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Capstone Jun 8 - 14 25 questions
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Monday 8 June 2026

Keystones #159 · Five questions · Open this day only

  1. 1. Number

    Rationalise the denominator: 6/√12

    Answer: √3 (or 3√3⁄3)
  2. 2. Algebra

    Factorise: 8x² + 10x - 12

    Answer: (4x - 3)(2x + 4)
  3. 3. Geometry

    Adjacent = 19cm, angle = 53°. Find opposite

    Answer: 25.2cm
  4. 4. Ratio

    A price of £325.35 includes a 35% increase. What was the price before the increase?

    Answer: £241.00
  5. 5. Statistics

    The mean of 4 numbers is 21. If 3 of them are 28, 21, 30, what is the missing number?

    Answer: 5

Tuesday 9 June 2026

Keystones #160 · Five questions · Open this day only

  1. 1. Number

    Rationalise: 5/√5

    Answer: 5√5⁄5
  2. 2. Algebra

    Factorise: 8x² + 2x - 10

    Answer: (2x - 2)(4x + 5)
  3. 3. Geometry

    Adjacent = 29cm, angle = 45°. Find opposite

    Answer: 29cm
  4. 4. Ratio

    A price of £755.20 includes a 28% increase. What was the price before the increase?

    Answer: £590.00
  5. 5. Statistics

    The mean of 4 numbers is 36. If 3 of them are 15, 20, 18, what is the missing number?

    Answer: 91

Wednesday 10 June 2026

Keystones #161 · Five questions · Open this day only

  1. 1. Number

    Rationalise: 3/√3

    Answer: 3√3⁄3
  2. 2. Algebra

    Factorise: 8x² + 4x - 4

    Answer: (4x - 2)(2x + 2)
  3. 3. Geometry

    Adjacent = 19cm, angle = 52°. Find opposite

    Answer: 24.3cm
  4. 4. Ratio

    A price of £748.03 includes a 27% increase. What was the price before the increase?

    Answer: £589.00
  5. 5. Statistics

    The mean of 6 numbers is 23. If 5 of them are 34, 27, 29, 26, 31, what is the missing number?

    Answer: -9

Thursday 11 June 2026

Keystones #162 · Five questions · Open this day only

  1. 1. Number

    Rationalise the denominator: 1/√2

    Answer: √2⁄2
  2. 2. Algebra

    Factorise: 12x² -10x - 8

    Answer: (3x - 4)(4x + 2)
  3. 3. Geometry

    Adjacent = 20cm, angle = 43°. Find opposite

    Answer: 18.7cm
  4. 4. Ratio

    A price of £811.35 includes a 35% increase. What was the price before the increase?

    Answer: £601.00
  5. 5. Statistics

    The mean of 5 numbers is 22. If 4 of them are 15, 16, 20, 22, what is the missing number?

    Answer: 37

Friday 12 June 2026

Keystones #163 · Five questions · Open this day only

  1. 1. Number

    Rationalise: 6/√3

    Answer: 6√3⁄3
  2. 2. Algebra

    Factorise: 12x² -3x - 9

    Answer: (3x - 3)(4x + 3)
  3. 3. Geometry

    Adjacent = 17cm, angle = 45°. Find opposite

    Answer: 17cm
  4. 4. Ratio

    A price of £462.50 includes a 25% increase. What was the price before the increase?

    Answer: £370.00
  5. 5. Statistics

    The mean of 4 numbers is 28. If 3 of them are 25, 35, 26, what is the missing number?

    Answer: 26