Daily Practice · Higher Plus

October 1988 5-a-day

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October 1988

31 sheets · 155 questions · Grades 8-9

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The batch download puts all 5 tiers' October 1988 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in October 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 October 1988A car covers 190 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  2. 2nd October 1988The point (-2, 0) lies on y = f(x). Write down its image on y = -f(x).
  3. 3rd October 1988y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
  4. 4th October 1988A cuboid measures 4 cm by 8 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  5. 5th October 1988A bag holds 6 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  6. 6th October 1988A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
  7. 7th October 1988Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
  8. 8th October 1988Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
  9. 9th October 1988y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 36.
  10. 10th October 1988The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
  11. 11th October 1988A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/22. Work out r.
  12. 12th October 1988On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
  13. 13th October 1988Simplify sqrt(72) + sqrt(98), giving your answer in the form a sqrt(b).
  14. 14th October 1988f(x) = 5x + 9 and g(x) = 6x - 6. Work out fg(6).
  15. 15th October 1988A train slows steadily from 37 m/s to rest in 4 seconds. Work out its deceleration.
  16. 16th October 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.
  17. 17th October 1988The probability of winning a game is 1/10. A player expects 13 wins. How many games did they play?
  18. 18th October 1988A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
  19. 19th October 1988A rectangle is 11 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
  20. 20th October 1988The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
  21. 21st October 1988y is inversely proportional to x^2. When x = 3, y = 36. Work out y when x = 6.
  22. 22nd October 1988In a vector proof you find that vector PQ = 5a - 3b and vector RS = 15a - 9b. What does this show about PQ and RS?
  23. 23rd October 1988A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
  24. 24th October 1988On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  25. 25th October 1988Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
  26. 26th October 1988A quadratic sequence starts 1, 6, 13, 22. Work out the second difference, and the coefficient of n^2.
  27. 27th October 1988y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
  28. 28th October 1988A cuboid measures 10 cm by 9 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  29. 29th October 1988A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  30. 30th October 1988A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
  31. 31st October 1988A block has mass 430 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

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