Daily Practice · Higher Plus
September 1982 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1982 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1982
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1982A 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?
- 2nd September 1982On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd September 1982Rationalise the denominator of 60/sqrt(5), giving your answer in its simplest form.
- 4th September 1982A quadratic sequence starts 1, 12, 29, 52. Work out the second difference, and the coefficient of n^2.
- 5th September 1982A train slows steadily from 13 m/s to rest in 4 seconds. Work out its deceleration.
- 6th September 1982A cuboid measures 11 cm by 12 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th September 1982A bag holds 7 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th September 1982A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 9th September 1982Simplify sqrt(72) + sqrt(8), giving your answer in the form a sqrt(b).
- 10th September 1982Solve x^2 - 6x + 8 > 0.
- 11th September 1982y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 12th September 1982The 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.
- 13th September 1982A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 14th September 1982On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 15th September 1982A rectangle is 18 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th September 1982Write x^2 - 8x - 4 in the form (x + a)^2 + b.
- 17th September 1982y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 18th September 1982In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 19th September 1982The probability of winning a game is 1/5. A player expects 6 wins. How many games did they play?
- 20th September 1982A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 21st September 1982Expand and simplify (4 + sqrt(5))(4 - sqrt(5)).
- 22nd September 1982Work out the coordinates of the turning point of y = x^2 - 2x + 9.
- 23rd September 1982y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 4.
- 24th September 1982In a vector proof you find that vector PQ = 2a - 2b and vector RS = 10a - 10b. What does this show about PQ and RS?
- 25th September 1982A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 26th September 1982On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 27th September 1982A block has mass 640 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th September 1982Simplify (x^2 - 2x - 48)/(x + 6).
- 29th September 1982A train slows steadily from 34 m/s to rest in 10 seconds. Work out its deceleration.
- 30th September 1982A cuboid measures 5 cm by 10 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.