Keystones Cornerstone — Jul 30 - Aug 5 | Maths Vault

Change pack

Cornerstone Jul 30 - Aug 5 25 questions

Monday 27 July 2026

Keystones #42 · Five questions · Open this day only

1. Number

Simplify: x⁵ × x⁵

Answer: x¹⁰
2. Algebra

Expand: 3(x + 9)

Answer: 3x + 27
3. Geometry

Find the area of a circle with radius 6cm

Answer: 113.cm²
4. Ratio

Simplify the ratio 25:35

Answer: 5:7
5. Statistics

Find the mean of: 19, 10, 8

Answer: 12.333333333333

Tuesday 28 July 2026

Keystones #43 · Five questions · Open this day only

1. Number

Calculate: 26 + (38)

Answer: 64
2. Algebra

Factorise: 24x + 32

Answer: 4(6x + 8)
3. Geometry

Opposite = 6cm, hypotenuse = 8.5cm. Find the angle

Answer: 45° (approximately)
4. Ratio

Simplify the ratio 12:18

Answer: 2:3
5. Statistics

Find the range of: 26, 29, 23, 31, 15

Answer: 16

Wednesday 29 July 2026

Keystones #44 · Five questions · Open this day only

1. Number

Calculate: 29 + 52

Answer: 29 + 52 = 81
2. Algebra

Factorise: 4x² + 4x

Answer: 4x(x + 1)
3. Geometry

Calculate the hypotenuse when a = 5cm and b = 15cm

Answer: 15.81cm
4. Ratio

Calculate 10% of 160

Answer: 16
5. Statistics

Calculate the mean of: 42, 41, 24, 15, 30, 20, 44, 44

Answer: 32.5

Thursday 30 July 2026

Keystones #45 · Five questions · Open this day only

1. Number

Calculate: 51 + 23

Answer: 51 + 23 = 74
2. Algebra

Collect like terms: 5x + 8y + 6x + 3y

Answer: 11x + 11y
3. Geometry

Find the distance between (5, 5) and (11, 11)

Answer: 8.49
4. Ratio

Calculate 50% of 68

Answer: 34
5. Statistics

Calculate the mean of: 33, 17, 11, 49, 12, 39, 9, 35

Answer: 25.6

Friday 31 July 2026

Keystones #46 · Five questions · Open this day only

1. Number

Add: ⁵⁄₇ + ⁴⁄₆

Answer: ²⁹⁄₂₁
2. Algebra

Solve: x + 14 = 22

Answer: x = 8
3. Geometry

Opposite = 15cm, adjacent = 8cm. Calculate the angle

Answer: 61.9°
4. Ratio

Calculate 50% of 117

Answer: 58.5
5. Statistics

Find the mean of: 14, 14, 6, 19

Answer: 13.25