Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

29th November 2025

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

1
Proof3 marks
Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
2
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 3, y = 81. Work out the positive value of x when y = 81.
3
3d Pythagoras and Trigonometry3 marks
A cuboid measures 9 cm by 6 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
4
Conditional Probability3 marks
A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
5
Histograms3 marks
A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?

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