Daily Practice · Higher Plus

July 1964 5-a-day

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July 1964

31 sheets · 155 questions · Grades 8-9

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Every sheet in July 1964

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

  1. 1st July 1964A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
  2. 2nd July 1964On 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?
  3. 3rd July 1964Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
  4. 4th July 1964The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
  5. 5th July 1964y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
  6. 6th July 1964A cuboid measures 14 cm by 14 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  7. 7th July 1964A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  8. 8th July 1964A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
  9. 9th July 1964Simplify sqrt(18) + sqrt(18), giving your answer in the form a sqrt(b).
  10. 10th July 1964A quadratic sequence starts 8, 19, 38, 65. Work out the second difference, and the coefficient of n^2.
  11. 11th July 1964y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 36.
  12. 12th July 1964A cuboid measures 7 cm by 9 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  13. 13th July 1964A bag holds 5 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  14. 14th July 1964On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
  15. 15th July 1964A rectangle is 23 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
  16. 16th July 1964Solve x^2 + 11x + 24 < 0.
  17. 17th July 1964A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
  18. 18th July 1964The 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.
  19. 19th July 1964A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 6/55. Work out r.
  20. 20th July 1964A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
  21. 21st July 1964Expand and simplify (3 + sqrt(11))(3 - sqrt(11)).
  22. 22nd July 1964Write x^2 - 8x - 14 in the form (x + a)^2 + b.
  23. 23rd July 1964y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
  24. 24th July 1964In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
  25. 25th July 1964The probability of winning a game is 5/8. A player expects 30 wins. How many games did they play?
  26. 26th July 1964On 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?
  27. 27th July 1964A block has mass 700 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  28. 28th July 1964Work out the coordinates of the turning point of y = x^2 - 12x + 7.
  29. 29th July 1964y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
  30. 30th July 1964In a vector proof you find that vector PQ = 6a + 4b and vector RS = 12a + 8b. What does this show about PQ and RS?
  31. 31st July 1964A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.

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