Daily Practice · Higher Plus
June 1964 5-a-day
Printing for a group?
The batch download puts all 5 tiers' June 1964 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1964
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1964A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 2nd June 1964A 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?
- 3rd June 1964A rectangle is 19 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th June 1964Use the iteration x(n+1) = cube root of (8x(n) + 9) with x(0) = 2. Work out x(1) to 3 decimal places.
- 5th June 1964y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 6th June 1964A cuboid measures 13 cm by 9 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th June 1964A 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?
- 8th June 1964On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th June 1964Expand and simplify (5 + sqrt(5))(5 - sqrt(5)).
- 10th June 1964Work out the nth term of the quadratic sequence -2, 7, 22, 43, ...
- 11th June 1964y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 12th June 1964A cuboid measures 10 cm by 13 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th June 1964A bag holds 3 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th June 1964A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 15th June 1964A block has mass 590 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th June 1964The point (1, -1) lies on y = f(x). Write down its image on y = f(x - 1).
- 17th June 1964y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 81.
- 18th June 1964The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 19th June 1964A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 20th June 1964On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st June 1964x = 175 and y = 31, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd June 1964Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 23rd June 1964A train slows steadily from 32 m/s to rest in 5 seconds. Work out its deceleration.
- 24th June 1964In 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.
- 25th June 1964The probability of winning a game is 3/5. A player expects 45 wins. How many games did they play?
- 26th June 1964A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?
- 27th June 1964A car covers 230 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th June 1964f(x) = 5x + 5 and g(x) = 6x + 7. Work out fg(1).
- 29th June 1964y is inversely proportional to x^2. When x = 2, y = 64. Work out y when x = 4.
- 30th June 1964In a vector proof you find that vector PQ = 6a + b and vector RS = 18a + 3b. What does this show about PQ and RS?