Daily Practice · Higher Plus
June 1962 5-a-day
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The batch download puts all 5 tiers' June 1962 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1962
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1962A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 2nd June 1962A car covers 870 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.
- 3rd June 1962Solve 8x^2 + 10x - 25 = 0.
- 4th June 1962y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 81.
- 5th June 1962In 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.
- 6th June 1962The probability of winning a game is 1/2. A player expects 25 wins. How many games did they play?
- 7th June 1962On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th June 1962Rationalise the denominator of 15/sqrt(5), giving your answer in its simplest form.
- 9th June 1962f(x) = 7x - 12. Work out the inverse function f^-1(x).
- 10th June 1962A train slows steadily from 33 m/s to rest in 4 seconds. Work out its deceleration.
- 11th June 1962In a vector proof you find that vector PQ = a - 3b and vector RS = 4a - 12b. What does this show about PQ and RS?
- 12th June 1962A bag holds 5 red and n blue counters. The probability of taking a red is 5/7. Work out n.
- 13th June 1962A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 14th June 1962Simplify sqrt(8) + sqrt(2), giving your answer in the form a sqrt(b).
- 15th June 1962Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 16th June 1962y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 17th June 1962A cuboid measures 12 cm by 12 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th June 1962A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th June 1962On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 20th June 1962A rectangle is 11 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st June 1962Use the iteration x(n+1) = cube root of (2x(n) + 6) with x(0) = 2. Work out x(1) to 3 decimal places.
- 22nd June 1962y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 23rd June 1962A cuboid measures 5 cm by 8 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th June 1962A bag holds 5 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th June 1962A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 0.8. How many values in total?
- 26th June 1962Expand and simplify (5 + sqrt(7))(5 - sqrt(7)).
- 27th June 1962Work out the nth term of the quadratic sequence 0, 6, 14, 24, ...
- 28th June 1962y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 25.
- 29th June 1962The 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.
- 30th June 1962A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.