Daily Practice

Higher Plus

16th December 1957

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

1
3d Pythagoras and Trigonometry3 marks
A cuboid measures 11 cm by 9 cm by 5 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 3 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 2.5, one 20 units wide with density 3.5. How many values in total?
4
Bounds3 marks
A block has mass 860 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
5
Proof3 marks
Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.

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