Daily Practice · Higher Plus
July 1982 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1982 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1982
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1982y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 2nd July 1982A cuboid measures 3 cm by 6 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd July 1982A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th July 1982On 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?
- 5th July 1982A block has mass 630 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th July 1982Write 7/(x - 6) + 4/(x + 3) as a single fraction.
- 7th July 1982y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 8th July 1982A cuboid measures 5 cm by 6 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th July 1982A bag holds 7 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th July 1982A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 11th July 1982x = 83 and y = 50, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th July 1982Solve 12x^2 - 11x - 5 = 0.
- 13th July 1982y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 25.
- 14th July 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.
- 15th July 1982A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 16th July 1982On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 17th July 1982A car covers 200 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 18th July 1982f(x) = 2x + 5. Work out the inverse function f^-1(x).
- 19th July 1982A train slows steadily from 18 m/s to rest in 5 seconds. Work out its deceleration.
- 20th July 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.
- 21st July 1982The probability of winning a game is 1/8. A player expects 10 wins. How many games did they play?
- 22nd July 1982A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 23rd July 1982Rationalise the denominator of 30/sqrt(6), giving your answer in its simplest form.
- 24th July 1982Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.
- 25th July 1982y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 26th July 1982In a vector proof you find that vector PQ = 6a - 6b and vector RS = 30a - 30b. What does this show about PQ and RS?
- 27th July 1982A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 28th July 1982On 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?
- 29th July 1982Simplify sqrt(18) + sqrt(8), giving your answer in the form a sqrt(b).
- 30th July 1982Use the iteration x(n+1) = cube root of (5x(n) + 3) with x(0) = 5. Work out x(1) to 3 decimal places.
- 31st July 1982y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.