Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

27th July 2026

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

1
Completing the Square3 marks
Work out the coordinates of the turning point of y = x^2 + 10x - 1.
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 = 576.
3
3d Pythagoras and Trigonometry3 marks
A cuboid measures 13 cm by 12 cm by 14 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 8 red and 3 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 20 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?

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