Daily Practice · Higher Plus
January 1983 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1983 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1983
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1983A car covers 360 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 2nd January 1983Work out the coordinates of the turning point of y = x^2 - 8x + 1.
- 3rd January 1983A train slows steadily from 13 m/s to rest in 5 seconds. Work out its deceleration.
- 4th January 1983A cuboid measures 8 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th January 1983A bag holds 4 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th January 1983A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 7th January 1983Rationalise the denominator of 24/sqrt(3), giving your answer in its simplest form.
- 8th January 1983Simplify (x^2 - 3x - 18)/(x + 3).
- 9th January 1983y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 10th January 1983The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 11th January 1983A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/55. Work out r.
- 12th January 1983On 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?
- 13th January 1983Simplify sqrt(50) + sqrt(18), giving your answer in the form a sqrt(b).
- 14th January 1983In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
- 15th January 1983y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 16th January 1983In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 17th January 1983The probability of winning a game is 3/5. A player expects 12 wins. How many games did they play?
- 18th January 1983A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 19th January 1983A rectangle is 16 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th January 1983Make x the subject of 8x + 7 = y(x + 7).
- 21st January 1983y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 9.
- 22nd January 1983In a vector proof you find that vector PQ = 3a + 4b and vector RS = 12a + 16b. What does this show about PQ and RS?
- 23rd January 1983A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.
- 24th January 1983On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th January 1983Expand and simplify (3 + sqrt(6))(3 - sqrt(6)).
- 26th January 1983Write 3/(x + 1) + 2/(x + 6) as a single fraction.
- 27th January 1983A train slows steadily from 34 m/s to rest in 8 seconds. Work out its deceleration.
- 28th January 1983A cuboid measures 10 cm by 10 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th January 1983A bag holds 4 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th January 1983A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 31st January 1983A block has mass 530 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.