Daily Practice · Higher Plus

October 1968 5-a-day

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October 1968

31 sheets · 155 questions · Grades 8-9

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Every sheet in October 1968

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 1968In 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.
  2. 2nd October 1968The probability of winning a game is 3/5. A player expects 21 wins. How many games did they play?
  3. 3rd October 1968A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
  4. 4th October 1968Rationalise the denominator of 121/sqrt(11), giving your answer in its simplest form.
  5. 5th October 1968Work out the coordinates of the turning point of y = x^2 - 4x - 13.
  6. 6th October 1968y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
  7. 7th October 1968In a vector proof you find that vector PQ = 2a + 3b and vector RS = 8a + 12b. What does this show about PQ and RS?
  8. 8th October 1968A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
  9. 9th October 1968On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
  10. 10th October 1968Simplify sqrt(72) + sqrt(98), giving your answer in the form a sqrt(b).
  11. 11th October 1968Simplify (x^2 - 9x + 8)/(x - 1).
  12. 12th October 1968y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
  13. 13th October 1968A cuboid measures 11 cm by 13 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  14. 14th October 1968A bag holds 9 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  15. 15th October 1968A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
  16. 16th October 1968A rectangle is 30 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
  17. 17th October 1968In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
  18. 18th October 1968y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 49.
  19. 19th October 1968A cuboid measures 8 cm by 12 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  20. 20th October 1968A bag holds 4 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  21. 21st October 1968On 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?
  22. 22nd October 1968Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
  23. 23rd October 1968Make x the subject of 6x + 3 = y(x + 3).
  24. 24th October 1968A train slows steadily from 39 m/s to rest in 5 seconds. Work out its deceleration.
  25. 25th October 1968The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
  26. 26th October 1968A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 6/55. Work out r.
  27. 27th October 1968A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
  28. 28th October 1968A block has mass 410 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  29. 29th October 1968Write 6/(x - 2) + 3/(x - 6) as a single fraction.
  30. 30th October 1968y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
  31. 31st October 1968In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.

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