Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

12th August 2025

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

1
Surds3 marks
Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
2
Quadratic Simultaneous Equations3 marks
Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
3
Direct and Inverse Proportion Depth3 marks
y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 16.
4
The Cosine Rule3 marks
A triangle has sides of 16 cm and 8 cm with an angle of 77° between them. Work out the third side, to 1 decimal place.
5
Conditional Probability3 marks
A bag holds 7 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

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