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Mathematical Reasoning

Practice Worksheet • New York State Edition (Version 2)

24 MULTIPLE CHOICE + 1 CONSTRUCTED RESPONSE
Recommended time: 50 minutes
Student Copy • Write Answers by Hand
Arithmetic & Number Sense • 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.

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

STIMULUS 1 Data Table • Arithmetic & Data Analysis

Weekly Tool Rental Data — Riverside Hardware

DayTools RentedRental Revenue ($)
Monday18270
Tuesday24360
Wednesday15225
Thursday32480
Friday45675
Saturday58870
Sunday36540

Source: Practice data for GED preparation.

1. What was the total rental revenue for the entire week?
A. $3,360
B. $3,420
C. $3,510
D. $3,600
Answer:
2. On the day with the highest revenue, what was the revenue per tool rented?
A. $12.50
B. $18.75
C. $15.00
D. $20.00
Answer:
3. Approximately what percent of the week's total tool rentals occurred on Saturday and Sunday combined?
A. 29%
B. 35%
C. 47%
D. 41%
Answer:
4. What is the range of daily rental revenue for the week?
A. $540
B. $645
C. $600
D. $675
Answer:
5. Based on the table, which statement is best supported by the data?
A. The store charges a different rate per tool on each day of the week.
B. Revenue and number of tools rented are unrelated to each other.
C. The store charges a constant rate of $15 per tool rented, every day.
D. Tool rentals decreased every single day of the week.
Answer:
6. What was the average (mean) number of tools rented per day over the week?
A. 32.6
B. 30.0
C. 29.7
D. 28.3
Answer:
STIMULUS 2 Graph • Data Analysis & Algebra

Savings Account Balance (First 6 Months)

Source: Practice data for GED preparation.

7. Between which two consecutive months did the account balance increase the most?
A. Month 1 to Month 2
B. Month 2 to Month 3
C. Month 3 to Month 4
D. Month 5 to Month 6
Answer:
8. What was the average (mean) account balance over the six months?
A. $760
B. $800
C. $850
D. $820
Answer:
9. If the balance continued increasing at the same rate as it did from Month 5 to Month 6, what would the balance be at Month 7?
A. $1,100
B. $1,130
C. $1,150
D. $1,200
Answer:
10. Which statement best describes the overall trend in the account balance from Month 1 to Month 6?
A. The balance decreased overall, with some months showing gains.
B. The balance increased overall, though the size of the monthly increase varied.
C. The balance stayed exactly the same every month.
D. The balance doubled every month.
Answer:
STIMULUS 3 Geometry • Measurement & Pythagorean Theorem

Backyard Deck with a Triangular Flower Bed

A homeowner is building a rectangular deck measuring 20 feet by 14 feet. In one corner of the deck, a triangular flower bed will be cut out. The flower bed is a right triangle with legs measuring 9 feet and 12 feet.
11. What is the total area of the rectangular deck, before removing the flower bed?
A. 260 square feet
B. 280 square feet
C. 300 square feet
D. 320 square feet
Answer:
12. What is the perimeter of the rectangular deck?
A. 60 feet
B. 64 feet
C. 68 feet
D. 72 feet
Answer:
13. The triangular flower bed cut into one corner of the deck has legs measuring 9 feet and 12 feet. What is the length of the third side (the hypotenuse) of the flower bed?
A. 14 feet
B. 15 feet
C. 16 feet
D. 21 feet
Answer:
14. What is the area of the triangular flower bed?
A. 48 square feet
B. 60 square feet
C. 54 square feet
D. 108 square feet
Answer:
15. After the triangular flower bed is removed from the deck, how much decking area remains?
A. 226 square feet
B. 232 square feet
C. 220 square feet
D. 254 square feet
Answer:
16. If edging material is needed around the entire triangular flower bed, how many feet of edging are required?
A. 30 feet
B. 33 feet
C. 39 feet
D. 36 feet
Answer:
STIMULUS 4 Probability & Data Analysis

Marbles in a Bag

A bag contains 8 red marbles, 5 blue marbles, and 7 green marbles. A marble is drawn at random.
17. If one marble is drawn at random, what is the probability that it is red?
A. 8/20 = 2/5
B. 8/19
C. 5/20 = 1/4
D. 7/20
Answer:
18. Using the same bag, what is the probability that a marble drawn at random is either blue or green?
A. 5/20
B. 7/20
C. 12/20 = 3/5
D. 8/20 = 2/5
Answer:
19. A red marble is drawn and not replaced. What is the probability that the next marble drawn is also red?
A. 8/20
B. 8/19
C. 7/20
D. 7/19
Answer:
20. Which statement is best supported by the information about the bag of marbles?
A. Drawing a green marble is more likely than drawing a blue marble.
B. The bag contains an equal number of marbles of each color.
C. Drawing a red marble is less likely than drawing a blue marble.
D. There are more blue marbles than red and green marbles combined.
Answer:
QUESTIONS 21–24 Core Skills • Algebra, Geometry, Number Sense & Functions
21. Solve for x: 5x + 6 = 41
A. x = 6
B. x = 7
C. x = 8
D. x = 9.4
Answer:
22. Which expression is equivalent to 4(x − 3) + 2x?
A. 6x − 12
B. 6x − 3
C. 4x − 12
D. x − 12
Answer:
23. A rectangle has a perimeter of 38 feet and a length of 11 feet. What is its width?
A. 8 feet
B. 9.5 feet
C. 16 feet
D. 19 feet
Answer:
24. A function is defined as f(x) = 3x² + 2x − 1. What is the value of f(3)?
A. 26
B. 32
C. 29
D. 38
Answer:
CONSTRUCTED RESPONSE

Linear Functions & Break-Even Analysis

Directions:

A small print shop makes and sells custom T-shirts. The monthly fixed costs (rent, equipment, etc.) are $600. Each shirt costs $5 in materials and labor to produce. The shirts are sold for $17 each.

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

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

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

Part D: If the shop sells 90 shirts 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 before the real GED test.

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 taking the real GED Mathematical Reasoning test?

— End of Student-Facing Test —

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 formula for area vs. perimeter" 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 deck and flower bed, label every side) and for data questions (highlight 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 physical objects (an actual bag of colored items) before introducing the without-replacement wrinkle.
  • Revisit the Pythagorean theorem and common triples (3-4-5, 9-12-15) since these appear often on the GED.
  • Review key formulas frequently (area, perimeter, slope, percent change) 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, home projects, shopping discounts).
  • 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. B — Total revenue: 270 + 360 + 225 + 480 + 675 + 870 + 540 = $3,420.
2. C — Saturday has the highest revenue ($870) with 58 tools rented: 870 ÷ 58 = $15.00 per tool.
3. D — Weekend rentals: 58 + 36 = 94. Total weekly rentals: 18+24+15+32+45+58+36 = 228. 94 ÷ 228 ≈ 41.2%, which rounds to 41%.
4. B — Highest daily revenue is $870 (Saturday), lowest is $225 (Wednesday). Range = 870 − 225 = $645.
5. C — Dividing revenue by tools rented gives exactly $15.00 for every single day, confirming a constant per-tool rate.
6. A — Average tools rented: (18+24+15+32+45+58+36) ÷ 7 = 228 ÷ 7 ≈ 32.6.
7. C — Month-to-month changes are +150, +70, +180, +150, +50. The largest is +180, from Month 3 to Month 4.
8. D — Average balance: (500+650+720+900+1050+1100) ÷ 6 = 4,920 ÷ 6 = $820.
9. C — Month 5 to Month 6 increased by $50 (1,050 → 1,100). Projecting the same increase: 1,100 + 50 = $1,150.
10. B — The balance rises overall from $500 to $1,100, though the size of the increase varies month to month (e.g., +180 vs. +50).
11. B — Area of rectangle = length × width = 20 × 14 = 280 square feet.
12. C — Perimeter of rectangle = 2 × (20 + 14) = 2 × 34 = 68 feet.
13. B — Using the Pythagorean theorem: 9² + 12² = 81 + 144 = 225. √225 = 15 feet.
14. C — Area of right triangle = (9 × 12) ÷ 2 = 108 ÷ 2 = 54 square feet.
15. A — Remaining deck area = total deck area − triangle area = 280 − 54 = 226 square feet.
16. D — Edging needed = perimeter of the triangle = 9 + 12 + 15 = 36 feet.
17. A — Probability of red = number of red marbles ÷ total marbles = 8 ÷ 20 = 2/5.
18. C — Probability of blue or green = (5 + 7) ÷ 20 = 12/20 = 3/5.
19. D — After one red marble is removed, 7 red marbles remain out of 19 total marbles: 7/19.
20. A — Green marbles (7) outnumber blue marbles (5), so drawing green is more likely than drawing blue. The other statements are all false: the colors are not equal (8, 5, 7), red (8) is more likely than blue (5) (not less), and blue (5) does not outnumber red and green combined (15).
21. B — 5x + 6 = 41 → 5x = 35 → x = 7.
22. A — Distribute: 4(x − 3) + 2x = 4x − 12 + 2x = 6x − 12.
23. A — Perimeter = 2(length + width) → 38 = 2(11 + width) → 19 = 11 + width → width = 8 feet.
24. B — f(3) = 3(3)² + 2(3) − 1 = 3(9) + 6 − 1 = 27 + 6 − 1 = 32.
Constructed Response sample solution: Part A: C = 600 + 5x. Part B: R = 17x. Part C: Break-even when R = C → 17x = 600 + 5x → 12x = 600 → x = 50 shirts. Part D: At 90 shirts, revenue = 17(90) = $1,530; cost = 600 + 5(90) = $1,050; profit = $480. The break-even point (50 shirts) is where the shop neither makes nor loses money — selling fewer than 50 shirts results in a loss, and selling more than 50 results in a profit.
Each answer was calculated directly from the source table, chart, and scenario values. If anything looks off, recompute from the source data — that is the authority.
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