Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

1st February 2026

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

1
Histograms3 marks
A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
2
Bounds3 marks
x = 177 and y = 31, each correct to the nearest whole number. Work out the upper bound of x - y.
3
Completing the Square3 marks
Write x^2 - 4x - 8 in the form (x + a)^2 + b.
4
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 5, y = 175. Work out the positive value of x when y = 567.
5
3d Pythagoras and Trigonometry3 marks
A cuboid measures 5 cm by 14 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.

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