Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
- 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, 6 blue and 3 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 5 units wide with density 0.8. How many values in total?
- 4Surds3 marks
Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 5Algebraic Fractions3 marks
Simplify (x^2 + 2x - 3)/(x + 3).
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