Daily Practice · Higher Plus

Daily Practice - Higher Plus

Grades 8-9 - exam-stretch algebra, geometry and reasoning.

19th October 1999

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) = 6/11. Work out r.
3
Histograms2 marks
On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
4
Surds3 marks
Expand and simplify (7 + sqrt(6))(7 - sqrt(6)).
5
Iteration3 marks
Use the iteration x(n+1) = cube root of (10x(n) + 7) with x(0) = 5. Work out x(1) to 3 decimal places.

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