Daily Practice

Higher Plus

11th March 1967

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 two tangents are drawn to a circle from the same external point. State the reason being quoted.
2
Probability Equation Questions3 marks
A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/45. Work out r.
3
Histograms3 marks
A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
4
Bounds3 marks
A car covers 100 m (to the nearest 10 m) in 3 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 + 9 and g(x) = 2x - 8. Work out fg(1).

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