Daily Practice · Higher Plus
January 1982 5-a-day
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The batch download puts all 5 tiers' January 1982 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1982
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1982Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 2nd January 1982y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 81.
- 3rd January 1982A cuboid measures 15 cm by 15 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th January 1982A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th January 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?
- 6th January 1982A rectangle is 26 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th January 1982Use the iteration x(n+1) = cube root of (9x(n) + 2) with x(0) = 5. Work out x(1) to 3 decimal places.
- 8th January 1982A train slows steadily from 18 m/s to rest in 8 seconds. Work out its deceleration.
- 9th January 1982A cuboid measures 7 cm by 6 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th January 1982A bag holds 5 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th January 1982A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 12th January 1982Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 13th January 1982Work out the nth term of the quadratic sequence 10, 15, 22, 31, ...
- 14th January 1982y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 15th January 1982The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 16th January 1982A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 17th January 1982On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 18th January 1982A block has mass 460 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th January 1982The point (4, 1) lies on y = f(x). Write down its image on y = -f(x).
- 20th January 1982y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 21st January 1982In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 22nd January 1982The probability of winning a game is 1/4. A player expects 12 wins. How many games did they play?
- 23rd January 1982A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 24th January 1982x = 99 and y = 85, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th January 1982Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 26th January 1982y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 4.
- 27th January 1982In a vector proof you find that vector PQ = 2a + 5b and vector RS = 10a + 25b. What does this show about PQ and RS?
- 28th January 1982A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 29th January 1982On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th January 1982A car covers 210 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 31st January 1982f(x) = 4x - 6 and g(x) = 2x - 3. Work out fg(6).