Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

9th February 2026

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

1
Inverse and Composite Functions3 marks
f(x) = 6x + 4. Work out the inverse function f^-1(x).
2
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 4, y = 96. Work out the positive value of x when y = 216.
3
Proof of the Circle Theorems2 marks
In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
4
Probability Equation Questions3 marks
A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
5
Histograms3 marks
A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?

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