Daily Practice · Higher Plus

September 1965 5-a-day

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September 1965

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' September 1965 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in September 1965

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

  1. 1st September 1965A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
  2. 2nd September 1965Simplify sqrt(32) + sqrt(50), giving your answer in the form a sqrt(b).
  3. 3rd September 1965Write x^2 + 10x - 14 in the form (x + a)^2 + b.
  4. 4th September 1965y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
  5. 5th September 1965A cuboid measures 4 cm by 8 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  6. 6th September 1965A bag holds 4 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  7. 7th September 1965On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  8. 8th September 1965A rectangle is 29 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
  9. 9th September 1965Work out the coordinates of the turning point of y = x^2 - 8x - 4.
  10. 10th September 1965y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
  11. 11th September 1965The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
  12. 12th September 1965A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
  13. 13th September 1965A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
  14. 14th September 1965Expand and simplify (6 + sqrt(2))(6 - sqrt(2)).
  15. 15th September 1965Simplify (x^2 + 4x - 12)/(x + 6).
  16. 16th September 1965y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 36.
  17. 17th September 1965In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
  18. 18th September 1965The probability of winning a game is 3/5. A player expects 9 wins. How many games did they play?
  19. 19th September 1965On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  20. 20th September 1965A block has mass 250 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  21. 21st September 1965In an algebraic proof, how would you write a multiple of 9 in terms of an integer n?
  22. 22nd September 1965A train slows steadily from 37 m/s to rest in 5 seconds. Work out its deceleration.
  23. 23rd September 1965In a vector proof you find that vector PQ = 3a - 6b and vector RS = 15a - 30b. What does this show about PQ and RS?
  24. 24th September 1965A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
  25. 25th September 1965A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
  26. 26th September 1965x = 178 and y = 56, each correct to the nearest whole number. Work out the upper bound of x - y.
  27. 27th September 1965Make x the subject of 7x + 2 = y(x + 2).
  28. 28th September 1965y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
  29. 29th September 1965A cuboid measures 3 cm by 5 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  30. 30th September 1965A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?

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