Daily Practice · Higher Plus

April 1973 5-a-day

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April 1973

30 sheets · 150 questions · Grades 8-9

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Every sheet in April 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 April 1973y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
  2. 2nd April 1973The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
  3. 3rd April 1973A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.
  4. 4th April 1973A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
  5. 5th April 1973Simplify sqrt(45) + sqrt(5), giving your answer in the form a sqrt(b).
  6. 6th April 1973In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 9 in terms of an integer n?
  7. 7th April 1973y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 4.
  8. 8th April 1973In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
  9. 9th April 1973The probability of winning a game is 3/5. A player expects 48 wins. How many games did they play?
  10. 10th April 1973On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
  11. 11th April 1973A rectangle is 12 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
  12. 12th April 1973Make x the subject of 4x + 3 = y(x + 3).
  13. 13th April 1973A train slows steadily from 27 m/s to rest in 4 seconds. Work out its deceleration.
  14. 14th April 1973In a vector proof you find that vector PQ = a - 5b and vector RS = 4a - 20b. What does this show about PQ and RS?
  15. 15th April 1973A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
  16. 16th April 1973A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
  17. 17th April 1973Expand and simplify (6 + sqrt(5))(6 - sqrt(5)).
  18. 18th April 1973Write 7/(x - 6) + 5/(x - 2) as a single fraction.
  19. 19th April 1973y is inversely proportional to x^2. When x = 3, y = 64. Work out y when x = 4.
  20. 20th April 1973A cuboid measures 9 cm by 8 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  21. 21st April 1973A 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?
  22. 22nd April 1973On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  23. 23rd April 1973A block has mass 420 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  24. 24th April 1973Solve 12x^2 - x - 20 = 0.
  25. 25th April 1973y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
  26. 26th April 1973A cuboid measures 11 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  27. 27th April 1973A bag holds 4 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  28. 28th April 1973A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
  29. 29th April 1973x = 59 and y = 19, each correct to the nearest whole number. Work out the upper bound of x - y.
  30. 30th April 1973f(x) = 4x + 5. Work out the inverse function f^-1(x).

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