Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

1st November 2025

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

1
Proof of the Circle Theorems2 marks
In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
2
Probability Equation Questions3 marks
A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
3
Histograms3 marks
A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
4
Bounds3 marks
A car covers 750 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
5
Inverse and Composite Functions3 marks
f(x) = 6x - 8 and g(x) = 6x - 6. Work out fg(6).

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