Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

27th August 2026

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

1
Direct and Inverse Proportion Depth3 marks
y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
2
The Cosine Rule3 marks
A triangle has sides of 8 cm and 10 cm with an angle of 136° between them. Work out the third side, to 1 decimal place.
3
Conditional Probability3 marks
A bag holds 7 red, 3 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 10-wide classes from 0, with frequency densities 1, 0.5, 3, 2. Which class contains the median?
5
Surds3 marks
Simplify sqrt(27) + sqrt(3), giving your answer in the form a sqrt(b).

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