Daily Practice · Higher Plus
June 1957 5-a-day
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The batch download puts all 5 tiers' June 1957 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1957In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 2nd June 1957The probability of winning a game is 7/10. A player expects 63 wins. How many games did they play?
- 3rd June 1957A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 4th June 1957Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 5th June 1957Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 6th June 1957y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 16.
- 7th June 1957In a vector proof you find that vector PQ = a + b and vector RS = 3a + 3b. What does this show about PQ and RS?
- 8th June 1957A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 9th June 1957On 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?
- 10th June 1957A block has mass 640 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.
- 11th June 1957Use the iteration x(n+1) = cube root of (3x(n) + 6) with x(0) = 4. Work out x(1) to 3 decimal places.
- 12th June 1957A train slows steadily from 31 m/s to rest in 5 seconds. Work out its deceleration.
- 13th June 1957A cuboid measures 10 cm by 4 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th June 1957A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th June 1957A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 16th June 1957x = 192 and y = 171, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th June 1957Work out the nth term of the quadratic sequence 0, 7, 20, 39, ...
- 18th June 1957y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 19th June 1957A cuboid measures 4 cm by 4 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th June 1957A bag holds 3 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st June 1957On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd June 1957A car covers 620 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.
- 23rd June 1957The point (3, 0) lies on y = f(x). Write down its image on y = f(x + 2).
- 24th June 1957y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 25th June 1957The 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.
- 26th June 1957A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 27th June 1957A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 28th June 1957Rationalise the denominator of 77/sqrt(7), giving your answer in its simplest form.
- 29th June 1957Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 30th June 1957y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 81.