Daily Practice - Higher Plus
14th September 1993
- 1Perpendicular Lines and the equation of a tangent3 marks
The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 2Conditional Probability3 marks
A bag holds 3 red, 3 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 20 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 4Surds3 marks
Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).
- 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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