Daily Practice

Higher Plus

4th January 1983

5 questions · 14 marks · Grades 8-9 · 51 question types in this band

1
3d Pythagoras and Trigonometry3 marks
A cuboid measures 8 cm by 5 cm by 8 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 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
3
Histograms2 marks
On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
4
Surds3 marks
Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
5
Inverse and Composite Functions3 marks
f(x) = 4x + 4. Work out the inverse function f^-1(x).

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