Daily Practice · Higher Plus

Daily Practice - Higher Plus

Grades 8-9 - exam-stretch algebra, geometry and reasoning.

8th July 2026

5 questions · 15 marks · Grades 8-9 · 51 question types in this band

1
Bounds3 marks
A rectangle is 16 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
2
Proof3 marks
Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
3
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
4
The Cosine Rule3 marks
A triangle has sides of 6 cm and 11 cm with an angle of 39° between them. Work out the third side, to 1 decimal place.
5
Conditional Probability3 marks
A bag holds 6 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

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