Daily Practice · Higher Plus

July 1973 5-a-day

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July 1973

31 sheets · 155 questions · Grades 8-9

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Every sheet in July 1973

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

  1. 1st July 1973The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
  2. 2nd July 1973A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
  3. 3rd July 1973On 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?
  4. 4th July 1973A rectangle is 7 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
  5. 5th July 1973Work out the coordinates of the turning point of y = x^2 + 2x + 9.
  6. 6th July 1973y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
  7. 7th July 1973In 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.
  8. 8th July 1973The probability of winning a game is 1/4. A player expects 12 wins. How many games did they play?
  9. 9th July 1973A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
  10. 10th July 1973Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
  11. 11th July 1973Simplify (x^2 - 12x + 35)/(x - 7).
  12. 12th July 1973y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 49.
  13. 13th July 1973In a vector proof you find that vector PQ = 4a + 4b and vector RS = 8a + 8b. What does this show about PQ and RS?
  14. 14th July 1973A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
  15. 15th July 1973On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  16. 16th July 1973A block has mass 330 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  17. 17th July 1973In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
  18. 18th July 1973A train slows steadily from 38 m/s to rest in 5 seconds. Work out its deceleration.
  19. 19th July 1973A cuboid measures 3 cm by 7 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  20. 20th July 1973A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  21. 21st July 1973A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
  22. 22nd July 1973x = 39 and y = 29, each correct to the nearest whole number. Work out the upper bound of x - y.
  23. 23rd July 1973Make x the subject of 8x + 4 = y(x + 4).
  24. 24th July 1973y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
  25. 25th July 1973A cuboid measures 14 cm by 6 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  26. 26th July 1973A bag holds 3 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  27. 27th July 1973On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
  28. 28th July 1973A car covers 540 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 July 1973Write 6/(x - 3) + 7/(x + 2) as a single fraction.
  30. 30th July 1973y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
  31. 31st July 1973The 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.

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