Daily Practice

Higher Plus

23rd July 1985

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

1
Conditional Probability3 marks
A bag holds 6 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
2
Histograms3 marks
On a histogram the bar for 40 < x <= 45 has a frequency density of 0.4. How many values are in that class?
3
Surds3 marks
Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
4
Proof3 marks
Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
5
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.

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