Daily Practice · Higher Plus

April 1953 5-a-day

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April 1953

30 sheets · 150 questions · Grades 8-9

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Every sheet in April 1953

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 1953A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
  2. 2nd April 1953Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
  3. 3rd April 1953Use the iteration x(n+1) = cube root of (8x(n) + 8) with x(0) = 5. Work out x(1) to 3 decimal places.
  4. 4th April 1953y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
  5. 5th April 1953A cuboid measures 5 cm by 3 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  6. 6th April 1953A 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?
  7. 7th April 1953On 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?
  8. 8th April 1953A rectangle is 12 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
  9. 9th April 1953Work out the nth term of the quadratic sequence 0, 2, 6, 12, ...
  10. 10th April 1953y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
  11. 11th April 1953A cuboid measures 8 cm by 14 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  12. 12th April 1953A bag holds 4 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  13. 13th April 1953A 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?
  14. 14th April 1953Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
  15. 15th April 1953The point (3, 3) lies on y = f(x). Write down its image on y = -f(x).
  16. 16th April 1953y is directly proportional to sqrt(x). When x = 49, y = 56. Work out y when x = 9.
  17. 17th April 1953The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
  18. 18th April 1953A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/66. Work out r.
  19. 19th April 1953On 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?
  20. 20th April 1953A block has mass 640 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  21. 21st April 1953Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
  22. 22nd April 1953A train slows steadily from 12 m/s to rest in 10 seconds. Work out its deceleration.
  23. 23rd April 1953In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
  24. 24th April 1953The probability of winning a game is 2/5. A player expects 10 wins. How many games did they play?
  25. 25th April 1953A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
  26. 26th April 1953x = 49 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.
  27. 27th April 1953f(x) = 2x + 3 and g(x) = 4x - 4. Work out fg(5).
  28. 28th April 1953y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
  29. 29th April 1953In a vector proof you find that vector PQ = 6a + 4b and vector RS = 12a + 8b. What does this show about PQ and RS?
  30. 30th April 1953A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.

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