Daily Practice

Higher Plus

22nd December 1981

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 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
3
Histograms3 marks
A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
4
Surds3 marks
Expand and simplify (5 + sqrt(7))(5 - sqrt(7)).
5
Proof3 marks
Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.

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