Daily Practice · Higher Plus
December 1988 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1988 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1988
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1988Make x the subject of 3x + 5 = y(x + 5).
- 2nd December 1988A train slows steadily from 33 m/s to rest in 4 seconds. Work out its deceleration.
- 3rd December 1988A cuboid measures 10 cm by 12 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th December 1988A bag holds 7 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th December 1988A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 6th December 1988Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 7th December 1988Write 4/(x - 1) + 7/(x) as a single fraction.
- 8th December 1988y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 9th December 1988The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 10th December 1988A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 11th December 1988On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th December 1988A block has mass 680 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th December 1988Solve 6x^2 + 13x + 5 = 0.
- 14th December 1988y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 15th December 1988In 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.
- 16th December 1988The probability of winning a game is 1/2. A player expects 30 wins. How many games did they play?
- 17th December 1988A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 18th December 1988x = 172 and y = 109, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th December 1988f(x) = 7x + 2. Work out the inverse function f^-1(x).
- 20th December 1988y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 4.
- 21st December 1988In a vector proof you find that vector PQ = 2a + 2b and vector RS = 6a + 6b. What does this show about PQ and RS?
- 22nd December 1988A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 23rd December 1988On 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?
- 24th December 1988A car covers 770 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.
- 25th December 1988Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 26th December 1988A train slows steadily from 38 m/s to rest in 4 seconds. Work out its deceleration.
- 27th December 1988A cuboid measures 12 cm by 9 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th December 1988A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th December 1988A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 30th December 1988Rationalise the denominator of 50/sqrt(5), giving your answer in its simplest form.
- 31st December 1988Use the iteration x(n+1) = cube root of (9x(n) + 8) with x(0) = 5. Work out x(1) to 3 decimal places.