Daily Practice · Higher Plus

September 1985 5-a-day

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September 1985

30 sheets · 150 questions · Grades 8-9

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Every sheet in September 1985

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

  1. 1st September 1985y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
  2. 2nd September 1985In 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.
  3. 3rd September 1985The probability of winning a game is 4/5. A player expects 40 wins. How many games did they play?
  4. 4th September 1985A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
  5. 5th September 1985Simplify sqrt(32) + sqrt(18), giving your answer in the form a sqrt(b).
  6. 6th September 1985The point (2, 0) lies on y = f(x). Write down its image on y = f(x - 2).
  7. 7th September 1985y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 36.
  8. 8th September 1985In a vector proof you find that vector PQ = 2a + b and vector RS = 6a + 3b. What does this show about PQ and RS?
  9. 9th September 1985A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
  10. 10th September 1985On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  11. 11th September 1985A rectangle is 20 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
  12. 12th September 1985Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
  13. 13th September 1985A train slows steadily from 23 m/s to rest in 8 seconds. Work out its deceleration.
  14. 14th September 1985A cuboid measures 5 cm by 5 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  15. 15th September 1985A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  16. 16th September 1985A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
  17. 17th September 1985Expand and simplify (6 + sqrt(7))(6 - sqrt(7)).
  18. 18th September 1985f(x) = 4x + 9 and g(x) = 3x + 3. Work out fg(2).
  19. 19th September 1985y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
  20. 20th September 1985A cuboid measures 9 cm by 7 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  21. 21st September 1985A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  22. 22nd September 1985On 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?
  23. 23rd September 1985A block has mass 520 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  24. 24th September 1985The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
  25. 25th September 1985y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 4.
  26. 26th September 1985The 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.
  27. 27th September 1985A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
  28. 28th September 1985A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
  29. 29th September 1985x = 158 and y = 118, each correct to the nearest whole number. Work out the upper bound of x - y.
  30. 30th September 1985A quadratic sequence starts 13, 34, 65, 106. Work out the second difference, and the coefficient of n^2.

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