Daily Practice · Higher Plus
September 1958 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1958 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1958
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1958A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 2nd September 1958A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 3rd September 1958A rectangle is 16 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th September 1958Solve x^2 + 10x + 21 > 0.
- 5th September 1958y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 36.
- 6th September 1958A cuboid measures 14 cm by 6 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th September 1958A bag holds 9 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th September 1958On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 9th September 1958Expand and simplify (6 + sqrt(5))(6 - sqrt(5)).
- 10th September 1958Write x^2 - 12x - 6 in the form (x + a)^2 + b.
- 11th September 1958A train slows steadily from 24 m/s to rest in 5 seconds. Work out its deceleration.
- 12th September 1958A cuboid measures 12 cm by 8 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th September 1958A bag holds 7 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th September 1958A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 15th September 1958A block has mass 200 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th September 1958Work out the coordinates of the turning point of y = x^2 - 16x - 14.
- 17th September 1958y is inversely proportional to x^2. When x = 5, y = 27. Work out y when x = 3.
- 18th September 1958The 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.
- 19th September 1958A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/66. Work out r.
- 20th September 1958On 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?
- 21st September 1958x = 57 and y = 45, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd September 1958Simplify (x^2 - 13x + 42)/(x - 7).
- 23rd September 1958y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 24th September 1958In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 25th September 1958The probability of winning a game is 3/4. A player expects 12 wins. How many games did they play?
- 26th September 1958A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 27th September 1958A car covers 180 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.
- 28th September 1958In an algebraic proof, how would you write an odd number in terms of an integer n?
- 29th September 1958y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 16.
- 30th September 1958In a vector proof you find that vector PQ = 4a + 2b and vector RS = 8a + 4b. What does this show about PQ and RS?