Daily Practice

Higher Plus

28th September 1979

5 questions · 15 marks · Grades 8-9 · 51 question types in this band

1
Perpendicular Lines and the equation of a tangent3 marks
The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
2
Conditional Probability3 marks
A bag holds 7 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
3
Histograms3 marks
A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
4
Surds3 marks
Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
5
Proof3 marks
Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.

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