Daily Practice · Higher Plus

Daily Practice - Higher Plus

Grades 8-9 - exam-stretch algebra, geometry and reasoning.

11th October 2007

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

1
Inverse and Composite Functions3 marks
f(x) = 5x + 6 and g(x) = 2x - 1. Work out fg(1).
2
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 6, y = 252. Work out the positive value of x when y = 448.
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, 3 blue and 2 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 10 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?

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