Daily Practice · Higher Plus

November 1957 5-a-day

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November 1957

30 sheets · 150 questions · Grades 8-9

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Every sheet in November 1957

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 1957Rationalise the denominator of 28/sqrt(7), giving your answer in its simplest form.
  2. 2nd November 1957Solve x^2 - 2x - 15 > 0.
  3. 3rd November 1957A train slows steadily from 28 m/s to rest in 4 seconds. Work out its deceleration.
  4. 4th November 1957In a vector proof you find that vector PQ = a - 3b and vector RS = 3a - 9b. What does this show about PQ and RS?
  5. 5th November 1957A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
  6. 6th November 1957A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
  7. 7th November 1957Simplify sqrt(45) + sqrt(125), giving your answer in the form a sqrt(b).
  8. 8th November 1957Write x^2 - 16x + 11 in the form (x + a)^2 + b.
  9. 9th November 1957y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
  10. 10th November 1957A cuboid measures 4 cm by 7 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  11. 11th November 1957A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  12. 12th November 1957On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
  13. 13th November 1957A rectangle is 28 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
  14. 14th November 1957Work out the coordinates of the turning point of y = x^2 - 12x - 1.
  15. 15th November 1957y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
  16. 16th November 1957A cuboid measures 5 cm by 9 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  17. 17th November 1957A bag holds 3 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  18. 18th November 1957A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
  19. 19th November 1957Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
  20. 20th November 1957Simplify (x^2 + 6x - 16)/(x - 2).
  21. 21st November 1957y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 4.
  22. 22nd November 1957The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
  23. 23rd November 1957A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
  24. 24th November 1957On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
  25. 25th November 1957A block has mass 700 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  26. 26th November 1957In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 5 in terms of an integer n?
  27. 27th November 1957A train slows steadily from 12 m/s to rest in 5 seconds. Work out its deceleration.
  28. 28th November 1957In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
  29. 29th November 1957The probability of winning a game is 3/5. A player expects 36 wins. How many games did they play?
  30. 30th November 1957A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?

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