Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

22nd July 2025

5 questions · 14 marks · Grades 8-9 · 51 question types in this band

1
3d Pythagoras and Trigonometry3 marks
A cuboid measures 13 cm by 14 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
2
Conditional Probability3 marks
A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
3
Histograms2 marks
On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
4
Surds3 marks
Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
5
Inverse and Composite Functions3 marks
f(x) = 6x - 7 and g(x) = 4x + 3. Work out fg(3).

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