Daily Practice · Higher Plus

April 1996 - Higher Plus 5-a-day

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April 1996

30 sheets · 150 questions · Grades 8-9

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The batch download puts all 5 tiers' April 1996 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in April 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 April 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.
  2. 2nd April 1996A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
  3. 3rd April 1996A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
  4. 4th April 1996Simplify sqrt(45) + sqrt(20), giving your answer in the form a sqrt(b).
  5. 5th April 1996Use the iteration x(n+1) = cube root of (12x(n) + 5) with x(0) = 2. Work out x(1) to 3 decimal places.
  6. 6th April 1996y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 4.
  7. 7th April 1996In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
  8. 8th April 1996The probability of winning a game is 2/5. A player expects 14 wins. How many games did they play?
  9. 9th April 1996On 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?
  10. 10th April 1996A rectangle is 27 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
  11. 11th April 1996Work out the nth term of the quadratic sequence 10, 15, 22, 31, ...
  12. 12th April 1996A train slows steadily from 34 m/s to rest in 5 seconds. Work out its deceleration.
  13. 13th April 1996In a vector proof you find that vector PQ = 4a + 6b and vector RS = 20a + 30b. What does this show about PQ and RS?
  14. 14th April 1996A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
  15. 15th April 1996A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
  16. 16th April 1996Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
  17. 17th April 1996The point (0, -3) lies on y = f(x). Write down its image on y = f(x) + 5.
  18. 18th April 1996y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
  19. 19th April 1996A cuboid measures 8 cm by 8 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  20. 20th April 1996A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  21. 21st April 1996On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  22. 22nd April 1996A block has mass 520 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  23. 23rd April 1996Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
  24. 24th April 1996y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
  25. 25th April 1996A cuboid measures 6 cm by 10 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  26. 26th April 1996A bag holds 7 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  27. 27th April 1996A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
  28. 28th April 1996x = 30 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
  29. 29th April 1996f(x) = 5x - 3 and g(x) = 5x + 6. Work out fg(-2).
  30. 30th April 1996y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 16.

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