Daily Practice · Higher Plus
May 1968 5-a-day
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The batch download puts all 5 tiers' May 1968 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1968
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1968A rectangle is 16 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd May 1968Use the iteration x(n+1) = cube root of (4x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.
- 3rd May 1968y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 9.
- 4th May 1968In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 5th May 1968The probability of winning a game is 1/4. A player expects 14 wins. How many games did they play?
- 6th May 1968On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th May 1968Expand and simplify (5 + sqrt(7))(5 - sqrt(7)).
- 8th May 1968Work out the nth term of the quadratic sequence 14, 22, 32, 44, ...
- 9th May 1968A train slows steadily from 21 m/s to rest in 10 seconds. Work out its deceleration.
- 10th May 1968In a vector proof you find that vector PQ = 5a - 5b and vector RS = 10a - 10b. What does this show about PQ and RS?
- 11th May 1968A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 12th May 1968A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 13th May 1968A block has mass 680 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th May 1968The point (5, -1) lies on y = f(x). Write down its image on y = -f(x).
- 15th May 1968y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
- 16th May 1968A cuboid measures 6 cm by 7 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th May 1968A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th May 1968On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th May 1968x = 40 and y = 25, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th May 1968Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 21st May 1968y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 22nd May 1968A cuboid measures 10 cm by 9 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd May 1968A bag holds 3 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th May 1968A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 25th May 1968A car covers 890 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 26th May 1968f(x) = 3x - 6 and g(x) = 6x + 7. Work out fg(-2).
- 27th May 1968y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 64.
- 28th May 1968The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 29th May 1968A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 30th May 1968On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 31st May 1968Rationalise the denominator of 56/sqrt(7), giving your answer in its simplest form.