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Ecolint Campus des NationsMathematics
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Pack A — Fluency

Ecolint Campus des NationsMathematics
Year 10 · Algebra

Pack A · Fluency

Name: _________________________________
Date: _________________ Class: ___________

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

BronzeQuestions 1–10
  1. 1.
    Simplify 5x+3x−2x5x + 3x - 2x.
     
  2. 2.
    Simplify 5a+3b+2a−b5a + 3b + 2a - b.
     
  3. 3.
    Expand 3(x+4)3(x + 4).
     
  4. 4.
    Expand −2(x−5)-2(x - 5).
     
  5. 5.
    Factorise 6x+96x + 9.
     
  6. 6.
    Factorise 4x2+6x4x^2 + 6x.
     
  7. 7.
    Simplify (4x)2(4x)^2.
     
  8. 8.
    Simplify val\sqrt{{val}}.
     
  9. 9.
    Find the value of 3x+2y3x + 2y when x=4x = 4 and y=5y = 5.
     
  10. 10.
    Solve 3x+5=173x + 5 = 17.
     
SilverQuestions 11–20
  1. 11.
    Expand (x+3)(x+5)(x + 3)(x + 5).
     
  2. 12.
    Expand (x−4)(x+3)(x - 4)(x + 3).
     
  3. 13.
    Expand (x+5)2(x + 5)^2.
     
  4. 14.
    Expand (x+6)(x−6)(x + 6)(x - 6).
     
  5. 15.
    Factorise x2+7x+12x^2 + 7x + 12.
     
  6. 16.
    Factorise x2+3x−10x^2 + 3x - 10.
     
  7. 17.
    Simplify a×b\sqrt{{a}} \times \sqrt{{b}}.
     
  8. 18.
    Simplify a+b\sqrt{{a}} + \sqrt{{b}}.
     
  9. 19.
    Solve 3(x−4)=93(x - 4) = 9.
     
  10. 20.
    When a=3a = 3 and b=−2b = -2, find the value of a2−3ab+2ba^2 - 3ab + 2b.
     
GoldQuestions 21–30
  1. 21.
    Factorise x2−49x^2 - 49.
     
  2. 22.
    Factorise 2x2+7x+32x^2 + 7x + 3.
     
  3. 23.
    Simplify (3+b)(3−b)(3 + \sqrt{{b}})(3 - \sqrt{{b}}).
     
  4. 24.
    Rationalise the denominator of nm\dfrac{{n}}{\sqrt{{m}}}.
     
  5. 25.
    Solve the system: {y=2x+1y=−x+7\begin{cases} y = 2x + 1 \\ y = -x + 7 \end{cases}
     
  6. 26.
    Solve the system: {2x+3y=152x+1y=9\begin{cases} 2x + 3y = 15 \\ 2x + 1y = 9 \end{cases}
     
  7. 27.
    Factorise fully 2x2−182x^2 - 18.
     
  8. 28.
    Solve x+ab=5\dfrac{x + {a}}{{b}} = 5.
     
  9. 29.
    Expand and simplify (x+2)(x+5)−(x+3)2(x + 2)(x + 5) - (x + 3)^2.
     
  10. 30.
    The sum of two numbers is 3030 and their difference is 66. Find both numbers.
     
PlatinumQuestions 31–40
  1. 31.
    Solve the system: {3x+2y=122x−5y=−11\begin{cases} 3x + 2y = 12 \\ 2x - 5y = -11 \end{cases}
     
  2. 32.
    Factorise fully 6x2−5x−46x^2 - 5x - 4.
     
  3. 33.
    Rationalise the denominator of na+b\dfrac{{n}}{{a} + \sqrt{{b}}}.
     
  4. 34.
    If x+1x=3x + \dfrac{1}{x} = 3 (with x>0x > 0), find x2+1x2x^2 + \dfrac{1}{x^2}.
     
  5. 35.
    A cinema sells adult tickets at £1212 and child tickets at £88. One evening it sold 8080 tickets for £832832. How many adult and child tickets were sold?
     
  6. 36.
    Solve x2+7x+12=0x^2 + 7x + 12 = 0.
     
  7. 37.
    Simplify x2−sqx+a\dfrac{x^2 - {sq}}{x + {a}}.
     
  8. 38.
    Solve simultaneously: y=x2y = x^2 and y=3x+4y = 3x + 4.
     
  9. 39.
    Simplify (a+b)2(\sqrt{{a}} + \sqrt{{b}})^2.
     
  10. 40.
    Find xx such that x2=50x^2 = 50, giving exact answers in surd form.