Daily Practice

Higher Plus

15th November 1988

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 a triangle is drawn from the ends of a diameter to a point on the circle. 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 1.2, one 25 units wide with density 0.6. How many values in total?
4
Surds3 marks
Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
5
Inverse and Composite Functions3 marks
f(x) = 7x + 12. Work out the inverse function f^-1(x).

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