Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

11th September 2025

5 questions · 14 marks · Grades 8-9 · 51 question types in this band

1
Surds3 marks
Simplify sqrt(45) + sqrt(20), giving your answer in the form a sqrt(b).
2
Inverse and Composite Functions3 marks
f(x) = 6x + 7 and g(x) = 5x + 1. Work out fg(-1).
3
Velocity Time Graphs2 marks
A train slows steadily from 36 m/s to rest in 4 seconds. Work out its deceleration.
4
The Cosine Rule3 marks
A triangle has sides of 10 cm and 17 cm with an angle of 44° between them. Work out the third side, to 1 decimal place.
5
Conditional Probability3 marks
A bag holds 6 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

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