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Free US Common Core Common Core US Math
Practice Paper

8 mixed-difficulty practice questions in the style of real US Common Core Common Core papers — answers, mark-scheme-style explanations, and the official exam structure all on one page.

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What the real US Common Core Common Core US Math paper looks like

Paper 1
Objective and short-answer questions covering the breadth of the specification.
Paper 2
Structured and extended-response questions testing depth of understanding.
Total exam time varies by board and tier — typically 2.5 to 3.5 hours.
Grading: See the official board specification for the current grading scale.

Mini practice paper: 8 questions

Mixed-difficulty questions from across the US Math syllabus. Tap "Show answer" after each to check yourself.

Q1 · Difficulty 1/3

If f(x) = 3x - 2, what is f(5)?

  1. 15
  2. 10
  3. 17
  4. 13
Show answer & explanation
✓ Answer: D — 13
f(5) = 3(5) - 2 = 15 - 2 = 13.
Q2 · Difficulty 1/3

Solve for x: 2(x + 3) = 14

  1. x = 5.5
  2. x = 3
  3. x = 4
  4. x = 7
Show answer & explanation
✓ Answer: C — x = 4
Distribute: 2x + 6 = 14. Subtract 6: 2x = 8. Divide by 2: x = 4.
Q3 · Difficulty 1/3

What is the mean of the data set: 4, 8, 6, 10, 2?

  1. 7
  2. 8
  3. 5
  4. 6
Show answer & explanation
✓ Answer: D — 6
Mean = sum ÷ count = (4 + 8 + 6 + 10 + 2) ÷ 5 = 30 ÷ 5 = 6.
Q4 · Difficulty 2/3

Simplify: √50

  1. 10√5
  2. 2√5
  3. 5√2
  4. 25
Show answer & explanation
✓ Answer: C — 5√2
√50 = √(25 × 2) = √25 × √2 = 5√2.
Q5 · Difficulty 2/3

A rectangle has a perimeter of 54 cm. Its length is 3 cm more than twice its width w. Which equation correctly models this situation?

  1. 2w + 3 = 54
  2. w(2w + 3) = 54
  3. 2(w + 2w + 3) = 54
  4. 2w + (2w + 3) = 54
Show answer & explanation
✓ Answer: C — 2(w + 2w + 3) = 54
Perimeter = 2(length + width). Length = 2w + 3, so the equation is 2(w + 2w + 3) = 54. Option C ignores the perimeter formula entirely. Option A uses multiplication (area formula), not addition. Option B adds only one length and one width instead of using the full perimeter formula.
Q6 · Difficulty 2/3

What is the quadratic formula?

  1. x = -b/2a
  2. x = (-b ± √(b² - 4ac)) / 2a
  3. x = b² - 4ac
  4. x = a + b + c
Show answer & explanation
✓ Answer: B — x = (-b ± √(b² - 4ac)) / 2a
The quadratic formula x = (-b ± √(b² - 4ac)) / 2a solves any equation of the form ax² + bx + c = 0.
Q7 · Difficulty 1/3

A student earns $12 per hour working at a store. Which expression represents the total amount earned after h hours?

  1. 12 + h
  2. 12 − h
  3. h ÷ 12
  4. 12h
Show answer & explanation
✓ Answer: D — 12h
Multiplying the rate ($12 per hour) by the number of hours h gives the total earnings, so the correct expression is 12h. Option A adds instead of multiplies, confusing rate with a sum. Option C divides, reversing the relationship. Option D subtracts hours from the rate, which has no real-world meaning here.
Q8 · Difficulty 2/3

Two triangles are similar. If one has sides 3, 4, 5 and the other has a shortest side of 6, what is its longest side?

  1. 8
  2. 10
  3. 12
  4. 15
Show answer & explanation
✓ Answer: B — 10
Scale factor = 6/3 = 2. Longest side = 5 × 2 = 10.
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US Common Core Common Core US Math FAQ

What does the US Common Core Common Core US Math exam look like?
The US Common Core Common Core US Math exam is structured across 2 components. Paper 1: Objective and short-answer questions covering the breadth of the specification. Paper 2: Structured and extended-response questions testing depth of understanding. Total exam time varies by board and tier — typically 2.5 to 3.5 hours.
Can I download a free US Common Core Common Core US Math past paper?
Real US Common Core past papers are published directly by US Common Core on their official website. Kramizo doesn't redistribute copyrighted past papers, but we do generate free AI-written practice papers in the exact same style — same command words, same difficulty tier, same mark conventions. Use this practice paper as warm-up, then time yourself on official past papers before exam day.
How is US Common Core Common Core US Math graded?
See the official board specification for the current grading scale. Kramizo's practice questions are tagged with difficulty 1-3 mapping roughly to the lower, middle, and top grade boundaries you'll encounter in the real exam.