Daily Practice · Higher Plus
January 1981 5-a-day
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The batch download puts all 5 tiers' January 1981 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1981
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1981y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 2nd January 1981In a vector proof you find that vector PQ = 2a + 3b and vector RS = 6a + 9b. What does this show about PQ and RS?
- 3rd January 1981A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 4th January 1981A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 5th January 1981A block has mass 590 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th January 1981Solve x^2 + 6x + 8 > 0.
- 7th January 1981y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 36.
- 8th January 1981A cuboid measures 14 cm by 3 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th January 1981A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th January 1981On 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?
- 11th January 1981x = 144 and y = 128, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th January 1981Write x^2 + 2x - 9 in the form (x + a)^2 + b.
- 13th January 1981A train slows steadily from 27 m/s to rest in 4 seconds. Work out its deceleration.
- 14th January 1981A cuboid measures 12 cm by 13 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th January 1981A bag holds 5 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th January 1981A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 17th January 1981A car covers 820 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 18th January 1981Work out the coordinates of the turning point of y = x^2 + 6x + 15.
- 19th January 1981y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
- 20th January 1981The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 21st January 1981A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
- 22nd January 1981On 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?
- 23rd January 1981Rationalise the denominator of 9/sqrt(3), giving your answer in its simplest form.
- 24th January 1981Simplify (x^2 + 7x + 12)/(x + 4).
- 25th January 1981y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 26th January 1981In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 27th January 1981The probability of winning a game is 1/5. A player expects 4 wins. How many games did they play?
- 28th January 1981A 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?
- 29th January 1981Simplify sqrt(8) + sqrt(50), giving your answer in the form a sqrt(b).
- 30th January 1981In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 7 in terms of an integer n?
- 31st January 1981y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 36.