Daily Practice · Higher Plus
May 1958 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1958 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1958
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1958Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 2nd May 1958y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 3rd May 1958In a vector proof you find that vector PQ = 5a + 4b and vector RS = 20a + 16b. What does this show about PQ and RS?
- 4th May 1958A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 5th May 1958A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 6th May 1958Expand and simplify (8 + sqrt(10))(8 - sqrt(10)).
- 7th May 1958f(x) = 5x - 6 and g(x) = 6x + 8. Work out fg(4).
- 8th May 1958y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 81.
- 9th May 1958A cuboid measures 6 cm by 11 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th May 1958A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th May 1958On 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?
- 12th May 1958A block has mass 660 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th May 1958The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 14th May 1958A train slows steadily from 34 m/s to rest in 10 seconds. Work out its deceleration.
- 15th May 1958A cuboid measures 12 cm by 10 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th May 1958A bag holds 6 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th May 1958A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 18th May 1958x = 81 and y = 43, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th May 1958A quadratic sequence starts 3, 7, 13, 21. Work out the second difference, and the coefficient of n^2.
- 20th May 1958y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 21st May 1958The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 22nd May 1958A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 23rd May 1958On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 24th May 1958A car covers 250 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 25th May 1958Solve x^2 + 6x - 7 < 0.
- 26th May 1958y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 27th May 1958In 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.
- 28th May 1958The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 29th May 1958A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 30th May 1958Rationalise the denominator of 99/sqrt(11), giving your answer in its simplest form.
- 31st May 1958Write x^2 + 6x + 5 in the form (x + a)^2 + b.