Daily Practice · Higher Plus
June 1968 5-a-day
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The batch download puts all 5 tiers' June 1968 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1968
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1968The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 2nd June 1968A train slows steadily from 18 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd June 1968In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 4th June 1968The probability of winning a game is 1/4. A player expects 6 wins. How many games did they play?
- 5th June 1968A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 6th June 1968Simplify sqrt(80) + sqrt(125), giving your answer in the form a sqrt(b).
- 7th June 1968A quadratic sequence starts 10, 15, 22, 31. Work out the second difference, and the coefficient of n^2.
- 8th June 1968y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
- 9th June 1968In a vector proof you find that vector PQ = 5a - 2b and vector RS = 25a - 10b. What does this show about PQ and RS?
- 10th June 1968A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 11th June 1968On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th June 1968A rectangle is 14 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th June 1968Solve x^2 + 9x + 14 < 0.
- 14th June 1968y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 15th June 1968A cuboid measures 14 cm by 4 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th June 1968A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th June 1968A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 18th June 1968Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 19th June 1968Write x^2 - 10x - 7 in the form (x + a)^2 + b.
- 20th June 1968y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 16.
- 21st June 1968A cuboid measures 14 cm by 8 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd June 1968A bag holds 4 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd June 1968On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 24th June 1968A block has mass 850 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th June 1968Work out the coordinates of the turning point of y = x^2 - 6x + 14.
- 26th June 1968A train slows steadily from 27 m/s to rest in 4 seconds. Work out its deceleration.
- 27th June 1968The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 28th June 1968A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 29th June 1968A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 30th June 1968x = 31 and y = 6, each correct to the nearest whole number. Work out the upper bound of x - y.