Daily Practice

Higher Plus

24th July 1987

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 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
3
Histograms3 marks
A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
4
Surds3 marks
Rationalise the denominator of 36/sqrt(6), giving your answer in its simplest form.
5
Proof3 marks
Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.

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