Daily Practice · Higher Plus

June 1996 - Higher Plus 5-a-day

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June 1996

30 sheets · 150 questions · Grades 8-9

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Every sheet in June 1996

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 1996A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
  2. 2nd June 1996A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
  3. 3rd June 1996A block has mass 250 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  4. 4th June 1996Simplify (x^2 + 5x - 6)/(x - 1).
  5. 5th June 1996y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
  6. 6th June 1996In 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.
  7. 7th June 1996The probability of winning a game is 1/5. A player expects 4 wins. How many games did they play?
  8. 8th June 1996On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
  9. 9th June 1996x = 86 and y = 50, each correct to the nearest whole number. Work out the upper bound of x - y.
  10. 10th June 1996In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
  11. 11th June 1996y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
  12. 12th June 1996In a vector proof you find that vector PQ = 5a + 4b and vector RS = 25a + 20b. What does this show about PQ and RS?
  13. 13th June 1996A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
  14. 14th June 1996A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
  15. 15th June 1996A car covers 470 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  16. 16th June 1996Make x the subject of 5x + 8 = y(x + 8).
  17. 17th June 1996y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 49.
  18. 18th June 1996A cuboid measures 6 cm by 3 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  19. 19th June 1996A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  20. 20th June 1996On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  21. 21st June 1996Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
  22. 22nd June 1996Write 7/(x + 6) + 3/(x - 1) as a single fraction.
  23. 23rd June 1996A train slows steadily from 29 m/s to rest in 8 seconds. Work out its deceleration.
  24. 24th June 1996A cuboid measures 6 cm by 5 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  25. 25th June 1996A bag holds 4 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  26. 26th June 1996A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?
  27. 27th June 1996Simplify sqrt(20) + sqrt(80), giving your answer in the form a sqrt(b).
  28. 28th June 1996Solve 15x^2 + 28x + 5 = 0.
  29. 29th June 1996y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
  30. 30th June 1996The 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.

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