Daily Practice · Higher Plus
May 1954 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1954 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1954
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1954A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd May 1954A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 3rd May 1954A block has mass 550 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 4th May 1954f(x) = 6x + 12. Work out the inverse function f^-1(x).
- 5th May 1954y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 64.
- 6th May 1954A cuboid measures 6 cm by 13 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th May 1954A bag holds 6 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th May 1954On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th May 1954x = 137 and y = 47, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th May 1954Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 11th May 1954A train slows steadily from 30 m/s to rest in 10 seconds. Work out its deceleration.
- 12th May 1954The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 13th May 1954A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/22. Work out r.
- 14th May 1954A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 15th May 1954A car covers 540 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.
- 16th May 1954Use the iteration x(n+1) = cube root of (9x(n) + 4) with x(0) = 3. Work out x(1) to 3 decimal places.
- 17th May 1954y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 18th May 1954In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 19th May 1954The probability of winning a game is 4/5. A player expects 32 wins. How many games did they play?
- 20th May 1954On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 21st May 1954Rationalise the denominator of 77/sqrt(7), giving your answer in its simplest form.
- 22nd May 1954Work out the nth term of the quadratic sequence 4, 3, 4, 7, ...
- 23rd May 1954y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 24th May 1954In a vector proof you find that vector PQ = 3a + b and vector RS = 6a + 2b. What does this show about PQ and RS?
- 25th May 1954A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 26th May 1954A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 27th May 1954Simplify sqrt(48) + sqrt(48), giving your answer in the form a sqrt(b).
- 28th May 1954The point (3, -5) lies on y = f(x). Write down its image on y = f(x - 3).
- 29th May 1954y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 9.
- 30th May 1954A cuboid measures 10 cm by 7 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st May 1954A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?