Daily Practice · Higher Plus

January 1970 5-a-day

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January 1970

31 sheets · 155 questions · Grades 8-9

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Every sheet in January 1970

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

  1. 1st January 1970A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
  2. 2nd January 1970A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
  3. 3rd January 1970A car covers 560 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  4. 4th January 1970Use the iteration x(n+1) = cube root of (4x(n) + 9) with x(0) = 3. Work out x(1) to 3 decimal places.
  5. 5th January 1970y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
  6. 6th January 1970A cuboid measures 13 cm by 10 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  7. 7th January 1970A 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?
  8. 8th January 1970On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  9. 9th January 1970Rationalise the denominator of 18/sqrt(6), giving your answer in its simplest form.
  10. 10th January 1970Work out the nth term of the quadratic sequence 5, 15, 29, 47, ...
  11. 11th January 1970y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
  12. 12th January 1970A cuboid measures 10 cm by 5 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  13. 13th January 1970A 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?
  14. 14th January 1970A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
  15. 15th January 1970Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
  16. 16th January 1970The point (-5, -5) lies on y = f(x). Write down its image on y = -f(x).
  17. 17th January 1970y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 9.
  18. 18th January 1970The 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.
  19. 19th January 1970A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
  20. 20th January 1970On 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?
  21. 21st January 1970A rectangle is 11 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
  22. 22nd January 1970Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
  23. 23rd January 1970A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
  24. 24th January 1970In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
  25. 25th January 1970The probability of winning a game is 1/5. A player expects 2 wins. How many games did they play?
  26. 26th January 1970A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
  27. 27th January 1970Expand and simplify (2 + sqrt(2))(2 - sqrt(2)).
  28. 28th January 1970f(x) = 6x - 9 and g(x) = 2x - 7. Work out fg(0).
  29. 29th January 1970y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
  30. 30th January 1970In a vector proof you find that vector PQ = 3a + 4b and vector RS = 15a + 20b. What does this show about PQ and RS?
  31. 31st January 1970A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.

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