Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

6th March 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 OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
2
Probability Equation Questions3 marks
A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/22. 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
Surds3 marks
Simplify sqrt(72) + sqrt(2), giving your answer in the form a sqrt(b).
5
Inverse and Composite Functions3 marks
f(x) = 5x - 9. Work out the inverse function f^-1(x).

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