Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

29th September 2026

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

1
Histograms3 marks
A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
2
Surds3 marks
Expand and simplify (3 + sqrt(2))(3 - sqrt(2)).
3
Factorising Harder Quadratics3 marks
Solve 5x^2 - 9x + 4 = 0.
4
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 5, y = 225. Work out the positive value of x when y = 81.
5
3d Pythagoras and Trigonometry3 marks
A cuboid measures 13 cm by 15 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.

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