Daily Practice · Higher Plus
July 1953 5-a-day
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The batch download puts all 5 tiers' July 1953 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1953A rectangle is 29 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd July 1953f(x) = 2x + 11. Work out the inverse function f^-1(x).
- 3rd July 1953A train slows steadily from 15 m/s to rest in 10 seconds. Work out its deceleration.
- 4th July 1953A cuboid measures 10 cm by 5 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th July 1953A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th July 1953A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 7th July 1953Expand and simplify (8 + sqrt(2))(8 - sqrt(2)).
- 8th July 1953Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 9th July 1953y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 10th July 1953A cuboid measures 11 cm by 12 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th July 1953A bag holds 6 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th July 1953On 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?
- 13th July 1953A block has mass 440 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th July 1953Use the iteration x(n+1) = cube root of (6x(n) + 7) with x(0) = 3. Work out x(1) to 3 decimal places.
- 15th July 1953y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 16th July 1953The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 17th July 1953A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
- 18th July 1953A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 19th July 1953x = 109 and y = 88, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th July 1953Work out the nth term of the quadratic sequence 1, -1, -1, 1, ...
- 21st July 1953y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 9.
- 22nd July 1953In 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.
- 23rd July 1953The probability of winning a game is 1/5. A player expects 6 wins. How many games did they play?
- 24th July 1953On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th July 1953A car covers 780 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.
- 26th July 1953The point (-4, -4) lies on y = f(x). Write down its image on y = f(x - 1).
- 27th July 1953A train slows steadily from 33 m/s to rest in 5 seconds. Work out its deceleration.
- 28th July 1953In a vector proof you find that vector PQ = 4a - 6b and vector RS = 8a - 12b. What does this show about PQ and RS?
- 29th July 1953A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.
- 30th July 1953A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 31st July 1953Rationalise the denominator of 33/sqrt(11), giving your answer in its simplest form.