Daily Practice · Higher Plus
May 1953 5-a-day
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The batch download puts all 5 tiers' May 1953 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 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?
- 2nd May 1953A car covers 180 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 3rd May 1953The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 4th May 1953y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 5th May 1953A cuboid measures 14 cm by 7 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th May 1953A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th May 1953A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 8th May 1953Rationalise the denominator of 30/sqrt(6), giving your answer in its simplest form.
- 9th May 1953A quadratic sequence starts 2, 17, 40, 71. Work out the second difference, and the coefficient of n^2.
- 10th May 1953y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 36.
- 11th May 1953A cuboid measures 9 cm by 11 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th May 1953A bag holds 4 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th May 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?
- 14th May 1953Simplify sqrt(18) + sqrt(98), giving your answer in the form a sqrt(b).
- 15th May 1953Solve x^2 - x - 6 < 0.
- 16th May 1953A train slows steadily from 38 m/s to rest in 5 seconds. Work out its deceleration.
- 17th May 1953The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 18th May 1953A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 19th May 1953A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 20th May 1953A rectangle is 6 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st May 1953Write x^2 + 10x + 13 in the form (x + a)^2 + b.
- 22nd May 1953y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 23rd May 1953In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 24th May 1953The probability of winning a game is 1/4. A player expects 8 wins. How many games did they play?
- 25th May 1953On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 26th May 1953Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
- 27th May 1953Work out the coordinates of the turning point of y = x^2 - 2x - 10.
- 28th May 1953y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 29th May 1953In a vector proof you find that vector PQ = a + 4b and vector RS = 3a + 12b. What does this show about PQ and RS?
- 30th May 1953A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 31st May 1953A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?