Daily Practice · Higher Plus
June 1974 5-a-day
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The batch download puts all 5 tiers' June 1974 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1974
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1974y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 2nd June 1974In 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.
- 3rd June 1974The probability of winning a game is 2/5. A player expects 52 wins. How many games did they play?
- 4th June 1974On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 5th June 1974A rectangle is 18 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th June 1974Solve 15x^2 - 13x - 6 = 0.
- 7th June 1974y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 8th June 1974In a vector proof you find that vector PQ = 5a - 6b and vector RS = 25a - 30b. What does this show about PQ and RS?
- 9th June 1974A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 10th June 1974A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 11th June 1974Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).
- 12th June 1974f(x) = 7x - 12. Work out the inverse function f^-1(x).
- 13th June 1974y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 64.
- 14th June 1974A cuboid measures 11 cm by 11 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th June 1974A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th June 1974On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 17th June 1974A block has mass 400 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th June 1974Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 19th June 1974A train slows steadily from 23 m/s to rest in 8 seconds. Work out its deceleration.
- 20th June 1974A cuboid measures 6 cm by 5 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st June 1974A bag holds 5 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd June 1974A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 23rd June 1974x = 138 and y = 118, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th June 1974Use the iteration x(n+1) = cube root of (3x(n) + 6) with x(0) = 1. Work out x(1) to 3 decimal places.
- 25th June 1974y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 26th June 1974The 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.
- 27th June 1974A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 28th June 1974On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 29th June 1974A car covers 430 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.
- 30th June 1974Work out the nth term of the quadratic sequence -3, -1, 5, 15, ...