Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
30th January 2002
- 1Perpendicular Lines and the equation of a tangent3 marks
The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 2Conditional Probability3 marks
A bag holds 3 red, 4 blue and 5 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 20 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 4Bounds3 marks
A rectangle is 30 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 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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