Daily Practice · Higher Plus
December 1981 5-a-day
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The batch download puts all 5 tiers' December 1981 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1981
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1981Expand and simplify (8 + sqrt(10))(8 - sqrt(10)).
- 2nd December 1981In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 3rd December 1981y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 4th December 1981A cuboid measures 10 cm by 7 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th December 1981A bag holds 7 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th December 1981A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 7th December 1981A block has mass 240 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th December 1981Make x the subject of 8x + 6 = y(x + 6).
- 9th December 1981y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 25.
- 10th December 1981A cuboid measures 14 cm by 6 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th December 1981A bag holds 3 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th December 1981On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 13th December 1981x = 120 and y = 48, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th December 1981Write 5/(x + 6) + 4/(x - 4) as a single fraction.
- 15th December 1981A train slows steadily from 16 m/s to rest in 8 seconds. Work out its deceleration.
- 16th December 1981The 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.
- 17th December 1981A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 18th December 1981A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 19th December 1981A car covers 740 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.
- 20th December 1981Solve 6x^2 + 7x - 3 = 0.
- 21st December 1981y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
- 22nd December 1981In 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.
- 23rd December 1981The probability of winning a game is 1/5. A player expects 2 wins. How many games did they play?
- 24th December 1981On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 25th December 1981Rationalise the denominator of 28/sqrt(7), giving your answer in its simplest form.
- 26th December 1981f(x) = 7x - 12. Work out the inverse function f^-1(x).
- 27th December 1981y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 28th December 1981In a vector proof you find that vector PQ = a + 4b and vector RS = 3a + 12b. What does this show about PQ and RS?
- 29th December 1981A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 30th December 1981A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 31st December 1981Simplify sqrt(20) + sqrt(20), giving your answer in the form a sqrt(b).