Daily Practice · Higher Plus

June 1976 5-a-day

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June 1976

30 sheets · 150 questions · Grades 8-9

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Every sheet in June 1976

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 1976Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
  2. 2nd June 1976y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 49.
  3. 3rd June 1976A cuboid measures 5 cm by 15 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  4. 4th June 1976A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  5. 5th June 1976On 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?
  6. 6th June 1976x = 182 and y = 149, each correct to the nearest whole number. Work out the upper bound of x - y.
  7. 7th June 1976Use the iteration x(n+1) = cube root of (2x(n) + 4) with x(0) = 5. Work out x(1) to 3 decimal places.
  8. 8th June 1976A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.
  9. 9th June 1976A cuboid measures 4 cm by 9 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  10. 10th June 1976A bag holds 4 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  11. 11th June 1976A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
  12. 12th June 1976A car covers 270 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  13. 13th June 1976Work out the nth term of the quadratic sequence 9, 17, 31, 51, ...
  14. 14th June 1976y is inversely proportional to x^2. When x = 3, y = 75. Work out y when x = 5.
  15. 15th June 1976The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
  16. 16th June 1976A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
  17. 17th June 1976On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  18. 18th June 1976Rationalise the denominator of 66/sqrt(6), giving your answer in its simplest form.
  19. 19th June 1976The point (0, -3) lies on y = f(x). Write down its image on y = f(-x).
  20. 20th June 1976y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
  21. 21st June 1976In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
  22. 22nd June 1976The probability of winning a game is 2/5. A player expects 16 wins. How many games did they play?
  23. 23rd June 1976A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
  24. 24th June 1976Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
  25. 25th June 1976Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
  26. 26th June 1976y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 36.
  27. 27th June 1976In a vector proof you find that vector PQ = a - 2b and vector RS = 4a - 8b. What does this show about PQ and RS?
  28. 28th June 1976A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.
  29. 29th June 1976On 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?
  30. 30th June 1976A rectangle is 24 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.

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