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Pack A — Fluency

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

Pack A · Fluency

Name: _________________________________
Date: _________________ Class: ___________

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

BronzeQuestions 1–10
  1. 1.
    Calculate −7+(−5)-7 + (-5).
     
  2. 2.
    Calculate 4−(−3)4 - (-3).
     
  3. 3.
    Calculate −6×4-6 \times 4.
     
  4. 4.
    Calculate −20÷4-20 \div 4.
     
  5. 5.
    Simplify 3x+5y+2x−1y3x + 5y + 2x - 1y.
     
  6. 6.
    Simplify 5a+3b−7a5a + 3b - 7a and identify the coefficient of bb.
     
  7. 7.
    Write a×a×5×aa \times a \times 5 \times a using exponent notation.
     
  8. 8.
    Calculate −5+3×4-5 + 3 \times 4 using the correct order of operations.
     
  9. 9.
    Write the algebraic product correctly: 3×a×a3 \times a \times a.
     
  10. 10.
    Expand 5(3+x)5(3 + x) using the distributive rule.
     
SilverQuestions 11–20
  1. 11.
    Calculate −3−−4×5-3 - -4 \times 5.
     
  2. 12.
    Calculate a−4c+7\dfrac{{a} - 4}{{c} + 7}.
     
  3. 13.
    Calculate (a)2({a})^2 and −a2-{a}^2 for a=5a = 5.
     
  4. 14.
    Expand and simplify 4(x+3)+5(x−2)4(x + 3) + 5(x - 2).
     
  5. 15.
    Simplify −3(x−5)-3(x - 5).
     
  6. 16.
    Simplify 4p×3q4p \times 3q.
     
  7. 17.
    Simplify (3x)2(3x)^2.
     
  8. 18.
    Calculate (−3)+(−4)×2−(−5)(-3) + (-4) \times 2 - (-5).
     
  9. 19.
    Expand −(3x−5y+2)-(3x - 5y + 2).
     
  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 2x(3x−4)2x(3x - 4).
     
  2. 22.
    Simplify 5x−[3(2−x)−4]5x - [3(2 - x) - 4].
     
  3. 23.
    Find the value of a2−3ba^2 - 3b when a=−4a = -4 and b=−2b = -2.
     
  4. 24.
    Find xw2xw^2 when x=5x = 5 and w=−2w = -2.
     
  5. 25.
    Calculate the value of a2−32c\dfrac{{a}^2 - 3^2}{{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 5(x+y)−3(x−y)5(x + y) - 3(x - y).
     
  8. 28.
    A square has side −2x+5-2x + 5. Write an expression for its perimeter and simplify.
     
  9. 29.
    Calculate (−4)3(-4)^3.
     
  10. 30.
    Simplify (3xy)(4x2y)(3xy)(4x^2 y).
     
PlatinumQuestions 31–40
  1. 31.
    Simplify −3(2x−4)−(5x+6)-3(2x - 4) - (5x + 6).
     
  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 (2x−3)(x+4)(2x - 3)(x + 4) 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 −£250-£250. Three deposits of £80, £60 and £120 are made, then a withdrawal of £40. 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 3(x+2y)−2(3x−y)+5(2x+y)3(x + 2y) - 2(3x - y) + 5(2x + 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 5x2−3xy+2x2+7xy−4y25x^2 - 3xy + 2x^2 + 7xy - 4y^2.