Daily Practice · Higher Plus
May 1959 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1959 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1959
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1959Rationalise the denominator of 44/sqrt(11), giving your answer in its simplest form.
- 2nd May 1959Write 7/(x - 5) + 4/(x - 6) as a single fraction.
- 3rd May 1959y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 36.
- 4th May 1959A cuboid measures 15 cm by 15 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th May 1959A 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?
- 6th May 1959On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th May 1959Simplify sqrt(48) + sqrt(48), giving your answer in the form a sqrt(b).
- 8th May 1959Solve 15x^2 - 28x + 12 = 0.
- 9th May 1959A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
- 10th May 1959A cuboid measures 8 cm by 5 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th May 1959A bag holds 5 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th May 1959A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 13th May 1959A rectangle is 30 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th May 1959f(x) = 7x - 2. Work out the inverse function f^-1(x).
- 15th May 1959y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 16th May 1959The 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.
- 17th May 1959A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 18th May 1959On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 19th May 1959Expand and simplify (3 + sqrt(11))(3 - sqrt(11)).
- 20th May 1959Solve x^2 + y^2 = 625 and y = x + 17 simultaneously.
- 21st May 1959y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 22nd May 1959In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 23rd May 1959The probability of winning a game is 7/8. A player expects 42 wins. How many games did they play?
- 24th May 1959A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 25th May 1959A block has mass 800 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th May 1959Use the iteration x(n+1) = cube root of (4x(n) + 8) with x(0) = 1. Work out x(1) to 3 decimal places.
- 27th May 1959y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 81.
- 28th May 1959In a vector proof you find that vector PQ = 3a + 5b and vector RS = 12a + 20b. What does this show about PQ and RS?
- 29th May 1959A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 30th May 1959On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 31st May 1959x = 199 and y = 148, each correct to the nearest whole number. Work out the upper bound of x - y.