Daily Practice · Higher Plus

July 1995 - Higher Plus 5-a-day

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July 1995

31 sheets · 155 questions · Grades 8-9

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Every sheet in July 1995

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 1995A bag holds 7 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  2. 2nd July 1995A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
  3. 3rd July 1995A block has mass 750 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  4. 4th July 1995The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
  5. 5th July 1995y is inversely proportional to x^2. When x = 2, y = 64. Work out y when x = 4.
  6. 6th July 1995The 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.
  7. 7th July 1995A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
  8. 8th July 1995On 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?
  9. 9th July 1995x = 161 and y = 96, each correct to the nearest whole number. Work out the upper bound of x - y.
  10. 10th July 1995A quadratic sequence starts 7, 23, 49, 85. Work out the second difference, and the coefficient of n^2.
  11. 11th July 1995y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
  12. 12th July 1995In 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.
  13. 13th July 1995The probability of winning a game is 3/5. A player expects 78 wins. How many games did they play?
  14. 14th July 1995A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
  15. 15th July 1995A car covers 860 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  16. 16th July 1995Solve x^2 - 13x + 30 < 0.
  17. 17th July 1995y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 25.
  18. 18th July 1995In a vector proof you find that vector PQ = 3a + 4b and vector RS = 9a + 12b. What does this show about PQ and RS?
  19. 19th July 1995A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
  20. 20th July 1995On 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?
  21. 21st July 1995Rationalise the denominator of 9/sqrt(3), giving your answer in its simplest form.
  22. 22nd July 1995Write x^2 - 8x - 4 in the form (x + a)^2 + b.
  23. 23rd July 1995A train slows steadily from 28 m/s to rest in 10 seconds. Work out its deceleration.
  24. 24th July 1995A cuboid measures 7 cm by 9 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  25. 25th July 1995A 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?
  26. 26th July 1995A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 0.6. How many values in total?
  27. 27th July 1995Simplify sqrt(80) + sqrt(125), giving your answer in the form a sqrt(b).
  28. 28th July 1995Work out the coordinates of the turning point of y = x^2 - 6x - 12.
  29. 29th July 1995y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.
  30. 30th July 1995A cuboid measures 9 cm by 10 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  31. 31st July 1995A bag holds 5 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?

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