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Capstone Jan 12 - 18 25 questions
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Monday 12 January 2026

Keystones #12 · Five questions · Open this day only

  1. 1. Number

    Rationalise: 4/√3

    Answer: 4√3⁄3
  2. 2. Algebra

    Factorise: 9x² -3x - 20

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

    Adjacent = 17cm, angle = 58°. Find opposite

    Answer: 27.2cm
  4. 4. Ratio

    A price of £270.60 includes a 23% increase. What was the price before the increase?

    Answer: £220.00
  5. 5. Statistics

    The mean of 5 numbers is 35. If 4 of them are 36, 43, 43, 38, what is the missing number?

    Answer: 15

Tuesday 13 January 2026

Keystones #13 · Five questions · Open this day only

  1. 1. Number

    Rationalise: 6/√2

    Answer: 6√2⁄2
  2. 2. Algebra

    Factorise: 4x² + 0x - 16

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

    Adjacent = 15cm, angle = 50°. Find opposite

    Answer: 17.9cm
  4. 4. Ratio

    A price of £584.96 includes a 28% increase. What was the price before the increase?

    Answer: £457.00
  5. 5. Statistics

    The mean of 6 numbers is 33. If 5 of them are 15, 35, 40, 17, 44, what is the missing number?

    Answer: 47

Wednesday 14 January 2026

Keystones #14 · Five questions · Open this day only

  1. 1. Number

    Rationalise: 6/√5

    Answer: 6√5⁄5
  2. 2. Algebra

    Factorise: 6x² + 9x - 15

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

    Adjacent = 25cm, angle = 31°. Find opposite

    Answer: 15cm
  4. 4. Ratio

    A price of £382.52 includes a 31% increase. What was the price before the increase?

    Answer: £292.00
  5. 5. Statistics

    The mean of 5 numbers is 26. If 4 of them are 20, 17, 44, 36, what is the missing number?

    Answer: 13

Thursday 15 January 2026

Keystones #15 · Five questions · Open this day only

  1. 1. Number

    Rationalise: 5/√5

    Answer: 5√5⁄5
  2. 2. Algebra

    Factorise: 8x² -10x - 25

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

    Adjacent = 30cm, angle = 39°. Find opposite

    Answer: 24.3cm
  4. 4. Ratio

    A price of £844.80 includes a 20% increase. What was the price before the increase?

    Answer: £704.00
  5. 5. Statistics

    The mean of 6 numbers is 32. If 5 of them are 47, 36, 32, 17, 44, what is the missing number?

    Answer: 16

Friday 16 January 2026

Keystones #16 · 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 -4x - 6

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

    Adjacent = 22cm, angle = 40°. Find opposite

    Answer: 18.5cm
  4. 4. Ratio

    A price of £603.88 includes a 24% increase. What was the price before the increase?

    Answer: £487.00
  5. 5. Statistics

    The mean of 5 numbers is 22. If 4 of them are 43, 18, 36, 37, what is the missing number?

    Answer: -24