Daily Practice · Higher Plus

January 1988 5-a-day

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January 1988

31 sheets · 155 questions · Grades 8-9

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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.

  1. 1st January 1988A train slows steadily from 28 m/s to rest in 8 seconds. Work out its deceleration.
  2. 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.
  3. 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?
  4. 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?
  5. 5th January 1988Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
  6. 6th January 1988Write x^2 - 16x + 9 in the form (x + a)^2 + b.
  7. 7th January 1988y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
  8. 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.
  9. 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?
  10. 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?
  11. 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.
  12. 12th January 1988Work out the coordinates of the turning point of y = x^2 - 12x + 1.
  13. 13th January 1988y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
  14. 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.
  15. 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.
  16. 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?
  17. 17th January 1988x = 86 and y = 54, each correct to the nearest whole number. Work out the upper bound of x - y.
  18. 18th January 1988Simplify (x^2 - 5x - 14)/(x - 7).
  19. 19th January 1988y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 49.
  20. 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.
  21. 21st January 1988The probability of winning a game is 4/5. A player expects 44 wins. How many games did they play?
  22. 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?
  23. 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.
  24. 24th January 1988In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
  25. 25th January 1988A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.
  26. 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?
  27. 27th January 1988A bag holds 5 red and n blue counters. The probability of taking a red is 5/9. Work out n.
  28. 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?
  29. 29th January 1988Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
  30. 30th January 1988Make x the subject of 2x + 7 = y(x + 7).
  31. 31st January 1988y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.

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