Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
24th June 2003
- 1Perpendicular Lines and the equation of a tangent3 marks
The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 2Conditional Probability3 marks
A bag holds 6 red, 5 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 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 4Surds3 marks
Expand and simplify (3 + sqrt(6))(3 - sqrt(6)).
- 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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