Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

31st July 2025

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

1
Surds3 marks
Simplify sqrt(27) + sqrt(108), giving your answer in the form a sqrt(b).
2
Factorising Harder Quadratics3 marks
Solve 15x^2 + 13x + 2 = 0.
3
Direct and Inverse Proportion Depth3 marks
y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
4
The Cosine Rule3 marks
A triangle has sides 4 cm, 15 cm and 16 cm. Work out the angle opposite the 4 cm side, to 1 decimal place.
5
Probability Equation Questions3 marks
A bag holds 8 red and n blue counters. The probability of taking a red is 8/15. Work out n.

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