Daily Practice · Higher Plus
August 1982 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1982 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1982
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1982A cuboid measures 15 cm by 4 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd August 1982A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd August 1982A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 4th August 1982A rectangle is 18 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th August 1982Work out the nth term of the quadratic sequence 9, 23, 45, 75, ...
- 6th August 1982y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 81.
- 7th August 1982A cuboid measures 5 cm by 7 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th August 1982A bag holds 6 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th August 1982On 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?
- 10th August 1982Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).
- 11th August 1982The point (0, -3) lies on y = f(x). Write down its image on y = f(x + 1).
- 12th August 1982A train slows steadily from 24 m/s to rest in 4 seconds. Work out its deceleration.
- 13th August 1982The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 14th August 1982A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 15th August 1982A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 16th August 1982A block has mass 330 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th August 1982Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 18th August 1982y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 19th August 1982In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 20th August 1982The probability of winning a game is 3/4. A player expects 21 wins. How many games did they play?
- 21st August 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?
- 22nd August 1982x = 151 and y = 132, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd August 1982f(x) = 6x - 6 and g(x) = 6x + 9. Work out fg(0).
- 24th August 1982y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 25th August 1982In a vector proof you find that vector PQ = a + 5b and vector RS = 3a + 15b. What does this show about PQ and RS?
- 26th August 1982A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 27th August 1982A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 28th August 1982A car covers 770 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th August 1982The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 30th August 1982y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 4.
- 31st August 1982A cuboid measures 14 cm by 10 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.