Change pack
Capstone Jul 27 - Aug 2 25 questions
PDF (questions) PDF (answers)

Monday 27 July 2026

Keystones #208 · Five questions · Open this day only

  1. 1. Number

    Rationalise the denominator: 6/√12

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

    Factorise: 16x² -12x - 10

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

    Adjacent = 14cm, angle = 57°. Find opposite

    Answer: 21.6cm
  4. 4. Ratio

    A price of £258.30 includes a 26% increase. What was the price before the increase?

    Answer: £205.00
  5. 5. Statistics

    The mean of 6 numbers is 39. If 5 of them are 16, 22, 40, 36, 49, what is the missing number?

    Answer: 71

Tuesday 28 July 2026

Keystones #209 · Five questions · Open this day only

  1. 1. Number

    Rationalise: 5/√2

    Answer: 5√2⁄2
  2. 2. Algebra

    Factorise: 16x² + 0x - 25

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

    Adjacent = 29cm, angle = 55°. Find opposite

    Answer: 41.4cm
  4. 4. Ratio

    A price of £332.74 includes a 27% increase. What was the price before the increase?

    Answer: £262.00
  5. 5. Statistics

    The mean of 6 numbers is 31. If 5 of them are 43, 31, 49, 33, 16, what is the missing number?

    Answer: 14

Wednesday 29 July 2026

Keystones #210 · Five questions · Open this day only

  1. 1. Number

    Rationalise: 4/√3

    Answer: 4√3⁄3
  2. 2. Algebra

    Factorise: 6x² + 0x - 6

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

    Adjacent = 23cm, angle = 52°. Find opposite

    Answer: 29.4cm
  4. 4. Ratio

    A price of £866.25 includes a 25% increase. What was the price before the increase?

    Answer: £693.00
  5. 5. Statistics

    The mean of 5 numbers is 21. If 4 of them are 29, 32, 35, 34, what is the missing number?

    Answer: -25

Thursday 30 July 2026

Keystones #211 · Five questions · Open this day only

  1. 1. Number

    Rationalise: 3/√3

    Answer: 3√3⁄3
  2. 2. Algebra

    Factorise: 4x² + 2x - 12

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

    Adjacent = 13cm, angle = 30°. Find opposite

    Answer: 7.5cm
  4. 4. Ratio

    A price of £460.20 includes a 18% increase. What was the price before the increase?

    Answer: £390.00
  5. 5. Statistics

    The mean of 6 numbers is 26. If 5 of them are 33, 16, 43, 27, 36, what is the missing number?

    Answer: 1

Friday 31 July 2026

Keystones #212 · Five questions · Open this day only

  1. 1. Number

    Rationalise: 2/√2

    Answer: 2√2⁄2
  2. 2. Algebra

    Factorise: 12x² + 3x - 9

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

    Adjacent = 18cm, angle = 45°. Find opposite

    Answer: 18cm
  4. 4. Ratio

    A price of £1,057.05 includes a 35% increase. What was the price before the increase?

    Answer: £783.00
  5. 5. Statistics

    The mean of 6 numbers is 31. If 5 of them are 48, 39, 37, 38, 45, what is the missing number?

    Answer: -21