Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
10th June 2017
- 1Perpendicular Lines and the equation of a tangent3 marks
The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 2Conditional Probability3 marks
A bag holds 5 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3Histograms2 marks
On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4Bounds3 marks
A car covers 540 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 5Proof3 marks
Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
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