Daily Practice · Higher Plus
June 1955 5-a-day
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The batch download puts all 5 tiers' June 1955 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1955
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1955A bag holds 7 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd June 1955A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 3rd June 1955Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.
- 4th June 1955Write 2/(x - 3) + 3/(x + 2) as a single fraction.
- 5th June 1955y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 6th June 1955The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 7th June 1955A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 8th June 1955On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th June 1955Simplify sqrt(27) + sqrt(147), giving your answer in the form a sqrt(b).
- 10th June 1955Solve 6x^2 - 7x + 2 = 0.
- 11th June 1955y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 12th June 1955In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 13th June 1955The probability of winning a game is 7/10. A player expects 63 wins. How many games did they play?
- 14th June 1955A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 15th June 1955A rectangle is 23 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th June 1955f(x) = 7x + 11. Work out the inverse function f^-1(x).
- 17th June 1955y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 81.
- 18th June 1955In a vector proof you find that vector PQ = 3a + 4b and vector RS = 9a + 12b. What does this show about PQ and RS?
- 19th June 1955A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 20th June 1955On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st June 1955Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
- 22nd June 1955Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 23rd June 1955A train slows steadily from 39 m/s to rest in 4 seconds. Work out its deceleration.
- 24th June 1955A cuboid measures 7 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th June 1955A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th June 1955A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 27th June 1955A block has mass 720 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th June 1955Use the iteration x(n+1) = cube root of (4x(n) + 4) with x(0) = 2. Work out x(1) to 3 decimal places.
- 29th June 1955y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 30th June 1955A cuboid measures 4 cm by 8 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.