Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

22nd October 2025

5 questions · 13 marks · Grades 8-9 · 51 question types in this band

1
Histograms2 marks
On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
2
Bounds3 marks
A rectangle is 18 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
3
Completing the Square3 marks
Write x^2 - 4x - 7 in the form (x + a)^2 + b.
4
Velocity Time Graphs3 marks
A tram runs at 12 m/s for 10 s, then slows steadily to rest over 4 s. Work out its average speed for the whole journey, to 2 decimal places.
5
Proof of the Circle Theorems2 marks
In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.

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