Daily Practice · Higher Plus
June 1952 5-a-day
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The batch download puts all 5 tiers' June 1952 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1952
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1952Use the iteration x(n+1) = cube root of (3x(n) + 1) with x(0) = 2. Work out x(1) to 3 decimal places.
- 2nd June 1952y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 3rd June 1952In a vector proof you find that vector PQ = 5a + 5b and vector RS = 15a + 15b. What does this show about PQ and RS?
- 4th June 1952A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 5th June 1952A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 6th June 1952Rationalise the denominator of 99/sqrt(11), giving your answer in its simplest form.
- 7th June 1952Work out the nth term of the quadratic sequence 6, 10, 16, 24, ...
- 8th June 1952y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 81.
- 9th June 1952A cuboid measures 11 cm by 6 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th June 1952A 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?
- 11th June 1952On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th June 1952Simplify sqrt(18) + sqrt(8), giving your answer in the form a sqrt(b).
- 13th June 1952The point (-1, -5) lies on y = f(x). Write down its image on y = f(x) - 1.
- 14th June 1952A train slows steadily from 13 m/s to rest in 10 seconds. Work out its deceleration.
- 15th June 1952A cuboid measures 4 cm by 12 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th June 1952A bag holds 4 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th June 1952A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 18th June 1952A rectangle is 4 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th June 1952Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 20th June 1952y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 21st June 1952The 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.
- 22nd June 1952A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 23rd June 1952On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th June 1952Expand and simplify (8 + sqrt(6))(8 - sqrt(6)).
- 25th June 1952f(x) = 4x - 1 and g(x) = 6x + 5. Work out fg(1).
- 26th June 1952y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 27th June 1952In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 28th June 1952The probability of winning a game is 7/10. A player expects 42 wins. How many games did they play?
- 29th June 1952A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 30th June 1952A block has mass 520 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.