Daily Practice · Higher Plus
June 1953 5-a-day
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The batch download puts all 5 tiers' June 1953 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 1953A block has mass 730 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd June 1953Simplify (x^2 - 10x + 21)/(x - 7).
- 3rd June 1953y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 25.
- 4th June 1953A cuboid measures 6 cm by 4 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th June 1953A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th June 1953On 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?
- 7th June 1953x = 134 and y = 95, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th June 1953In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 9th June 1953A train slows steadily from 14 m/s to rest in 10 seconds. Work out its deceleration.
- 10th June 1953A cuboid measures 9 cm by 9 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th June 1953A bag holds 5 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th June 1953A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 13th June 1953A car covers 860 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.
- 14th June 1953Make x the subject of 8x + 4 = y(x + 4).
- 15th June 1953y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
- 16th June 1953The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 17th June 1953A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 18th June 1953On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 19th June 1953Rationalise the denominator of 77/sqrt(7), giving your answer in its simplest form.
- 20th June 1953Write 4/(x + 4) + 4/(x + 3) as a single fraction.
- 21st June 1953y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 22nd June 1953In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 23rd June 1953The probability of winning a game is 4/5. A player expects 48 wins. How many games did they play?
- 24th June 1953A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 25th June 1953Simplify sqrt(50) + sqrt(18), giving your answer in the form a sqrt(b).
- 26th June 1953Solve 4x^2 + 15x + 9 = 0.
- 27th June 1953y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 81.
- 28th June 1953In a vector proof you find that vector PQ = 2a - 4b and vector RS = 10a - 20b. What does this show about PQ and RS?
- 29th June 1953A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 30th June 1953On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?