Daily Practice · Higher Plus
May 1957 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1957 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1957y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 2nd May 1957In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 3rd May 1957The probability of winning a game is 3/5. A player expects 30 wins. How many games did they play?
- 4th May 1957On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 5th May 1957x = 104 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th May 1957In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 7th May 1957y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 8th May 1957In a vector proof you find that vector PQ = 5a + 5b and vector RS = 10a + 10b. What does this show about PQ and RS?
- 9th May 1957A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 10th May 1957A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 11th May 1957A car covers 700 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.
- 12th May 1957Make x the subject of 2x + 5 = y(x + 5).
- 13th May 1957y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 36.
- 14th May 1957A cuboid measures 11 cm by 7 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th May 1957A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th May 1957On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 17th May 1957Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 18th May 1957Write 2/(x - 3) + 2/(x - 2) as a single fraction.
- 19th May 1957A train slows steadily from 17 m/s to rest in 10 seconds. Work out its deceleration.
- 20th May 1957A cuboid measures 8 cm by 12 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st May 1957A bag holds 7 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd May 1957A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 23rd May 1957Simplify sqrt(50) + sqrt(72), giving your answer in the form a sqrt(b).
- 24th May 1957Solve 12x^2 + 31x + 20 = 0.
- 25th May 1957y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 26th May 1957The 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.
- 27th May 1957A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 28th May 1957On 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?
- 29th May 1957A rectangle is 17 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th May 1957f(x) = 2x + 3. Work out the inverse function f^-1(x).
- 31st May 1957y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.