Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

10th March 2026

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

1
Surds3 marks
Expand and simplify (5 + sqrt(10))(5 - sqrt(10)).
2
Iteration3 marks
Use the iteration x(n+1) = cube root of (5x(n) + 8) with x(0) = 3. Work out x(1) to 3 decimal places.
3
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
4
The Cosine Rule3 marks
A triangle has sides of 14 cm and 13 cm with an angle of 115° between them. Work out the third side, to 1 decimal place.
5
Conditional Probability3 marks
A bag holds 7 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

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