Daily Practice

Higher Plus

8th January 1991

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

1
Inverse and Composite Functions3 marks
f(x) = 2x + 7 and g(x) = 3x + 4. Work out fg(-1).
2
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 5, y = 125. Work out the positive value of x when y = 320.
3
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.
4
Conditional Probability3 marks
A bag holds 4 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 20 units wide with frequency density 1.5, one 5 units wide with density 1.4. How many values in total?

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