Daily Practice · Higher Plus
December 1991 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1991 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1991The probability of winning a game is 1/2. A player expects 22 wins. How many games did they play?
- 2nd December 1991A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 3rd December 1991Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
- 4th December 1991Write x^2 - 16x + 5 in the form (x + a)^2 + b.
- 5th December 1991y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 16.
- 6th December 1991In a vector proof you find that vector PQ = 2a - 2b and vector RS = 6a - 6b. What does this show about PQ and RS?
- 7th December 1991A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 8th December 1991On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th December 1991A block has mass 830 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.
- 10th December 1991Work out the coordinates of the turning point of y = x^2 + 16x + 8.
- 11th December 1991A train slows steadily from 40 m/s to rest in 8 seconds. Work out its deceleration.
- 12th December 1991A cuboid measures 13 cm by 10 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th December 1991A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th December 1991A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 15th December 1991x = 44 and y = 9, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th December 1991Simplify (x^2 + 2x - 24)/(x - 4).
- 17th December 1991y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 18th December 1991A cuboid measures 8 cm by 12 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th December 1991A bag holds 7 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th December 1991On 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?
- 21st December 1991A car covers 670 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd December 1991In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 23rd December 1991y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 24th December 1991The 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.
- 25th December 1991A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 26th December 1991A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 27th December 1991Rationalise the denominator of 12/sqrt(3), giving your answer in its simplest form.
- 28th December 1991Make x the subject of 3x + 5 = y(x + 5).
- 29th December 1991y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 9.
- 30th December 1991In 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.
- 31st December 1991The probability of winning a game is 4/5. A player expects 12 wins. How many games did they play?