Grade 6 Expressions & Equations Practice

Question 1 of 27Score 0/0Medium

Question 1 of 27: Evaluate 2a² + 3 when a = 3.

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Answer key for parents & teachers (27 questions)
  1. Evaluate 2a² + 3 when a = 3. — 21. 2(3)² + 3 = 2(9) + 3 = 18 + 3 = 21.
  2. Evaluate m³ − 2m when m = 4. — 56. (4)³ − 2(4) = 64 − 8 = 56.
  3. Evaluate (x + y)² when x = 2 and y = 3. — 25. (2 + 3)² = (5)² = 25.
  4. Evaluate 3x² − 2x + 1 when x = 3. — 22. 3(3)² − 2(3) + 1 = 3(9) − 6 + 1 = 27 − 6 + 1 = 22.
  5. Which expression represents "seven more than twice a number n"? — 2n + 7. "Twice a number n" = 2n. "Seven more than" means add 7. Expression: 2n + 7.
  6. Evaluate |x − 10| when x = 3. — 7. |3 − 10| = |−7| = 7.
  7. Evaluate 4p² − p when p = 5. — 95. 4(5)² − 5 = 4(25) − 5 = 100 − 5 = 95.
  8. In 7x² − 3x + 9, what is the coefficient of x²? — 7. The coefficient is the numerical factor in front of a variable term. The coefficient of x² is 7.
  9. A store charges d dollars for delivery plus $5 per item. Write an expression for total cost of n items. — 5n + d. Cost per item × number of items + delivery fee = 5n + d.
  10. Solve: 2x + 3 = 11 — x = 4. 2x + 3 = 11 → 2x = 8 → x = 4.
  11. Solve: 4y − 5 = 19 — y = 6. 4y − 5 = 19 → 4y = 24 → y = 6.
  12. Solve: x/3 + 2 = 7 — x = 15. x/3 + 2 = 7 → x/3 = 5 → x = 15.
  13. Which graph on a number line represents x ≤ 3? — Closed circle at 3, shaded to the left. x ≤ 3 includes 3 (closed circle) and all values less than 3 (shaded left).
  14. Solve: 6 − 2x = 0 — x = 3. 6 − 2x = 0 → −2x = −6 → x = 3.
  15. A number divided by 4 is less than 6. Write this as an inequality and solve. — n/4 < 6, so n < 24. "A number divided by 4 is less than 6" → n/4 < 6. Multiply both sides by 4: n < 24.
  16. Solve: 3(x − 2) = 15 — x = 7. 3(x − 2) = 15 → x − 2 = 5 → x = 7.
  17. Which value of x makes 2x + 5 > 13 true? — x = 5. 2x + 5 > 13 → 2x > 8 → x > 4. Only x = 5 is greater than 4.
  18. Solve: 5x + 2 ≤ 22 — x ≤ 4. 5x + 2 ≤ 22 → 5x ≤ 20 → x ≤ 4.
  19. Which equation has x = 6 as its solution? — 2x − 3 = 9. Check: 2(6) − 3 = 12 − 3 = 9 ✓. So 2x − 3 = 9 has solution x = 6.
  20. For y = 3x, complete the table: x = 0, 1, 2, 3. The y values are: — 0, 3, 6, 9. y = 3×0=0, 3×1=3, 3×2=6, 3×3=9.
  21. If y = 6x and x = 8, what is y? — 48. y = 6 × 8 = 48.
  22. A car uses 0.05 gallons of gas per mile. Equation for gallons G used after m miles: — G = 0.05m. Gallons DEPEND on miles: G = 0.05 × m = 0.05m.
  23. For y = 2x, if y = 14, what is x? — 7. 2x = 14 → x = 14 ÷ 2 = 7.
  24. The graph of a proportional relationship always passes through: — The origin (0, 0). A proportional relationship y = kx always passes through the ORIGIN (0, 0). When x = 0, y = k×0 = 0.
  25. Sam earns $9.50 per hour. Total earnings E for h hours worked: — E = 9.50h. Earnings depend on hours: E = 9.50h. Hours worked (h) is independent.
  26. A recipe needs 2 cups of flour per batch. For b batches, flour needed F = ? — F = 2b. F = 2 × b = 2b. The amount of flour depends on how many batches.
  27. From a table: x = 1→y = 4, x = 2→y = 8, x = 3→y = 12. The rule is: — y = 4x. Each y is 4 times x: 4×1=4, 4×2=8, 4×3=12. Rule: y = 4x.