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Ecolint Campus des NationsMathematics
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Pack B — Fluency

Ecolint Campus des NationsMathematics
Year 10 · Algebra

Pack B · Fluency

Name: _________________________________
Date: _________________ Class: ___________

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

BronzeQuestions 1–10
  1. 1.
    Simplify 7y+2y−4y7y + 2y - 4y.
     
  2. 2.
    Simplify 5a+3b+2a−b5a + 3b + 2a - b.
     
  3. 3.
    Expand 5(x+2)5(x + 2).
     
  4. 4.
    Expand −4(x−3)-4(x - 3).
     
  5. 5.
    Factorise 8x+128x + 12.
     
  6. 6.
    Factorise 9x2+12x9x^2 + 12x.
     
  7. 7.
    Simplify (7x)2(7x)^2.
     
  8. 8.
    Simplify val\sqrt{{val}}.
     
  9. 9.
    Find the value of 3x+2y3x + 2y when x=6x = 6 and y=3y = 3.
     
  10. 10.
    Solve 4x+2=184x + 2 = 18.
     
SilverQuestions 11–20
  1. 11.
    Expand (x+4)(x+7)(x + 4)(x + 7).
     
  2. 12.
    Expand (x−5)(x+2)(x - 5)(x + 2).
     
  3. 13.
    Expand (x+6)2(x + 6)^2.
     
  4. 14.
    Expand (x+8)(x−8)(x + 8)(x - 8).
     
  5. 15.
    Factorise x2+9x+20x^2 + 9x + 20.
     
  6. 16.
    Factorise x2+2x−15x^2 + 2x - 15.
     
  7. 17.
    Simplify a×b\sqrt{{a}} \times \sqrt{{b}}.
     
  8. 18.
    Simplify a+b\sqrt{{a}} + \sqrt{{b}}.
     
  9. 19.
    Solve 5(x−2)=255(x - 2) = 25.
     
  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 x2−100x^2 - 100.
     
  2. 22.
    Factorise 3x2+8x+43x^2 + 8x + 4.
     
  3. 23.
    Simplify (4+b)(4−b)(4 + \sqrt{{b}})(4 - \sqrt{{b}}).
     
  4. 24.
    Rationalise the denominator of nm\dfrac{{n}}{\sqrt{{m}}}.
     
  5. 25.
    Solve the system: {y=3x+2y=−x+14\begin{cases} y = 3x + 2 \\ y = -x + 14 \end{cases}
     
  6. 26.
    Solve the system: {3x+4y=263x+2y=16\begin{cases} 3x + 4y = 26 \\ 3x + 2y = 16 \end{cases}
     
  7. 27.
    Factorise fully 2x2−502x^2 - 50.
     
  8. 28.
    Solve x+ab=7\dfrac{x + {a}}{{b}} = 7.
     
  9. 29.
    Expand and simplify (x+1)(x+6)−(x+2)2(x + 1)(x + 6) - (x + 2)^2.
     
  10. 30.
    The sum of two numbers is 5050 and their difference is 1010. Find both numbers.
     
PlatinumQuestions 31–40
  1. 31.
    Solve the system: {2x+3y=125x−2y=11\begin{cases} 2x + 3y = 12 \\ 5x - 2y = 11 \end{cases}
     
  2. 32.
    Factorise fully 4x2−4x−34x^2 - 4x - 3.
     
  3. 33.
    Rationalise the denominator of na+b\dfrac{{n}}{{a} + \sqrt{{b}}}.
     
  4. 34.
    If x+1x=4x + \dfrac{1}{x} = 4 (with x>0x > 0), find x2+1x2x^2 + \dfrac{1}{x^2}.
     
  5. 35.
    A cinema sells adult tickets at £1515 and child tickets at £1010. One evening it sold 6060 tickets for £750750. How many adult and child tickets were sold?
     
  6. 36.
    Solve x2+8x+15=0x^2 + 8x + 15 = 0.
     
  7. 37.
    Simplify x2−sqx+a\dfrac{x^2 - {sq}}{x + {a}}.
     
  8. 38.
    Solve simultaneously: y=x2y = x^2 and y=5x+6y = 5x + 6.
     
  9. 39.
    Simplify (a+b)2(\sqrt{{a}} + \sqrt{{b}})^2.
     
  10. 40.
    Find xx such that x2=72x^2 = 72, giving exact answers in surd form.