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Pack B — Fluency

Ecolint Campus des NationsMathematics
Year 8 · 8.7 Algebra Expressions

Pack B · Fluency

Name: _________________________________
Date: _________________ Class: ___________

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

BronzeQuestions 1–10
  1. 1.
    Find the value of 3x+43x + 4 when x=−2x = -2.
     
  2. 2.
    Simplify 5x×65x \times 6.
     
  3. 3.
    Expand 6(x+5)6(x + 5).
     
  4. 4.
    Expand x(5x−4)x(5x - 4).
     
  5. 5.
    Factorise 12x+1812x + 18.
     
  6. 6.
    Factorise 10x2+25x10x^2 + 25x.
     
  7. 7.
    Simplify axb\dfrac{{a}x}{{b}}.
     
  8. 8.
    Identify which is equivalent to 5(x+7)5(x + 7): (5x+7)(5x + 7) or (5x+35)(5x + 35)?
     
  9. 9.
    Substitute a=4,b=−2a = 4, b = -2 into ab+5ab + 5.
     
  10. 10.
    Simplify 5p+2q+8p5p + 2q + 8p.
     
SilverQuestions 11–20
  1. 11.
    Substitute x=−3,y=4,z=7x = -3, y = 4, z = 7 into 2x+3y−z2x + 3y - z.
     
  2. 12.
    Expand and simplify 3(x+5)+2(x−7)3(x + 5) + 2(x - 7).
     
  3. 13.
    Factorise 15x2−9xy15x^2 - 9xy.
     
  4. 14.
    Simplify ax2bx\dfrac{{a}x^2}{{b}x}.
     
  5. 15.
    Simplify ax+15c\dfrac{{a}x + 15}{{c}} by factorising.
     
  6. 16.
    Expand and simplify −5(x−2)−3(x+1)-5(x - 2) - 3(x + 1).
     
  7. 17.
    Simplify 6ab9a\dfrac{6ab}{9a} by cancelling common factors.
     
  8. 18.
    Show that 4(x+y)+2(x−y)4(x + y) + 2(x - y) is equivalent to (c)x+(d)y(c)x + (d)y. Find cc and dd for a=4,b=2a = 4, b = 2.
     
  9. 19.
    Factorise x2+9xx^2 + 9x.
     
  10. 20.
    Pete has three times as many songs on his phone as Sabrina. Sabrina has 75 fewer songs than Elena. Elena has xx songs. Write expressions for (a) Sabrina, (b) Pete.
     
GoldQuestions 21–30
  1. 21.
    Expand −4(x−2)−(7x+1)-4(x - 2) - (7x + 1).
     
  2. 22.
    Factorise fully 27x2+18x27x^2 + 18x.
     
  3. 23.
    Simplify ax2+8xcx\dfrac{{a}x^2 + 8x}{{c}x}.
     
  4. 24.
    Show that the expressions (x+3)2−9(x + 3)^2 - 9 and x2+6xx^2 + 6x are equivalent by expanding the first.
     
  5. 25.
    Factorise a2b+ab2a^2 b + a b^2.
     
  6. 26.
    Substitute x=−3,y=2x = -3, y = 2 into 2x2−3xy+y22x^2 - 3xy + y^2.
     
  7. 27.
    Factorise 4(x+3)+y(x+3)4(x + 3) + y(x + 3).
     
  8. 28.
    Simplify ax+bx\dfrac{{a}}{x} + \dfrac{{b}}{x}.
     
  9. 29.
    Simplify x3+x4\dfrac{x}{3} + \dfrac{x}{4}.
     
  10. 30.
    A rectangle has length (2x+3)(2x + 3) and width (x−1)(x - 1). Find a simplified expression for the perimeter, and evaluate when x=4x = 4.
     
PlatinumQuestions 31–40
  1. 31.
    Expand and simplify 4x(x+2)−3(5x−7)4x(x + 2) - 3(5x - 7).
     
  2. 32.
    Factorise 3x2+12x+93x^2 + 12x + 9 by first taking out a common factor.
     
  3. 33.
    Simplify ax2−15xcx2+9x\dfrac{{a}x^2 - 15x}{{c}x^2 + 9x}.
     
  4. 34.
    In a rectangle, the two long sides are labelled 3y3y cm and (y+3)(y + 3) cm; the two short sides are labelled zz cm and (4z−6)(4z - 6) cm. (a) Find yy. (b) Find zz.
     
  5. 35.
    Two similar triangles have a side ratio of x+215=xd\dfrac{x+2}{15} = \dfrac{x}{{d}}. Find xx.
     
  6. 36.
    A student won 300 of his first 500 games and then won the next xx games. He has now won 80% of all games. Find xx.
     
  7. 37.
    Factorise a2−b2a^2 - b^2 (difference of squares).
     
  8. 38.
    A field has dimensions (x+5)(x + 5) m by (x+2)(x + 2) m. Write an expression for its area, expand, and find the area when x=8x = 8.
     
  9. 39.
    Find the value of xx for which the area of a square of side xx is equal to the perimeter 4x4x.
     
  10. 40.
    Simplify x+32−x−13\dfrac{x + 3}{2} - \dfrac{x - 1}{3}.