Daily Practice · Higher Plus

June 1969 5-a-day

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June 1969

30 sheets · 150 questions · Grades 8-9

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Every sheet in June 1969

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 1969x = 150 and y = 131, each correct to the nearest whole number. Work out the upper bound of x - y.
  2. 2nd June 1969f(x) = 2x - 12. Work out the inverse function f^-1(x).
  3. 3rd June 1969y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
  4. 4th June 1969In a vector proof you find that vector PQ = 4a + 2b and vector RS = 8a + 4b. What does this show about PQ and RS?
  5. 5th June 1969A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
  6. 6th June 1969On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  7. 7th June 1969A car covers 230 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  8. 8th June 1969Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.
  9. 9th June 1969y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
  10. 10th June 1969A cuboid measures 14 cm by 12 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  11. 11th June 1969A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  12. 12th June 1969A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
  13. 13th June 1969Rationalise the denominator of 30/sqrt(3), giving your answer in its simplest form.
  14. 14th June 1969Use the iteration x(n+1) = cube root of (5x(n) + 2) with x(0) = 1. Work out x(1) to 3 decimal places.
  15. 15th June 1969y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 64.
  16. 16th June 1969A cuboid measures 13 cm by 11 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  17. 17th June 1969A bag holds 3 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  18. 18th June 1969On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
  19. 19th June 1969Simplify sqrt(45) + sqrt(125), giving your answer in the form a sqrt(b).
  20. 20th June 1969Work out the nth term of the quadratic sequence 7, 20, 41, 70, ...
  21. 21st June 1969A train slows steadily from 25 m/s to rest in 5 seconds. Work out its deceleration.
  22. 22nd June 1969The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
  23. 23rd June 1969A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
  24. 24th June 1969A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
  25. 25th June 1969A rectangle is 23 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
  26. 26th June 1969The point (-4, -1) lies on y = f(x). Write down its image on y = f(x) - 1.
  27. 27th June 1969y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
  28. 28th June 1969In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
  29. 29th June 1969The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
  30. 30th June 1969On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?

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