Daily Practice · Higher Plus
May 1967 5-a-day
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The batch download puts all 5 tiers' May 1967 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1967
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1967A block has mass 530 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd May 1967Solve x^2 + x - 6 < 0.
- 3rd May 1967y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 4th May 1967The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 5th May 1967A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 6th May 1967A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 7th May 1967x = 97 and y = 43, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th May 1967Write x^2 - 16x + 6 in the form (x + a)^2 + b.
- 9th May 1967y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 81.
- 10th May 1967In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 11th May 1967The probability of winning a game is 1/2. A player expects 22 wins. How many games did they play?
- 12th May 1967On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 13th May 1967A car covers 490 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 14th May 1967Work out the coordinates of the turning point of y = x^2 - 12x - 6.
- 15th May 1967A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
- 16th May 1967In a vector proof you find that vector PQ = 6a - 2b and vector RS = 12a - 4b. What does this show about PQ and RS?
- 17th May 1967A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 18th May 1967A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 19th May 1967Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 20th May 1967Simplify (x^2 - 7x + 12)/(x - 4).
- 21st May 1967y is inversely proportional to x^2. When x = 2, y = 64. Work out y when x = 4.
- 22nd May 1967A cuboid measures 3 cm by 12 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd May 1967A bag holds 6 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th May 1967On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 25th May 1967Simplify sqrt(27) + sqrt(48), giving your answer in the form a sqrt(b).
- 26th May 1967In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 27th May 1967y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 28th May 1967A cuboid measures 13 cm by 10 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th May 1967A bag holds 6 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th May 1967A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 31st May 1967A rectangle is 29 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.