Daily Practice · Higher Plus

October 1978 5-a-day

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October 1978

31 sheets · 155 questions · Grades 8-9

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Every sheet in October 1978

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 1978The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
  2. 2nd October 1978y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
  3. 3rd October 1978The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
  4. 4th October 1978A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.
  5. 5th October 1978On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  6. 6th October 1978Rationalise the denominator of 88/sqrt(11), giving your answer in its simplest form.
  7. 7th October 1978A quadratic sequence starts 7, 12, 21, 34. Work out the second difference, and the coefficient of n^2.
  8. 8th October 1978y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
  9. 9th October 1978In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
  10. 10th October 1978The probability of winning a game is 5/8. A player expects 15 wins. How many games did they play?
  11. 11th October 1978A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
  12. 12th October 1978Simplify sqrt(75) + sqrt(12), giving your answer in the form a sqrt(b).
  13. 13th October 1978Solve x^2 + 4x - 12 < 0.
  14. 14th October 1978y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 4.
  15. 15th October 1978In a vector proof you find that vector PQ = a - 4b and vector RS = 2a - 8b. What does this show about PQ and RS?
  16. 16th October 1978A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
  17. 17th October 1978On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  18. 18th October 1978A rectangle is 28 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
  19. 19th October 1978Write x^2 + 14x - 14 in the form (x + a)^2 + b.
  20. 20th October 1978A train slows steadily from 26 m/s to rest in 4 seconds. Work out its deceleration.
  21. 21st October 1978A cuboid measures 12 cm by 4 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  22. 22nd October 1978A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  23. 23rd October 1978A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
  24. 24th October 1978Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
  25. 25th October 1978Work out the coordinates of the turning point of y = x^2 + 8x - 4.
  26. 26th October 1978y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
  27. 27th October 1978A cuboid measures 7 cm by 9 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  28. 28th October 1978A bag holds 3 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  29. 29th October 1978On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
  30. 30th October 1978A block has mass 790 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  31. 31st October 1978Simplify (x^2 + 3x - 18)/(x + 6).

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