Daily Practice

Higher Plus

5th August 1975

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

1
Surds3 marks
Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
2
Factorising Harder Quadratics3 marks
Solve 4x^2 - 11x - 3 = 0.
3
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
4
The Cosine Rule3 marks
A triangle has sides of 15 cm and 7 cm with an angle of 114° between them. Work out the third side, to 1 decimal place.
5
Conditional Probability3 marks
A bag holds 6 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

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