Free Grade 3 Algebraic Proof Quizzes
Free Grade 3 quizzes for Algebraic Proof: 12 real questions with a full answer key and worked solutions. An expression uses letters for numbers. Substitute a value to evaluate it, collect like terms to simplify it, and multiply every term in a bracket to expand it.
Free
Core
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify algebraic proof
Identify algebraic proof accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain algebraic proof
Explain algebraic proof accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate algebraic proof
Calculate algebraic proof accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare algebraic proof
Compare algebraic proof accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Algebraic Proof works
An expression uses letters for numbers. Substitute a value to evaluate it, collect like terms to simplify it, and multiply every term in a bracket to expand it.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Find the value of 3x + 9 when x = 6.[1]
- 2.Find the value of 9x + 7 when x = 6.[1]
- 3.Find the value of 3x + 19 when x = 5.[1]
- 4.Find the value of 3x + 17 when x = 8.[1]
- 5.Simplify 8x + 6y + 5x − 7y.[2]
- 6.Simplify 6x + 7y + 7x − 8y.[2]
- 7.Simplify 7x + 4y + 3x − 7y.[2]
- 8.Simplify 9x + 6y + 2x − 5y.[2]
- 9.Expand 3(4x + 4).[3]
- 10.Expand 2(3x + 6).[3]
- 11.Expand 3(2x + 9).[3]
- 12.Expand 4(2x + 8).[3]
Show answers and working
1. 27
Replace x with 6: 3 × 6 + 9. 18 + 9 = 27.
2. 61
Replace x with 6: 9 × 6 + 7. 54 + 7 = 61.
3. 34
Replace x with 5: 3 × 5 + 19. 15 + 19 = 34.
4. 41
Replace x with 8: 3 × 8 + 17. 24 + 17 = 41.
5. 13x − 1y
Collect x terms: 8x + 5x = 13x. Collect y terms: 6y − 7y = -1y.
6. 13x − 1y
Collect x terms: 6x + 7x = 13x. Collect y terms: 7y − 8y = -1y.
7. 10x − 3y
Collect x terms: 7x + 3x = 10x. Collect y terms: 4y − 7y = -3y.
8. 11x + 1y
Collect x terms: 9x + 2x = 11x. Collect y terms: 6y − 5y = 1y.
9. 12x + 12
Multiply each term inside by 3. 3 × 4x = 12x, 3 × 4 = 12.
10. 6x + 12
Multiply each term inside by 2. 2 × 3x = 6x, 2 × 6 = 12.
11. 6x + 27
Multiply each term inside by 3. 3 × 2x = 6x, 3 × 9 = 27.
12. 8x + 32
Multiply each term inside by 4. 4 × 2x = 8x, 4 × 8 = 32.
Worked examples
Find the value of 4x + 1 when x = 7.
- Replace x with 7: 4 × 7 + 1.
- 28 + 1 = 29.
- Answer: 29
Simplify 3x + 9y + 4x − 2y.
- Collect x terms: 3x + 4x = 7x.
- Collect y terms: 9y − 2y = 7y.
- Answer: 7x + 7y
Expand 4(3x + 2).
- Multiply each term inside by 4.
- 4 × 3x = 12x, 4 × 2 = 8.
- Answer: 12x + 8
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Reads 3x as 3 + x, or as 3 with x stuck on.
Correction: 3x means 3 × x.
Only multiplies the first term when expanding.
Correction: Draw arrows from the outside to every inside term.
Teacher tips
- · Use algebra tiles to show collecting like terms.
Parent tips
- · Ask what 'number of pizzas × price' is for different orders.
Real-life applications
- · Formulas for cost: total = 5n + 2 for n items plus delivery.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Algebraic Proof
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Algebraic Proof quiz really free?
- Yes. Every quizzes on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Counterexamples, Matrices. Each one has its own free lesson, worksheet and quiz.
- How is the quiz sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Algebraic Proof?
- Move on to Proof by Exhaustion, Problem Solving, which build directly on this idea.
Related resources
Stuck on Algebraic Proof? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor