Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
8th August 2016
- 13d Pythagoras and Trigonometry3 marks
A cuboid measures 6 cm by 5 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2Conditional Probability3 marks
A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3Histograms3 marks
A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 4Bounds3 marks
A block has mass 900 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5Proof3 marks
Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
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