Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

17th October 2024

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

1
Proof3 marks
Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
2
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 6, y = 324. Work out the positive value of x when y = 144.
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 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
5
Histograms3 marks
A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?

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