Daily Practice

Higher Plus

17th November 1977

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

1
Proof3 marks
Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
2
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 3, y = 81. Work out the positive value of x when y = 324.
3
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.
4
Conditional Probability3 marks
A bag holds 3 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
5
Histograms3 marks
A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?

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