Daily Practice · Higher Plus

September 1977 5-a-day

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September 1977

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' September 1977 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in September 1977

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 1977y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 36.
  2. 2nd September 1977A cuboid measures 12 cm by 7 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  3. 3rd September 1977A bag holds 6 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  4. 4th September 1977On 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?
  5. 5th September 1977A block has mass 350 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  6. 6th September 1977Write x^2 + 16x + 4 in the form (x + a)^2 + b.
  7. 7th September 1977A train slows steadily from 39 m/s to rest in 8 seconds. Work out its deceleration.
  8. 8th September 1977The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
  9. 9th September 1977A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
  10. 10th September 1977A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
  11. 11th September 1977x = 75 and y = 28, each correct to the nearest whole number. Work out the upper bound of x - y.
  12. 12th September 1977Work out the coordinates of the turning point of y = x^2 - 2x - 4.
  13. 13th September 1977y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
  14. 14th September 1977In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
  15. 15th September 1977The probability of winning a game is 1/4. A player expects 5 wins. How many games did they play?
  16. 16th September 1977On 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?
  17. 17th September 1977A car covers 290 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  18. 18th September 1977Simplify (x^2 + 11x + 28)/(x + 7).
  19. 19th September 1977y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
  20. 20th September 1977In a vector proof you find that vector PQ = 5a + 3b and vector RS = 25a + 15b. What does this show about PQ and RS?
  21. 21st September 1977A bag holds 8 red and n blue counters. The probability of taking a red is 8/15. Work out n.
  22. 22nd September 1977A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
  23. 23rd September 1977Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
  24. 24th September 1977In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
  25. 25th September 1977y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 81.
  26. 26th September 1977A cuboid measures 6 cm by 10 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  27. 27th September 1977A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  28. 28th September 1977On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
  29. 29th September 1977Simplify sqrt(12) + sqrt(147), giving your answer in the form a sqrt(b).
  30. 30th September 1977Make x the subject of 7x + 6 = y(x + 6).

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