Daily Practice · Higher Plus
May 1955 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1955 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1955
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1955A cuboid measures 13 cm by 12 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd May 1955A bag holds 5 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd May 1955On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th May 1955A rectangle is 26 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th May 1955Write x^2 - 16x - 1 in the form (x + a)^2 + b.
- 6th May 1955A train slows steadily from 25 m/s to rest in 8 seconds. Work out its deceleration.
- 7th May 1955The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 8th May 1955A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 9th May 1955A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 10th May 1955Expand and simplify (8 + sqrt(6))(8 - sqrt(6)).
- 11th May 1955Work out the coordinates of the turning point of y = x^2 + 8x - 1.
- 12th May 1955y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 13th May 1955In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 14th May 1955The probability of winning a game is 3/4. A player expects 90 wins. How many games did they play?
- 15th May 1955On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th May 1955A block has mass 320 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th May 1955Simplify (x^2 - x - 2)/(x + 1).
- 18th May 1955y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 19th May 1955In a vector proof you find that vector PQ = 5a - 4b and vector RS = 25a - 20b. What does this show about PQ and RS?
- 20th May 1955A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 21st May 1955A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 22nd May 1955x = 189 and y = 173, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd May 1955In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 24th May 1955y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 25.
- 25th May 1955A cuboid measures 9 cm by 15 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th May 1955A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th May 1955On 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?
- 28th May 1955A car covers 730 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th May 1955Make x the subject of 7x + 8 = y(x + 8).
- 30th May 1955A train slows steadily from 14 m/s to rest in 8 seconds. Work out its deceleration.
- 31st May 1955A cuboid measures 6 cm by 14 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.