Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

16th December 1999

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

1
Inverse and Composite Functions3 marks
f(x) = 4x - 7 and g(x) = 2x - 5. Work out fg(-1).
2
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^2. When x = 4, y = 144. Work out the positive value of x when y = 225.
3
3d Pythagoras and Trigonometry3 marks
A cuboid measures 13 cm by 10 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
4
Conditional Probability3 marks
A bag holds 9 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
5
Histograms3 marks
A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?

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