Daily Practice · Higher Plus
June 1956 5-a-day
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The batch download puts all 5 tiers' June 1956 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1956
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1956A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 2nd June 1956On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 3rd June 1956x = 140 and y = 69, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th June 1956A quadratic sequence starts 9, 20, 35, 54. Work out the second difference, and the coefficient of n^2.
- 5th June 1956y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 6th June 1956In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 7th June 1956The probability of winning a game is 5/8. A player expects 15 wins. How many games did they play?
- 8th June 1956A 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?
- 9th June 1956A car covers 370 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th June 1956Solve x^2 + 10x + 16 > 0.
- 11th June 1956y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 64.
- 12th June 1956In a vector proof you find that vector PQ = 4a + 2b and vector RS = 16a + 8b. What does this show about PQ and RS?
- 13th June 1956A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 14th June 1956On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 15th June 1956Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
- 16th June 1956Write x^2 - 6x - 5 in the form (x + a)^2 + b.
- 17th June 1956A train slows steadily from 31 m/s to rest in 8 seconds. Work out its deceleration.
- 18th June 1956A cuboid measures 10 cm by 10 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th June 1956A bag holds 10 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th June 1956A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 21st June 1956Simplify sqrt(12) + sqrt(3), giving your answer in the form a sqrt(b).
- 22nd June 1956Work out the coordinates of the turning point of y = x^2 - 2x - 15.
- 23rd June 1956y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 24th June 1956A cuboid measures 10 cm by 13 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th June 1956A bag holds 6 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th June 1956On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 27th June 1956A rectangle is 12 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th June 1956Simplify (x^2 + 13x + 40)/(x + 8).
- 29th June 1956y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 30th June 1956The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.