Daily Practice

Higher Plus

1st March 1986

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 opposite angles of a cyclic quadrilateral are being proved. 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) = 28/45. Work out r.
3
Histograms2 marks
On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
4
Bounds3 marks
A car covers 260 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
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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