Daily Practice

Higher Plus

19th December 1969

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 (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
2
Conditional Probability3 marks
A bag holds 4 red, 7 blue and 3 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 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
4
Surds3 marks
Rationalise the denominator of 9/sqrt(3), giving your answer in its simplest form.
5
Proof3 marks
Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.

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