Daily Practice · Higher Plus
June 1977 5-a-day
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The batch download puts all 5 tiers' June 1977 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1977
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1977A rectangle is 24 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd June 1977Work out the coordinates of the turning point of y = x^2 - 2x + 13.
- 3rd June 1977A train slows steadily from 31 m/s to rest in 4 seconds. Work out its deceleration.
- 4th June 1977A cuboid measures 10 cm by 8 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th June 1977A bag holds 4 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th June 1977A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 7th June 1977Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 8th June 1977Simplify (x^2 - 5x - 24)/(x + 3).
- 9th June 1977y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
- 10th June 1977The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 11th June 1977A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 12th June 1977On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 13th June 1977A block has mass 380 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th June 1977In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 15th June 1977y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 16th June 1977In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 17th June 1977The probability of winning a game is 3/4. A player expects 54 wins. How many games did they play?
- 18th June 1977A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 19th June 1977x = 79 and y = 52, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th June 1977Make x the subject of 6x + 6 = y(x + 6).
- 21st June 1977y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 4.
- 22nd June 1977In a vector proof you find that vector PQ = 3a + 6b and vector RS = 9a + 18b. What does this show about PQ and RS?
- 23rd June 1977A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 24th June 1977On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th June 1977A car covers 220 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 26th June 1977Write 7/(x + 5) + 4/(x - 5) as a single fraction.
- 27th June 1977A train slows steadily from 18 m/s to rest in 4 seconds. Work out its deceleration.
- 28th June 1977A cuboid measures 11 cm by 15 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th June 1977A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th June 1977A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?