Daily Practice · Higher Plus
May 1982 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1982 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1982
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1982The point (6, -4) lies on y = f(x). Write down its image on y = f(x + 2).
- 2nd May 1982y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 16.
- 3rd May 1982A cuboid measures 8 cm by 14 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th May 1982A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th May 1982On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th May 1982Simplify sqrt(48) + sqrt(27), giving your answer in the form a sqrt(b).
- 7th May 1982Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 8th May 1982A train slows steadily from 14 m/s to rest in 8 seconds. Work out its deceleration.
- 9th May 1982A cuboid measures 6 cm by 5 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th May 1982A bag holds 4 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th May 1982A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 3.5. How many values in total?
- 12th May 1982A rectangle is 10 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th May 1982f(x) = 5x + 6 and g(x) = 5x - 3. Work out fg(2).
- 14th May 1982y is inversely proportional to x^2. When x = 5, y = 72. Work out y when x = 6.
- 15th May 1982The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 16th May 1982A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
- 17th May 1982On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 18th May 1982Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 19th May 1982The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 20th May 1982y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 21st May 1982In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 22nd May 1982The probability of winning a game is 3/5. A player expects 33 wins. How many games did they play?
- 23rd May 1982A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 24th May 1982A block has mass 450 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th May 1982A quadratic sequence starts 3, 10, 21, 36. Work out the second difference, and the coefficient of n^2.
- 26th May 1982y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 36.
- 27th May 1982In a vector proof you find that vector PQ = 6a - 6b and vector RS = 18a - 18b. What does this show about PQ and RS?
- 28th May 1982A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 29th May 1982On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 30th May 1982x = 120 and y = 57, each correct to the nearest whole number. Work out the upper bound of x - y.
- 31st May 1982Solve x^2 - 3x + 2 < 0.