Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
1st September 2007
- 1Perpendicular Lines and the equation of a tangent3 marks
The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 2Conditional Probability3 marks
A bag holds 3 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3Histograms3 marks
A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 4Bounds3 marks
A car covers 680 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 5Proof3 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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