Daily Practice · Higher Plus
December 1980 5-a-day
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The batch download puts all 5 tiers' December 1980 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1980
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1980Work out the nth term of the quadratic sequence -9, -8, -3, 6, ...
- 2nd December 1980y is inversely proportional to x^2. When x = 4, y = 18. Work out y when x = 3.
- 3rd December 1980In a vector proof you find that vector PQ = 5a - 2b and vector RS = 15a - 6b. What does this show about PQ and RS?
- 4th December 1980A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 5th December 1980On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th December 1980A car covers 380 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.
- 7th December 1980The point (-5, 6) lies on y = f(x). Write down its image on y = -f(x).
- 8th December 1980y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 9th December 1980A cuboid measures 6 cm by 7 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th December 1980A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th December 1980A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 12th December 1980Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 13th December 1980Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 14th December 1980y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 9.
- 15th December 1980A cuboid measures 4 cm by 6 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th December 1980A bag holds 7 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th December 1980On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th December 1980Simplify sqrt(48) + sqrt(147), giving your answer in the form a sqrt(b).
- 19th December 1980f(x) = 6x + 2 and g(x) = 2x + 7. Work out fg(1).
- 20th December 1980A train slows steadily from 33 m/s to rest in 5 seconds. Work out its deceleration.
- 21st December 1980The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 22nd December 1980A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 23rd December 1980A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 24th December 1980A rectangle is 20 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th December 1980The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 26th December 1980y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 27th December 1980In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 28th December 1980The probability of winning a game is 4/5. A player expects 52 wins. How many games did they play?
- 29th December 1980On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th December 1980Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 31st December 1980A quadratic sequence starts 11, 23, 45, 77. Work out the second difference, and the coefficient of n^2.