Daily Practice · Higher Plus

Daily Practice - Higher Plus

Grades 8-9 - exam-stretch algebra, geometry and reasoning.

4th August 1998

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

1
Surds3 marks
Expand and simplify (7 + sqrt(3))(7 - sqrt(3)).
2
Proof3 marks
Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
3
Direct and Inverse Proportion Depth3 marks
y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
4
The Cosine Rule3 marks
A triangle has sides of 16 cm and 12 cm with an angle of 93° between them. Work out the third side, to 1 decimal place.
5
Conditional Probability3 marks
A bag holds 6 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

You are looking at an earlier sheet. Today's sheet is the one that adds a day.

Your run is kept in this browser only, and there is no account.

Every sheet is deterministic: the same date always regenerates the same five questions. All of August 1998, including the monthly compilation PDF.