Daily Practice · Higher Plus

August 1994 - Higher Plus 5-a-day

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August 1994

31 sheets · 155 questions · Grades 8-9

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The batch download puts all 5 tiers' August 1994 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in August 1994

The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.

  1. 1st August 1994A block has mass 530 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  2. 2nd August 1994Use the iteration x(n+1) = cube root of (10x(n) + 7) with x(0) = 1. Work out x(1) to 3 decimal places.
  3. 3rd August 1994y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
  4. 4th August 1994A cuboid measures 6 cm by 8 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  5. 5th August 1994A bag holds 5 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  6. 6th August 1994On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
  7. 7th August 1994x = 47 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
  8. 8th August 1994Work out the nth term of the quadratic sequence 4, 11, 24, 43, ...
  9. 9th August 1994y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
  10. 10th August 1994The 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.
  11. 11th August 1994A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
  12. 12th August 1994A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
  13. 13th August 1994A car covers 410 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.
  14. 14th August 1994The point (1, -5) lies on y = f(x). Write down its image on y = f(x + 6).
  15. 15th August 1994y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 49.
  16. 16th August 1994In 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 August 1994The probability of winning a game is 3/4. A player expects 72 wins. How many games did they play?
  18. 18th August 1994On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  19. 19th August 1994Rationalise the denominator of 16/sqrt(2), giving your answer in its simplest form.
  20. 20th August 1994Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
  21. 21st August 1994A train slows steadily from 27 m/s to rest in 5 seconds. Work out its deceleration.
  22. 22nd August 1994In a vector proof you find that vector PQ = 5a - 4b and vector RS = 10a - 8b. What does this show about PQ and RS?
  23. 23rd August 1994A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
  24. 24th August 1994A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
  25. 25th August 1994Simplify sqrt(32) + sqrt(72), giving your answer in the form a sqrt(b).
  26. 26th August 1994f(x) = 2x - 8 and g(x) = 6x + 4. Work out fg(2).
  27. 27th August 1994y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
  28. 28th August 1994A cuboid measures 9 cm by 3 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  29. 29th August 1994A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  30. 30th August 1994On 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?
  31. 31st August 1994A rectangle is 27 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.

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