Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

30th December 2025

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 = 2, y = 75. Work out y when x = 5.
2
The Cosine Rule3 marks
A triangle has sides of 11 cm and 13 cm with an angle of 79° between them. Work out the third side, to 1 decimal place.
3
Conditional Probability3 marks
A bag holds 6 red, 5 blue and 4 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 0.5, 1, 2, 3. Which class contains the median?
5
Surds3 marks
Expand and simplify (8 + sqrt(10))(8 - sqrt(10)).

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