Daily Practice

Higher Plus

31st August 1970

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

1
Bounds3 marks
A block has mass 570 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
2
Proof3 marks
Prove that the sum of 6 consecutive integers is always a multiple of 3. 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 = 162. Work out y when x = 2.
4
The Cosine Rule3 marks
A triangle has sides of 5 cm and 8 cm with an angle of 143° between them. Work out the third side, to 1 decimal place.
5
Conditional Probability3 marks
A bag holds 3 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

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