Daily Practice

Higher Plus

21st June 1991

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

1
3d Pythagoras and Trigonometry3 marks
A cuboid measures 12 cm by 7 cm by 11 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 5 red and 8 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 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
4
Surds3 marks
Rationalise the denominator of 60/sqrt(5), giving your answer in its simplest form.
5
Proof3 marks
Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.

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