Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
10th January 2023
- 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 4 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3Histograms2 marks
On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4Surds3 marks
Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
- 5Proof3 marks
Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
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