Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

7th August 2026

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

1
Surds3 marks
Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
2
Completing the Square3 marks
Write x^2 - 16x - 15 in the form (x + a)^2 + b.
3
Direct and Inverse Proportion Depth3 marks
y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 9.
4
The Cosine Rule3 marks
A triangle has sides of 7 cm and 17 cm with an angle of 96° between them. Work out the third side, to 1 decimal place.
5
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?

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