Daily Practice

Higher Plus

10th August 1954

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 (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
2
Conditional Probability3 marks
A bag holds 4 red, 5 blue and 4 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 20 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
4
Surds3 marks
Expand and simplify (9 + sqrt(7))(9 - sqrt(7)).
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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