Daily Practice

Higher Plus

9th November 1987

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

1
3d Pythagoras and Trigonometry3 marks
A cuboid measures 5 cm by 5 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
2
Conditional Probability3 marks
A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
3
Histograms3 marks
A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
4
Bounds3 marks
A block has mass 680 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
5
Inverse and Composite Functions3 marks
f(x) = 3x - 8 and g(x) = 5x - 9. Work out fg(-1).

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