Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

19th March 2026

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

1
3d Pythagoras and Trigonometry3 marks
A cuboid measures 11 cm by 8 cm by 4 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 5 red and 5 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 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
4
Surds3 marks
Simplify sqrt(27) + sqrt(12), giving your answer in the form a sqrt(b).
5
Algebraic Fractions3 marks
Simplify (x^2 + 15x + 56)/(x + 7).

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