Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

4th November 2025

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

1
Surds3 marks
Expand and simplify (5 + sqrt(2))(5 - sqrt(2)).
2
Algebraic Fractions3 marks
Write 5/(x + 5) + 4/(x + 6) as a single fraction.
3
Direct and Inverse Proportion Depth3 marks
y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
4
The Sine Rule3 marks
In triangle ABC, angle A is 35°, side a is 19 cm and side b is 17 cm. Work out the acute angle B, to 1 decimal place.
5
Conditional Probability3 marks
A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?

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