Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

15th August 2025

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

1
3d Pythagoras and Trigonometry3 marks
A cuboid measures 7 cm by 13 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
2
Probability Equation Questions3 marks
A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
3
Histograms2 marks
On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
4
Surds3 marks
Rationalise the denominator of 49/sqrt(7), giving your answer in its simplest form.
5
Completing the Square3 marks
Write x^2 - 6x - 2 in the form (x + a)^2 + b.

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