Daily Practice

Higher Plus

5th March 1967

5 questions · 14 marks · Grades 8-9 · 51 question types in this band

1
Perpendicular Lines and the equation of a tangent3 marks
The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
2
Conditional Probability3 marks
A bag holds 3 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
3
Histograms2 marks
On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
4
Bounds3 marks
x = 151 and y = 53, each correct to the nearest whole number. Work out the upper bound of x - y.
5
Proof3 marks
Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.

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