Daily Practice · Higher Plus

June 1988 5-a-day

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June 1988

30 sheets · 150 questions · Grades 8-9

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Every sheet in June 1988

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

  1. 1st June 1988A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  2. 2nd June 1988On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
  3. 3rd June 1988Rationalise the denominator of 49/sqrt(7), giving your answer in its simplest form.
  4. 4th June 1988Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
  5. 5th June 1988y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
  6. 6th June 1988A cuboid measures 7 cm by 6 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  7. 7th June 1988A 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?
  8. 8th June 1988A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
  9. 9th June 1988Simplify sqrt(27) + sqrt(75), giving your answer in the form a sqrt(b).
  10. 10th June 1988Use the iteration x(n+1) = cube root of (9x(n) + 8) with x(0) = 5. Work out x(1) to 3 decimal places.
  11. 11th June 1988y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 9.
  12. 12th June 1988The 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.
  13. 13th June 1988A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
  14. 14th June 1988On 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?
  15. 15th June 1988A rectangle is 20 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
  16. 16th June 1988Work out the nth term of the quadratic sequence 7, 10, 15, 22, ...
  17. 17th June 1988A train slows steadily from 33 m/s to rest in 8 seconds. Work out its deceleration.
  18. 18th June 1988In 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.
  19. 19th June 1988The probability of winning a game is 1/8. A player expects 11 wins. How many games did they play?
  20. 20th June 1988A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
  21. 21st June 1988Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
  22. 22nd June 1988The point (4, -4) lies on y = f(x). Write down its image on y = -f(x).
  23. 23rd June 1988y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
  24. 24th June 1988In a vector proof you find that vector PQ = 6a + b and vector RS = 24a + 4b. What does this show about PQ and RS?
  25. 25th June 1988A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
  26. 26th June 1988On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
  27. 27th June 1988A block has mass 240 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  28. 28th June 1988Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
  29. 29th June 1988y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
  30. 30th June 1988A cuboid measures 12 cm by 7 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.

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