Daily Practice - Higher Plus
Grades 8-9 - exam-stretch algebra, geometry and reasoning.
18th June 2007
- 1Bounds3 marks
A block has mass 820 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2Quadratic Simultaneous Equations3 marks
Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 3Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 4The Cosine Rule3 marks
A triangle has sides of 10 cm and 18 cm with an angle of 58° between them. Work out the third side, to 1 decimal place.
- 5Conditional Probability3 marks
A bag holds 7 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
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