Daily Practice · Higher Plus

November 1963 5-a-day

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November 1963

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' November 1963 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in November 1963

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 1963f(x) = 7x - 3. Work out the inverse function f^-1(x).
  2. 2nd November 1963y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
  3. 3rd November 1963In a vector proof you find that vector PQ = 6a + 5b and vector RS = 18a + 15b. What does this show about PQ and RS?
  4. 4th November 1963A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
  5. 5th November 1963On 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?
  6. 6th November 1963A rectangle is 29 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
  7. 7th November 1963Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
  8. 8th November 1963y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
  9. 9th November 1963A cuboid measures 10 cm by 6 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  10. 10th November 1963A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  11. 11th November 1963A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
  12. 12th November 1963Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
  13. 13th November 1963Use the iteration x(n+1) = cube root of (2x(n) + 4) with x(0) = 4. Work out x(1) to 3 decimal places.
  14. 14th November 1963y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 25.
  15. 15th November 1963A cuboid measures 11 cm by 9 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  16. 16th November 1963A bag holds 4 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  17. 17th November 1963On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  18. 18th November 1963A block has mass 600 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  19. 19th November 1963Work out the nth term of the quadratic sequence 4, 5, 8, 13, ...
  20. 20th November 1963A train slows steadily from 18 m/s to rest in 5 seconds. Work out its deceleration.
  21. 21st November 1963The 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.
  22. 22nd November 1963A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/22. Work out r.
  23. 23rd November 1963A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
  24. 24th November 1963x = 181 and y = 19, each correct to the nearest whole number. Work out the upper bound of x - y.
  25. 25th November 1963The point (-5, 0) lies on y = f(x). Write down its image on y = -f(x).
  26. 26th November 1963y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
  27. 27th November 1963In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
  28. 28th November 1963The probability of winning a game is 4/5. A player expects 56 wins. How many games did they play?
  29. 29th November 1963On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  30. 30th November 1963A car covers 650 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.

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