Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

1st August 2025

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

1
Iteration3 marks
Use the iteration x(n+1) = cube root of (9x(n) + 2) with x(0) = 2. Work out x(1) to 3 decimal places.
2
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 6, y = 324. Work out the positive value of x when y = 324.
3
3d Pythagoras and Trigonometry3 marks
A cuboid measures 4 cm by 10 cm by 5 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 11 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 5 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?

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