Daily Practice · Higher Plus

October 2000 - Higher Plus 5-a-day

Every Higher Plus sheet published in October 2000, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.

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October 2000

31 sheets · 155 questions · Grades 8-9

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The batch download puts all 5 tiers' October 2000 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in October 2000

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 2000A cuboid measures 13 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  2. 2nd October 2000A 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?
  3. 3rd October 2000A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
  4. 4th October 2000A rectangle is 15 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
  5. 5th October 2000The point (5, -3) lies on y = f(x). Write down its image on y = f(x) - 6.
  6. 6th October 2000y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
  7. 7th October 2000The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
  8. 8th October 2000A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
  9. 9th October 2000On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  10. 10th October 2000Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
  11. 11th October 2000Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
  12. 12th October 2000y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
  13. 13th October 2000In 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.
  14. 14th October 2000The probability of winning a game is 1/10. A player expects 6 wins. How many games did they play?
  15. 15th October 2000A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
  16. 16th October 2000A block has mass 340 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  17. 17th October 2000f(x) = 5x + 4 and g(x) = 2x + 3. Work out fg(6).
  18. 18th October 2000y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 16.
  19. 19th October 2000In a vector proof you find that vector PQ = 3a + 6b and vector RS = 12a + 24b. What does this show about PQ and RS?
  20. 20th October 2000A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
  21. 21st October 2000On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
  22. 22nd October 2000x = 78 and y = 24, each correct to the nearest whole number. Work out the upper bound of x - y.
  23. 23rd October 2000The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
  24. 24th October 2000A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
  25. 25th October 2000A cuboid measures 5 cm by 5 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  26. 26th October 2000A bag holds 4 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  27. 27th October 2000A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
  28. 28th October 2000A car covers 240 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.
  29. 29th October 2000A quadratic sequence starts 1, 14, 35, 64. Work out the second difference, and the coefficient of n^2.
  30. 30th October 2000y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
  31. 31st October 2000A cuboid measures 4 cm by 5 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.

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