Daily Practice · Higher Plus

September 1968 5-a-day

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September 1968

30 sheets · 150 questions · Grades 8-9

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Every sheet in September 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 September 1968In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
  2. 2nd September 1968The probability of winning a game is 1/2. A player expects 10 wins. How many games did they play?
  3. 3rd September 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?
  4. 4th September 1968A rectangle is 17 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
  5. 5th September 1968f(x) = 6x - 2 and g(x) = 3x + 8. Work out fg(4).
  6. 6th September 1968A train slows steadily from 19 m/s to rest in 5 seconds. Work out its deceleration.
  7. 7th September 1968In a vector proof you find that vector PQ = 5a + b and vector RS = 20a + 4b. What does this show about PQ and RS?
  8. 8th September 1968A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
  9. 9th September 1968A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
  10. 10th September 1968Expand and simplify (5 + sqrt(10))(5 - sqrt(10)).
  11. 11th September 1968The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
  12. 12th September 1968y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
  13. 13th September 1968A cuboid measures 14 cm by 13 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  14. 14th September 1968A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  15. 15th September 1968On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
  16. 16th September 1968A block has mass 400 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  17. 17th September 1968A quadratic sequence starts 17, 35, 61, 95. Work out the second difference, and the coefficient of n^2.
  18. 18th September 1968y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
  19. 19th September 1968A cuboid measures 9 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  20. 20th September 1968A bag holds 7 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  21. 21st September 1968A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
  22. 22nd September 1968x = 38 and y = 24, each correct to the nearest whole number. Work out the upper bound of x - y.
  23. 23rd September 1968Solve x^2 + 10x + 16 < 0.
  24. 24th September 1968y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 9.
  25. 25th September 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 September 1968A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
  27. 27th September 1968On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
  28. 28th September 1968A car covers 370 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.
  29. 29th September 1968Write x^2 - 4x + 8 in the form (x + a)^2 + b.
  30. 30th September 1968A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.

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