Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

28th February 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 = 4, y = 16. Work out y when x = 9.
2
The Cosine Rule3 marks
A triangle has sides of 12 cm and 12 cm with an angle of 62° between them. Work out the third side, to 1 decimal place.
3
Conditional Probability3 marks
A bag holds 4 red, 4 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 2, 0.5, 1, 3. Which class contains the median?
5
Bounds3 marks
A car covers 790 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.

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