Daily Practice · Higher Plus
January 1988 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1988 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1988
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1988A train slows steadily from 28 m/s to rest in 8 seconds. Work out its deceleration.
- 2nd January 1988A cuboid measures 5 cm by 14 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd January 1988A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th January 1988A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 5th January 1988Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
- 6th January 1988Write x^2 - 16x + 9 in the form (x + a)^2 + b.
- 7th January 1988y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 8th January 1988A cuboid measures 6 cm by 10 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th January 1988A bag holds 7 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th January 1988On 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?
- 11th January 1988A block has mass 870 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th January 1988Work out the coordinates of the turning point of y = x^2 - 12x + 1.
- 13th January 1988y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 14th January 1988The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 15th January 1988A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 16th January 1988A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 17th January 1988x = 86 and y = 54, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th January 1988Simplify (x^2 - 5x - 14)/(x - 7).
- 19th January 1988y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 49.
- 20th January 1988In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 21st January 1988The probability of winning a game is 4/5. A player expects 44 wins. How many games did they play?
- 22nd January 1988On 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?
- 23rd January 1988A car covers 770 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 24th January 1988In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 25th January 1988A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.
- 26th January 1988In a vector proof you find that vector PQ = 3a - b and vector RS = 9a - 3b. What does this show about PQ and RS?
- 27th January 1988A bag holds 5 red and n blue counters. The probability of taking a red is 5/9. Work out n.
- 28th January 1988A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 29th January 1988Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
- 30th January 1988Make x the subject of 2x + 7 = y(x + 7).
- 31st January 1988y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.