7th Grade EOG Mathematics Test with Answer Key 2026-2027

 7th Grade Mathematics

End-of-Year Assessment

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Parent Preparation Guide & Complete Examination

 

 

Aligned To Texas TEKS Mathematics — Grade 7

Frameworks Used Bloom's Taxonomy Hess's Cognitive Rigor Matrix

 

FOR PARENTS: What Is This Document?   This guide contains a complete, rigorous 7th Grade mathematics examination aligned to the Texas Essential Knowledge and Skills (TEKS). It is designed to help parents understand what their child is expected to know by the end of 7th Grade and to prepare them for STAAR. Each question includes the specific TEKS standard, Bloom's Taxonomy level, Depth of Knowledge (DOK) level, a parent-friendly explanation of what the question measures, at-home support activities, and common mistakes to watch for.

 

 

 

PART 1: RATIONAL NUMBERS & OPERATIONS

 

Student Name: ___________________________    Date: _______________    Grade: 7

 

Directions: Read each question carefully. Show all your work. For multiple-choice questions, circle the letter of the best answer. For open-response questions, write your answer and explanation in the space provided.

 

Question 1   Bloom's: Apply  |  DOK: 2  |  TEKS: 7.3A

A diver descends 3/4 of a meter every second. How far has the diver descended after 8 seconds? Express your answer as a fraction and as a mixed number.

Answer: _______________________________________________

 

Question 2   Bloom's: Apply  |  DOK: 2  |  TEKS: 7.3B

A bank account has a balance of -$125.50. The owner deposits $200.75 and then withdraws $89.25. What is the final balance?

A)  -$14.00 B)  $14.00 C)  -$13.00 D)  $13.00

 

Question 3   Bloom's: Analyze  |  DOK: 3  |  TEKS: 7.3A

Explain why (-2/3) × (-5/4) gives a positive result. Give a real-world context that makes sense of multiplying two negative quantities.

Answer: _______________________________________________

 

 

PART 2: PROPORTIONALITY & PERCENT

 

Question 4   Bloom's: Apply  |  DOK: 2  |  TEKS: 7.4C

A store is having a 35% off sale. A jacket originally costs $84.99. What is the sale price? If sales tax is 8.25%, what is the final price the customer pays?

Answer: _______________________________________________

 

Question 5   Bloom's: Analyze  |  DOK: 3  |  TEKS: 7.4D

A TV's price increased from $320 to $368. By what percent did the price increase? Six months later it decreased back to $320. Was the percent decrease the same as the percent increase? Show your calculations and explain why or why not.

Answer: _______________________________________________

 

Question 6   Bloom's: Apply  |  DOK: 2  |  TEKS: 7.4A

A recipe for 6 people requires 2 1/4 cups of rice and 1 1/2 cups of broth. Recalculate the recipe for 10 people. Show your proportional reasoning.

Answer: _______________________________________________

 

 

PART 3: EXPRESSIONS, EQUATIONS & INEQUALITIES

 

Question 7   Bloom's: Apply  |  DOK: 2  |  TEKS: 7.10A

Solve the equation: 3(2x - 5) = 4x + 7. Check your solution.

A)  x = 11 B)  x = -11 C)  x = 2 D)  x = -2

 

Question 8   Bloom's: Analyze  |  DOK: 3  |  TEKS: 7.10C

A parking lot charges $3 to enter and $1.50 per hour. A competitor charges $0 entry and $2.25 per hour.  A) Write equations for the total cost at each lot (in terms of h = hours). B) For how many hours are the lots the SAME price? C) Which is cheaper for a 5-hour visit?

Answer: _______________________________________________

 

 

PART 4: GEOMETRY

 

Question 9   Bloom's: Apply  |  DOK: 2  |  TEKS: 7.9A

A circular swimming pool has a radius of 7 meters. Use π ≈ 3.14.  A) What is the circumference of the pool? B) What is the area of the water surface? C) A cover for the pool costs $12.50 per square meter. What does the cover cost?

Answer: _______________________________________________

 

Question 10   Bloom's: Analyze  |  DOK: 3  |  TEKS: 7.9D

A triangular prism has a triangular base with base 6 cm and height 4 cm. The prism is 10 cm long. Find: A) The volume of the prism. B) If a cube has the same volume, what must be the side length of the cube? (Round to the nearest tenth.)

Answer: _______________________________________________

 

 

PART 5: DATA & STATISTICS

 

Question 11   Bloom's: Apply  |  DOK: 2  |  TEKS: 7.12A

A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. One marble is drawn at random.  A) What is P(red)? B) What is P(not green)? C) Are red and green mutually exclusive? Explain.

Answer: _______________________________________________

 

Question 12   Bloom's: Evaluate  |  DOK: 3  |  TEKS: 7.12B

A game show claims: 'You have a 1 in 4 chance of winning because there are 4 doors and one prize.' Another player says: 'After I eliminated one wrong door, my chances improved to 1 in 3.'  Evaluate both claims. Which is correct and why? How does new information change probability?

Answer: _______________________________________________

 

 

PART 6: EXTENDED PROBLEM SOLVING

 

Question 13   Bloom's: Analyze  |  DOK: 3  |  TEKS: 7.4/7.10

A small business has monthly revenues and costs:    Revenue: $18 per item sold    Fixed costs: $240 per month    Variable cost: $9.50 per item  A) Write a profit equation P(n) for n items sold. B) How many items must be sold to make a profit? C) What is the profit on 80 items sold? D) The owner wants 20% profit margin on revenue. At 80 items, does she meet this goal?

Answer: _______________________________________________

 

Question 14   Bloom's: Create  |  DOK: 4  |  TEKS: All Domains

DESIGN CHALLENGE: You are planning a community fundraiser.  Using mathematics, create a complete plan that includes:    (1) A pricing model with at least 2 products/services    (2) Projected expenses and revenue (at least 3 expense categories)    (3) Break-even analysis: how many units must you sell?    (4) A savings/investment plan for the profits    (5) Probability of reaching your goal if 100 people attend and each has a 60% chance of purchasing  All calculations must be shown. Justify every decision.

Answer: _______________________________________________

 

 

COMPLETE ANSWER KEY

For Parent and Educator Use

 

 

Q#	Answer	Explanation	TEKS
1	6 meters (6/1) or 6 meters exactly. As fraction: 24/4 = 6.	(3/4) × 8 = 24/4 = 6 meters descended.	7.3A
2	B) $14.00	-125.50 + 200.75 = 75.25. 75.25 - 89.25 = -14.00. Wait: 75.25 - 89.25 = -14.00. CHECK: -14.00. Answer: -$14.00.	7.3B
3	Negative × negative = positive (multiplication sign rules). Example: losing $2/3 per day for -5 days backward in time = gaining money.	Two negatives multiplied: (-)(-)=(+). Rule: same signs → positive product. Contexts vary; valid examples earn full credit.	7.3A
4	Sale price: $55.24. Final with tax: $59.80.	Discount: 84.99 × 0.35 = $29.75. Sale price: $84.99 - $29.75 = $55.24. Tax: $55.24 × 0.0825 = $4.56. Final: $55.24 + $4.56 = $59.80.	7.4C
5	Increase: 15%. Decrease: 13.04%. They are NOT equal because the base (starting price) is different each time.	Increase: (368-320)/320 = 48/320 = 15%. Decrease: (368-320)/368 = 48/368 ≈ 13.04%. Different starting bases → different percents.	7.4D
6	Rice: 3 3/4 cups. Broth: 2 1/2 cups.	Scale factor = 10/6 = 5/3. Rice: 2 1/4 × 5/3 = 9/4 × 5/3 = 45/12 = 15/4 = 3 3/4. Broth: 3/2 × 5/3 = 15/6 = 5/2 = 2 1/2.	7.4A
7	A) x = 11	6x - 15 = 4x + 7 → 2x = 22 → x = 11. Check: 3(22-5) = 3(17)=51. 4(11)+7=51. ✓	7.10A
8	A) Lot 1: C = 3 + 1.5h. Lot 2: C = 2.25h. B) 3+1.5h=2.25h → h=4 hours. C) Lot 1: $10.50; Lot 2: $11.25 — Lot 1 is cheaper for 5 hours.	Set equal: 3+1.5h=2.25h → 3=0.75h → h=4. At 4 hrs, both cost $9. Beyond 4 hrs, Lot 1 is cheaper. At 5 hrs: Lot1=$10.50, Lot2=$11.25.	7.10C
9	A) C = 43.96 m. B) A = 153.86 m². C) $1,923.25.	C = 2πr = 2(3.14)(7) = 43.96m. A = πr² = 3.14×49 = 153.86 m². Cost: 153.86×$12.50 = $1,923.25.	7.9A
10	A) V = 120 cm³. B) Side ≈ 4.9 cm.	A) V = (1/2 × 6 × 4) × 10 = 12 × 10 = 120 cm³. B) s³ = 120 → s = ∛120 ≈ 4.93 ≈ 4.9 cm.	7.9D
11	A) P(red) = 4/12 = 1/3. B) P(not green) = 7/12. C) Yes — a marble can't be both red and green at the same time.	Total: 12 marbles. P(red)=4/12=1/3. P(not green)=7/12. Mutually exclusive = can't happen simultaneously — a marble is one color only.	7.12A
12	The second player is correct after one door is eliminated. Original: 1/4. After eliminating one wrong door: 1/3 (probability redistributes among 3 remaining doors).	Probability updates when new information is available. Original P(win)=1/4. When one losing door is removed, 3 remain — only one has prize. P(win now)=1/3. This is a simplified version of the Monty Hall problem.	7.12B
13	A) P=8.5n-240. B) n>28.24 → n=29 items. C) P=$440. D) Margin=440/1440=30.6%. Yes, exceeds 20%.	A) P=18n-(240+9.5n)=8.5n-240. B) 8.5n>240→n>28.24. C) 8.5(80)-240=680-240=$440. D) Revenue=18×80=$1,440. 440/1440=30.6%>20%. ✓	7.4/7.10
14	Answers vary widely. Full credit: valid pricing, complete expense/revenue model, correct break-even, investment plan, and correct probability calculation (P = binomial reasoning or 100 × 0.60 = 60 expected purchasers).	Expected purchasers: 100 × 0.60 = 60. Revenue = 60 × price. Compare to expenses for profit/loss analysis. Investment of profit at a stated rate for a stated time.	All Domains

 

 

PARENT GUIDE

Understanding Every Question: What It Measures & How to Help

 

 

Q1: Multiplying Fractions — Real-World Rate Problem TEKS 7.3A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students multiply a fraction by a whole number in a rate context — connecting fraction multiplication to physical quantities. This bridges into proportional reasoning and science applications. How to Help Your Child at Home: Time your child walking across a room. Calculate: 'If you take 2/3 of a step per second, how far in 12 seconds?' Use real measurements and rates to make fraction multiplication tangible. Watch For / Common Mistakes: Students may try to convert to decimals first (0.75 × 8 = 6) which works but misses the fraction skill. Encourage working in fraction form: 3/4 × 8/1 = 24/4 = 6.

 

Q2: Adding and Subtracting Rational Numbers — Banking Context TEKS 7.3B  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students apply integer and decimal operations to a banking context — a real-world scenario that makes negative numbers immediately meaningful and relevant. How to Help Your Child at Home: Open a mock bank account for your child. Track deposits and withdrawals in a ledger. When the balance goes negative, discuss what that means (overdraft). This is the most life-relevant application of negative numbers. Watch For / Common Mistakes: Multiple sequential operations create opportunities for sign errors. Encourage students to compute step by step, writing each intermediate balance, rather than trying to do it all at once.

 

Q3: Multiplying Negative Fractions — Justifying Sign Rules TEKS 7.3A  |  Bloom's: Analyze | DOK: 3

What This Question Measures: DOK 3 — students must not only apply the sign rule but explain WHY it works and construct a meaningful real-world model. This is conceptual understanding at its deepest level. How to Help Your Child at Home: Discuss: 'If losing $5 a week is negative, then UN-doing that loss for 3 weeks (going back in time) is positive.' The double negative creates a positive gain. Abstract math connected to real reasoning. Watch For / Common Mistakes: Students often apply the rule mechanically without understanding it. Push for the explanation: 'WHY do two negatives make a positive?' Accept any coherent real-world model.

 

Q4: Multi-Step Percent — Discount and Tax TEKS 7.4C  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students apply sequential percent operations in a shopping context — one of the most practically useful applications of 7th grade math and a direct STAAR expectation. How to Help Your Child at Home: Before any online or in-store purchase, estimate: 'What is 30% off? Then what is tax on that?' Make it a family game before checking out. The ability to estimate total cost is a core life skill. Watch For / Common Mistakes: Students may apply the discount to the original price correctly but then apply tax to the ORIGINAL price (not the discounted price). Tax is always calculated on the PRICE YOU PAY, not the original price.

 

Q5: Percent Increase and Decrease — The Asymmetry Problem TEKS 7.4D  |  Bloom's: Analyze | DOK: 3

What This Question Measures: Students discover that a percent increase and decrease of the same dollar amount are NOT the same percent — because the base changes. This is a sophisticated and counterintuitive insight with major real-world implications. How to Help Your Child at Home: This is the same math behind investment returns: losing 50% and then gaining 50% does NOT get you back to where you started. Explore this together: $100 → lose 50% = $50 → gain 50% = $75. Not $100! Watch For / Common Mistakes: Students may divide by the same number both times. The KEY insight: percent is always relative to the STARTING VALUE for that calculation. The starting value changes between increase and decrease.

 

Q6: Scaling Recipes — Proportional Reasoning with Mixed Numbers TEKS 7.4A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students scale a recipe using proportional reasoning — a skill that integrates fractions, ratios, and proportionality in a context that every person encounters throughout life. How to Help Your Child at Home: Cook or bake a recipe that serves 4 and scale it to serve 7 for a family gathering. Calculate every ingredient together. Discuss: what does it mean to scale proportionally vs. just guessing? Watch For / Common Mistakes: Students may multiply each ingredient by 10 instead of by the scale factor (10/6). The scale factor = new ÷ old (10/6 = 5/3). Multiplying by 10 would give way too much food!

 

Q7: Solving Multi-Step Equations with Distribution TEKS 7.10A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students apply the distributive property to expand brackets, then solve a two-step equation — a core algebraic skill directly tested on STAAR and essential for all future mathematics. How to Help Your Child at Home: Solve puzzles together: 'I'm thinking of a number. If I triple the result of doubling it minus 5, I get the same as 4 times the number plus 7. What's my number?' Writing equations from riddles makes algebra engaging. Watch For / Common Mistakes: Students often forget to distribute to BOTH terms: 3(2x-5) ≠ 6x-5. It equals 6x-15. Distributing incorrectly is the single most common error in 7th grade algebra.

 

Q8: Systems of Equations — Finding the Break-Even Point TEKS 7.10C  |  Bloom's: Analyze | DOK: 3

What This Question Measures: Students write two equations, set them equal to find the intersection (break-even point), and evaluate which is better for a specific case — sophisticated algebraic reasoning directly applicable to real consumer decisions. How to Help Your Child at Home: Compare two subscription services (streaming, gym memberships): one with a sign-up fee and low monthly rate vs. one with no fee but higher monthly rate. Calculate when they cost the same and which is better for your usage. Watch For / Common Mistakes: Students may correctly find the break-even point (4 hours) but then apply the WRONG conclusion for 5 hours. Always check: beyond the break-even point, which equation yields the lower value?

 

Q9: Circle Formulas — Circumference and Area with Real Costs TEKS 7.9A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students apply circle formulas (C = 2πr and A = πr²) in a multi-part problem that connects geometry to a real purchasing decision — integrating geometry with proportional reasoning. How to Help Your Child at Home: Measure circular objects (plates, pizzas, round tables). Calculate circumference and area. Research how much it would cost to put trim around or tile the surface. This makes circle geometry immediately applicable. Watch For / Common Mistakes: Students often use diameter when radius is needed (or vice versa). Reinforce: radius = half of diameter. For C = 2πr: use radius. For A = πr²: use radius. NEVER mix them up.

 

Q10: Volume of Prisms and Cube Roots TEKS 7.9D  |  Bloom's: Analyze | DOK: 3

What This Question Measures: Students find volume of a triangular prism AND work backward from volume to find a missing dimension — requiring cube root reasoning. This connects geometry with algebraic thinking. How to Help Your Child at Home: Build a triangular prism from cardboard. Fill it with sand or rice, then pour into a cubic container to compare volumes. Explore: 'If we reshape this volume into a cube, how big would the cube be?' Watch For / Common Mistakes: For Part A: students may use the slant side of the triangle instead of the perpendicular height (4 cm). For Part B: students may try to divide by 3 instead of taking the cube root. Connect: s³=120 is a new kind of equation.

 

Q11: Basic Probability — Calculating and Interpreting TEKS 7.12A  |  Bloom's: Apply | DOK: 2

What This Question Measures: Students calculate simple probabilities and reason about mutually exclusive events — foundational statistical literacy that applies to games, risk assessment, and decision-making throughout life. How to Help Your Child at Home: Play probability games with a bag of mixed candies or marbles. Draw one item, record the result, replace it. After 20 draws, compare actual results to predicted probabilities. Discuss: why don't results perfectly match predictions? Watch For / Common Mistakes: Students may add P(red) + P(green) when asked about P(not green). P(not green) = 1 - P(green) = 1 - 5/12 = 7/12. Reinforce: 'not green' means everything ELSE, which is 1 minus P(green).

 

Q12: Conditional Probability — How New Information Changes Odds TEKS 7.12B  |  Bloom's: Evaluate | DOK: 3

What This Question Measures: DOK 3 — students evaluate two probability claims and reason about how eliminating possibilities changes probability. This is introductory conditional probability, the most counterintuitive branch of statistics. How to Help Your Child at Home: Play the three-card version: lay 3 cards face down (one is the ace). After you pick one, reveal one non-ace. Should you switch? Experiment 20 times. Track wins. Discover: switching wins 2/3 of the time! Watch For / Common Mistakes: Most people (and students) intuitively think the odds are still 50/50 after one card is revealed. This is the heart of the problem. Use experimental results (not just logic) to convince skeptical students.

 

Q13: Profit, Break-Even, and Profit Margin — Business Algebra TEKS 7.4/7.10  |  Bloom's: Analyze | DOK: 3

What This Question Measures: Students integrate linear equations, proportional reasoning, and percent in a complete business analysis. This is the most economically relevant math in 7th grade — entrepreneurship, economics, and algebra in one problem. How to Help Your Child at Home: If your child has any interest in entrepreneurship, walk through this analysis with a real or hypothetical business. 'What would you sell? What would it cost? How much would you charge? When would you make money?' Watch For / Common Mistakes: Part D (profit margin) is the hardest: students may compute profit ÷ cost instead of profit ÷ revenue. Profit margin = profit ÷ REVENUE (what customers paid). This distinction matters enormously in real business.

 

Q14: Fundraiser Design — Integrated Mathematics Capstone TEKS All Domains  |  Bloom's: Create | DOK: 4

What This Question Measures: Bloom's CREATE at DOK 4. Students design a complete event using proportional reasoning, algebraic equations, probability, and financial planning — integrating all 7th grade domains in a real-world creative project. How to Help Your Child at Home: Actually plan a small fundraiser! A lemonade stand, a car wash, or a bake sale. Do all the math beforehand. Then run the event and compare predicted vs. actual results. This is the most powerful math education possible. Watch For / Common Mistakes: Students may produce a plan that is mathematically inconsistent (expenses > revenue at predicted sales but still shows profit). Check internal consistency: do all the numbers tell the same story?

 

 

Scoring Guide & Next Steps

 

 

Score	Performance Level	Recommended Action
27–30	Masters Grade Level	Excellent! Focus on enrichment and extension. Explore real-world applications and the next grade's preview topics.
22–26	Meets Grade Level	Strong! Review missed questions by domain. Use the Parent Guide tips for weak areas.
16–21	Approaches Grade Level	Spend 15 minutes daily on the domains where most questions were missed. Use hands-on activities from the guide.
0–15	Developing Foundational Skills	Schedule time with the teacher. Focus on the first two TEKS domains — they are the foundation for everything else.

 

 

 

This guide was developed using Texas TEKS Mathematics standards for Grade 7, Bloom's Revised Taxonomy, and Hess's Cognitive Rigor Matrix. All questions are original and written to mirror STAAR-aligned rigor. Designed to bridge classroom learning and home support.