Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

8th January 2026

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

1
Histograms3 marks
A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
2
Surds3 marks
Simplify sqrt(48) + sqrt(27), giving your answer in the form a sqrt(b).
3
Inverse and Composite Functions3 marks
f(x) = 3x - 7 and g(x) = 5x - 2. Work out fg(5).
4
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 2, y = 24. Work out the positive value of x when y = 96.
5
3d Pythagoras and Trigonometry3 marks
A cuboid measures 5 cm by 10 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.

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