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Ecolint Campus des NationsMathématiques
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Pack B — Fluency

Ecolint Campus des NationsMathematics
Year 8 · 8.5 Directed Number and Algebra Basics

Pack B · Fluency

Name: _________________________________
Date: _________________ Class: ___________

Answer all questions. Show your working. Questions are grouped by challenge level.

BronzeQuestions 1–10
  1. 1.
    Calculate 6+(−9)6 + (-9).
     
  2. 2.
    Calculate −5−(−8)-5 - (-8).
     
  3. 3.
    Calculate −7×−3-7 \times -3.
     
  4. 4.
    Calculate −36÷−9-36 \div -9.
     
  5. 5.
    Simplify 7x+4y+3x−6y7x + 4y + 3x - 6y.
     
  6. 6.
    Simplify 8a+4b−6a8a + 4b - 6a and identify the coefficient of bb.
     
  7. 7.
    Write a×a×7×aa \times a \times 7 \times a using exponent notation.
     
  8. 8.
    Calculate 12+−4×212 + -4 \times 2 using the correct order of operations.
     
  9. 9.
    Write the algebraic product correctly: 3×a×a3 \times a \times a.
     
  10. 10.
    Expand 4(7+x)4(7 + x) using the distributive rule.
     
SilverQuestions 11–20
  1. 11.
    Calculate 8−−2×−38 - -2 \times -3.
     
  2. 12.
    Calculate a−−5c+−3\dfrac{{a} - -5}{{c} + -3}.
     
  3. 13.
    Calculate (a)2({a})^2 and −a2-{a}^2 for a=6a = 6.
     
  4. 14.
    Expand and simplify 3(x+5)+2(x−7)3(x + 5) + 2(x - 7).
     
  5. 15.
    Simplify −4(x−7)-4(x - 7).
     
  6. 16.
    Simplify 7p×5q7p \times 5q.
     
  7. 17.
    Simplify (5x)2(5x)^2.
     
  8. 18.
    Calculate (8)+(−3)×−4−(6)(8) + (-3) \times -4 - (6).
     
  9. 19.
    Expand −(7x−2y+4)-(7x - 2y + 4).
     
  10. 20.
    Order from smallest to largest: −8,3,−2,0,5,−7-8, 3, -2, 0, 5, -7.
     
GoldQuestions 21–30
  1. 21.
    Expand 5x(2x−7)5x(2x - 7).
     
  2. 22.
    Simplify 4x−[2(5−x)−3]4x - [2(5 - x) - 3].
     
  3. 23.
    Find the value of a2−3ba^2 - 3b when a=5a = 5 and b=−3b = -3.
     
  4. 24.
    Find xw2xw^2 when x=−3x = -3 and w=4w = 4.
     
  5. 25.
    Calculate the value of a2−62c\dfrac{{a}^2 - 6^2}{{c}}.
     
  6. 26.
    Substitute and simplify: 3(x+2y)−2(x−y)3(x + 2y) - 2(x - y) when x=5,y=−1x = 5, y = -1.
     
  7. 27.
    Simplify 7(x+y)−2(x−y)7(x + y) - 2(x - y).
     
  8. 28.
    A square has side −2x+5-2x + 5. Write an expression for its perimeter and simplify.
     
  9. 29.
    Calculate (−5)3(-5)^3.
     
  10. 30.
    Simplify (5xy)(2x2y)(5xy)(2x^2 y).
     
PlatinumQuestions 31–40
  1. 31.
    Simplify −4(3x−2)−(7x+1)-4(3x - 2) - (7x + 1).
     
  2. 32.
    Find the value of −(p−q)2-(p - q)^2 when p=−3p = -3 and q=5q = 5.
     
  3. 33.
    The temperature in a town drops by 3°C each hour for 4 hours starting at −2°C-2°C. Find the temperature after 4 hours, showing each step.
     
  4. 34.
    Expand and simplify (5x−2)(x+3)(5x - 2)(x + 3) where this is the product of two single-variable expressions. (Apply the area model / FOIL.)
     
  5. 35.
    Substitute a=−3,b=2,c=−1a = -3, b = 2, c = -1 into a2b−bc+ac2a^2 b - bc + ac^2.
     
  6. 36.
    A bank account has balance −£320-£320. Three deposits of £100, £75 and £90 are made, then a withdrawal of £50. Find the final balance.
     
  7. 37.
    Investigate: is (−a)2=−a2(-a)^2 = -a^2? Find a case where they differ and a case where they agree (with a reason).
     
  8. 38.
    Simplify 4(x+2y)−3(4x−y)+2(3x+y)4(x + 2y) - 3(4x - y) + 2(3x + y).
     
  9. 39.
    A directed-number table game: each player rolls a die, and the result is multiplied by −1-1 if odd, +1+1 if even. After 5 rolls a player has scores 3, 4, 2, 5, 6. Find the player's total.
     
  10. 40.
    Simplify 8x2−2xy+1x2+5xy−6y28x^2 - 2xy + 1x^2 + 5xy - 6y^2.