Daily Practice · Higher Plus
September 1974 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1974 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1974
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1974The probability of winning a game is 2/5. A player expects 18 wins. How many games did they play?
- 2nd September 1974A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 3rd September 1974Expand and simplify (4 + sqrt(6))(4 - sqrt(6)).
- 4th September 1974Make x the subject of 4x + 6 = y(x + 6).
- 5th September 1974y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 6th September 1974In a vector proof you find that vector PQ = 4a + 5b and vector RS = 8a + 10b. What does this show about PQ and RS?
- 7th September 1974A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 8th September 1974On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th September 1974A block has mass 880 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th September 1974Write 3/(x - 1) + 3/(x + 6) as a single fraction.
- 11th September 1974y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 12th September 1974A cuboid measures 12 cm by 5 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th September 1974A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th September 1974A 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?
- 15th September 1974x = 194 and y = 163, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th September 1974Solve 10x^2 + 17x + 3 = 0.
- 17th September 1974y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 36.
- 18th September 1974A cuboid measures 8 cm by 14 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th September 1974A bag holds 3 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th September 1974On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st September 1974A car covers 550 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd September 1974f(x) = 5x - 10. Work out the inverse function f^-1(x).
- 23rd September 1974A train slows steadily from 18 m/s to rest in 10 seconds. Work out its deceleration.
- 24th September 1974The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 25th September 1974A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
- 26th September 1974A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 27th September 1974Rationalise the denominator of 12/sqrt(2), giving your answer in its simplest form.
- 28th September 1974Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 29th September 1974y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 30th September 1974In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.