Daily Practice · Higher Plus

February 1975 5-a-day

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February 1975

28 sheets · 140 questions · Grades 8-9

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Every sheet in February 1975

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 1975Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
  2. 2nd February 1975y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
  3. 3rd February 1975In a vector proof you find that vector PQ = 2a + 5b and vector RS = 4a + 10b. What does this show about PQ and RS?
  4. 4th February 1975A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
  5. 5th February 1975A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
  6. 6th February 1975Simplify sqrt(18) + sqrt(8), giving your answer in the form a sqrt(b).
  7. 7th February 1975f(x) = 6x + 4 and g(x) = 3x + 3. Work out fg(-2).
  8. 8th February 1975y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 9.
  9. 9th February 1975A cuboid measures 14 cm by 13 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  10. 10th February 1975A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  11. 11th February 1975On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
  12. 12th February 1975A rectangle is 26 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
  13. 13th February 1975The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
  14. 14th February 1975A train slows steadily from 39 m/s to rest in 8 seconds. Work out its deceleration.
  15. 15th February 1975A cuboid measures 14 cm by 5 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  16. 16th February 1975A bag holds 5 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  17. 17th February 1975A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
  18. 18th February 1975Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
  19. 19th February 1975A quadratic sequence starts 4, 15, 30, 49. Work out the second difference, and the coefficient of n^2.
  20. 20th February 1975y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
  21. 21st February 1975The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
  22. 22nd February 1975A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
  23. 23rd February 1975On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  24. 24th February 1975A block has mass 530 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  25. 25th February 1975Solve x^2 - x - 12 < 0.
  26. 26th February 1975y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
  27. 27th February 1975In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
  28. 28th February 1975The probability of winning a game is 1/2. A player expects 30 wins. How many games did they play?

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