Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

28th June 2026

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

1
Direct and Inverse Proportion Depth3 marks
y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 16.
2
The Cosine Rule3 marks
A triangle has sides of 13 cm and 9 cm with an angle of 38° between them. Work out the third side, to 1 decimal place.
3
Conditional Probability3 marks
A bag holds 5 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
4
Histograms3 marks
A histogram has four 20-wide classes from 0, with frequency densities 1, 3, 2, 0.5. Which class contains the median?
5
Bounds3 marks
x = 114 and y = 68, each correct to the nearest whole number. Work out the upper bound of x - y.

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