

B. 40 feet

C. 56 feet

D. 48 feet

Answer:

STIMULUS 4 Probability • Statistics

Raffle Ticket Probability

A community center is holding a raffle to raise funds. A total of 300 tickets have been sold. Jamal purchased 12 tickets. There is 1 grand prize winner and 4 second-prize winners. All tickets are placed in a drum and one ticket is drawn at random for each prize. Winning tickets are not returned to the drum.

13. What is the probability that Jamal wins the grand prize?

A. 12/300 = 1/25

B. 1/300

C. 12/288

D. 4/300

Answer:

14. What is the probability that Jamal does not win the grand prize?

A. 12/300

B. 288/300 = 24/25

C. 1/300

D. 299/300

Answer:

15. If Jamal does not win the grand prize, what is the probability he wins a second prize on the next draw?

A. 12/299

B. 12/300

C. 4/299

D. 48/299

Answer:

16. Which statement is best supported by the information?

A. Jamal has a greater than 50% chance of winning at least one prize.

B. Jamal’s probability of winning the grand prize is the same as any other ticket holder’s probability per ticket.

C. Jamal is guaranteed to win at least one prize since he purchased multiple tickets.

D. Buying more tickets decreases a person’s chance of winning.

Answer:

QUESTIONS 17–24 Core Skills • Algebra, Geometry, Number Sense & Functions

17. Solve for x: 4x − 9 = 19

A. x = 7

B. x = 4.75

C. x = 2.5

D. x = 28

Answer:

18. Which of the following expressions is equivalent to 3(x + 4) − 2x?

A. x + 12

B. 5x + 12

C. x + 4

D. x + 6

Answer:

19. A rectangle has a length of 15 inches and a width of 8 inches. What is its area in square inches?

A. 120

B. 46

C. 23

D. 240

Answer:

20. What is the slope of the line that passes through the points (2, 5) and (6, 13)?

A. 1

B. 2

C. 4

D. 8

Answer:

21. A shirt originally priced at $48 is on sale for 25% off. What is the sale price?

A. $36

B. $12

C. $60

D. $42

Answer:

22. Which value of x satisfies the inequality −3x + 7 > 16?

A. x < −3

B. x > −3

C. x < 3

D. x > 3

Answer:

23. A cylinder has a radius of 3 inches and a height of 10 inches. Using 3.14 for π, what is the approximate volume?

A. 94.2 cubic inches

B. 188.4 cubic inches

C. 282.6 cubic inches

D. 31.4 cubic inches

Answer:

24. A function is defined as f(x) = 2x² − 5. What is the value of f(4)?

A. 27

B. 32

C. 11

D. 37

Answer:

CONSTRUCTED RESPONSE

Linear Functions & Break-Even Analysis

Directions:

A small business makes and sells custom tote bags. The monthly fixed costs (rent, equipment, etc.) are $850. Each tote bag costs $6 in materials and labor to produce. The bags are sold for $22 each.

Part A: Write an equation for the total monthly cost C when x tote bags are produced.

Part B: Write an equation for the total monthly revenue R when x tote bags are sold.

Part C: How many tote bags must be sold in a month to break even (where revenue equals total cost)? Show all work.

Part D: If the business sells 120 tote bags in a month, what is the profit? Explain what the break-even point means for this business in 1–2 sentences.

Show all calculations and write your explanations below. Use additional paper if needed.

📝 Reflection

Take a few minutes to reflect on your performance. This helps you identify areas to review.

1. Which content area (Arithmetic, Algebra, Geometry, or Data/Probability) felt strongest for you on this test?

________________________________________________________________________________

2. Which type of question or skill was most challenging (e.g., multi-step word problems, interpreting graphs, geometry formulas, solving equations)?

________________________________________________________________________________

3. What is one specific topic or skill you plan to review before your next practice session?

________________________________________________________________________________

FOR INSTRUCTORS ONLY — DO NOT DISTRIBUTE TO STUDENTS

Mentor Guide

Effective Grading

Begin feedback with what the student did well to build confidence.
Use simple, clear rubrics focused on 2–3 key skills, especially for the Constructed Response.
Give credit for correct setup and reasoning, even when arithmetic slips lead to the wrong final number.
Provide specific, actionable feedback (e.g., "check your sign when dividing by a negative" rather than just "wrong").
Allow flexible response formats (talking through steps aloud, using a calculator, or drawing diagrams) when writing is difficult.
Focus on the student's growth by comparing their work to their own previous attempts.

Teaching Concepts Students May Have Missed

Break multi-step word problems into smaller steps: identify what's given, what's asked, then choose an operation.
Use visual supports for geometry (draw the triangle, label the legs and hypotenuse) and for data questions (highlight the relevant table cells or graph points).
Model one problem fully, then guide the student through a similar one, then have them try independently.
Connect probability questions to familiar real-life examples (raffles, dice, decks of cards) before introducing the without-replacement wrinkle.
Revisit sign rules for inequalities (flipping the symbol when dividing by a negative) since this is a common point of confusion.
Review key formulas frequently (area, perimeter, volume, slope) and check for understanding before moving on.
Reduce anxiety by allowing breaks and normalizing that multi-step problems take longer to work through.

General Tips for Mentors

Be patient and encouraging — celebrate small successes, especially with multi-step problems.
Adapt materials when needed (larger print, graph paper, a four-function calculator) since calculators are permitted on the real GED Math test.
Build student confidence and self-advocacy around asking for clarification on word problems.
Make problems relevant to the student's goals and daily life (budgeting, shopping discounts, measuring spaces).
Remind students that the real GED Mathematical Reasoning test is 115 minutes long, and help them build pacing habits during practice.

ANSWER KEY & EXPLANATIONS

For Instructor / Self-Check Use Only • Student version should not include this page

1. A — Total coffee sales: 312 + 378 + 295 + 425 + 510 + 620 + 480 = $3,020.

2. B — Tuesday has the highest combined revenue per customer: (378+112) ÷ 69 ≈ $7.10, the highest of all seven days.

3. C — Food total $963; grand total revenue $3,983. 963 ÷ 3,983 ≈ 24.2%, which rounds to 24%.

4. D — Highest coffee sales $620 (Saturday), lowest $295 (Wednesday). Range = 620 − 295 = $325.

5. A — Week-to-week changes are +250, −70, +220, +150. The largest increase is +250, from Week 1 to Week 2.

6. B — Sum of revenues (1,200 + 1,450 + 1,380 + 1,600 + 1,750) = 7,380 ÷ 5 = $1,476.

7. C — Increase from Week 4 to Week 5 is +150 (1,600 → 1,750). Projecting the same increase gives 1,750 + 150 = $1,900.

8. B — Revenue rises overall from $1,200 to $1,750, with exactly one weekly decrease (Week 2 to Week 3).

9. A — Pythagorean theorem: 6² + 8² = 36 + 64 = 100. √100 = 10 ft.

10. C — Perimeter = 6 + 8 + 10 = 24 feet.

11. A — Area of right triangle = (6 × 8) ÷ 2 = 24 square feet.

12. D — Doubling the legs gives 12 ft and 16 ft, with hypotenuse 20 ft (a scaled 3-4-5 triangle). New perimeter = 12 + 16 + 20 = 48 ft.

13. A — Probability = Jamal's tickets ÷ total tickets = 12/300 = 1/25.

14. B — P(not winning grand prize) = 1 − 12/300 = 288/300 = 24/25.

15. A — After the grand-prize ticket is removed (not Jamal's), 299 tickets remain and Jamal still holds 12 of them: 12/299.

16. B — Every individual ticket has the same 1/300 chance of being drawn for the grand prize, regardless of who holds it.

17. A — 4x − 9 = 19 → 4x = 28 → x = 7.

18. A — Distribute: 3(x+4) − 2x = 3x + 12 − 2x = x + 12.

19. A — Area = length × width = 15 × 8 = 120 square inches.

20. B — Slope m = (13 − 5) ÷ (6 − 2) = 8 ÷ 4 = 2.

21. A — 25% of 48 = 12. Sale price = 48 − 12 = $36.

22. A — −3x + 7 > 16 → −3x > 9 → x < −3 (the inequality flips when dividing by a negative number).

23. C — Volume = πr²h ≈ 3.14 × 3² × 10 = 3.14 × 9 × 10 = 282.6 cubic inches.

24. A — f(4) = 2(4)² − 5 = 2(16) − 5 = 32 − 5 = 27.

Revision note: Every answer above was independently recalculated from the source table, chart, and passage values rather than carried over from a prior draft. Corrections from the original version: Q5 (the largest week-to-week increase is Week 1→2, not Week 4→5), Q24 (f(4) = 27 is option A, not D), and Q7 (the answer choices were adjusted so the correctly projected value, $1,900, is actually one of the options). Q14 and Q16 were reworded, since their original phrasing allowed more than one defensible correct answer.

This is a practice worksheet for skill building.