Daily Practice · Higher Plus

November 1970 5-a-day

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November 1970

30 sheets · 150 questions · Grades 8-9

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Every sheet in November 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 November 1970y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 49.
  2. 2nd November 1970A cuboid measures 5 cm by 10 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  3. 3rd November 1970A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  4. 4th November 1970On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  5. 5th November 1970Simplify sqrt(75) + sqrt(75), giving your answer in the form a sqrt(b).
  6. 6th November 1970Use the iteration x(n+1) = cube root of (10x(n) + 7) with x(0) = 2. Work out x(1) to 3 decimal places.
  7. 7th November 1970A train slows steadily from 24 m/s to rest in 10 seconds. Work out its deceleration.
  8. 8th November 1970A cuboid measures 7 cm by 13 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  9. 9th November 1970A bag holds 6 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  10. 10th November 1970A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
  11. 11th November 1970A rectangle is 13 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
  12. 12th November 1970Work out the nth term of the quadratic sequence -1, 12, 33, 62, ...
  13. 13th November 1970y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
  14. 14th November 1970The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
  15. 15th November 1970A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
  16. 16th November 1970On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
  17. 17th November 1970Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
  18. 18th November 1970The point (-5, -3) lies on y = f(x). Write down its image on y = f(-x).
  19. 19th November 1970y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
  20. 20th November 1970In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
  21. 21st November 1970The probability of winning a game is 2/5. A player expects 30 wins. How many games did they play?
  22. 22nd November 1970A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
  23. 23rd November 1970A block has mass 810 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  24. 24th November 1970Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
  25. 25th November 1970y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 64.
  26. 26th November 1970In a vector proof you find that vector PQ = 6a - 2b and vector RS = 24a - 8b. What does this show about PQ and RS?
  27. 27th November 1970A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
  28. 28th November 1970On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
  29. 29th November 1970x = 72 and y = 38, each correct to the nearest whole number. Work out the upper bound of x - y.
  30. 30th November 1970f(x) = 6x - 2 and g(x) = 5x - 5. Work out fg(0).

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