Daily Practice

Higher Plus

14th March 1972

5 questions · 13 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 OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
2
Probability Equation Questions3 marks
A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
3
Histograms2 marks
On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
4
Surds3 marks
Expand and simplify (4 + sqrt(6))(4 - sqrt(6)).
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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