Daily Practice · Higher Plus
June 1954 5-a-day
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The batch download puts all 5 tiers' June 1954 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1954
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1954On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd June 1954A rectangle is 30 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd June 1954Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 4th June 1954A train slows steadily from 15 m/s to rest in 5 seconds. Work out its deceleration.
- 5th June 1954A cuboid measures 9 cm by 8 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th June 1954A bag holds 3 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th June 1954A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 8th June 1954Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
- 9th June 1954f(x) = 6x - 2 and g(x) = 3x - 6. Work out fg(6).
- 10th June 1954y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 11th June 1954The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 12th June 1954A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 21/55. Work out r.
- 13th June 1954On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 14th June 1954A block has mass 460 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 15th June 1954The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 16th June 1954y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 17th June 1954In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 18th June 1954The probability of winning a game is 1/8. A player expects 9 wins. How many games did they play?
- 19th June 1954A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?
- 20th June 1954x = 71 and y = 42, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st June 1954A quadratic sequence starts -2, 0, 4, 10. Work out the second difference, and the coefficient of n^2.
- 22nd June 1954y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 64.
- 23rd June 1954In a vector proof you find that vector PQ = 3a + 5b and vector RS = 6a + 10b. What does this show about PQ and RS?
- 24th June 1954A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 25th June 1954On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 26th June 1954A car covers 140 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 27th June 1954Solve x^2 + 5x - 6 > 0.
- 28th June 1954A train slows steadily from 29 m/s to rest in 8 seconds. Work out its deceleration.
- 29th June 1954A cuboid measures 7 cm by 9 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th June 1954A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?