Daily Practice · Higher Plus

February 1972 5-a-day

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February 1972

29 sheets · 145 questions · Grades 8-9

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The batch download puts all 5 tiers' February 1972 sheets in a single PDF, each tier behind its own divider page - 145 sheets in one file.

Every sheet in February 1972

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

  1. 1st February 1972A cuboid measures 7 cm by 13 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  2. 2nd February 1972A bag holds 6 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  3. 3rd February 1972On 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?
  4. 4th February 1972Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
  5. 5th February 1972Write x^2 + 8x + 13 in the form (x + a)^2 + b.
  6. 6th February 1972A train slows steadily from 24 m/s to rest in 4 seconds. Work out its deceleration.
  7. 7th February 1972The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
  8. 8th February 1972A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
  9. 9th February 1972A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
  10. 10th February 1972Simplify sqrt(80) + sqrt(20), giving your answer in the form a sqrt(b).
  11. 11th February 1972Work out the coordinates of the turning point of y = x^2 + 8x - 4.
  12. 12th February 1972y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
  13. 13th February 1972In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
  14. 14th February 1972The probability of winning a game is 1/8. A player expects 7 wins. How many games did they play?
  15. 15th February 1972On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
  16. 16th February 1972A rectangle is 17 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
  17. 17th February 1972Simplify (x^2 - 2x - 24)/(x + 4).
  18. 18th February 1972y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
  19. 19th February 1972In a vector proof you find that vector PQ = 5a - 5b and vector RS = 15a - 15b. What does this show about PQ and RS?
  20. 20th February 1972A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
  21. 21st February 1972A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
  22. 22nd February 1972Expand and simplify (5 + sqrt(5))(5 - sqrt(5)).
  23. 23rd February 1972In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
  24. 24th February 1972y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 81.
  25. 25th February 1972A cuboid measures 8 cm by 13 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  26. 26th February 1972A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  27. 27th February 1972On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  28. 28th February 1972A block has mass 520 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  29. 29th February 1972Make x the subject of 2x + 5 = y(x + 5).

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