Daily Practice · Higher Plus

Daily Practice - Higher Plus

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

15th June 2004

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

1
Surds3 marks
Expand and simplify (5 + sqrt(10))(5 - sqrt(10)).
2
Proof3 marks
Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
3
Direct and Inverse Proportion Depth3 marks
y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 16.
4
Vectors Proof Questions3 marks
OACB is a parallelogram with vector OA = a and vector OB = b. M is the point dividing AB in the ratio 3 : 1. Write vector OM in terms of a and b.
5
Probability Equation Questions3 marks
The probability of winning a game is 7/10. A player expects 28 wins. How many games did they play?

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