Daily Practice

Higher Plus

14th May 1985

5 questions · 15 marks · Grades 8-9 · 51 question types in this band

1
Surds3 marks
Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
2
Factorising Harder Quadratics3 marks
Solve 16x^2 - 8x - 15 = 0.
3
Direct and Inverse Proportion Depth3 marks
y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
4
The Cosine Rule3 marks
A triangle has sides of 8 cm and 15 cm with an angle of 33° between them. Work out the third side, to 1 decimal place.
5
Conditional Probability3 marks
A bag holds 6 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

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