Daily Practice · Higher Plus

April 1954 5-a-day

← Today's Higher Plus sheet

April 1954

30 sheets · 150 questions · Grades 8-9

Printing for a group?

The batch download puts all 5 tiers' April 1954 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.

Every sheet in April 1954

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 1954A 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?
  2. 2nd April 1954On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
  3. 3rd April 1954A car covers 690 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  4. 4th April 1954Simplify (x^2 + 7x + 12)/(x + 4).
  5. 5th April 1954y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
  6. 6th April 1954A cuboid measures 10 cm by 11 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  7. 7th April 1954A bag holds 3 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  8. 8th April 1954A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
  9. 9th April 1954Rationalise the denominator of 60/sqrt(5), giving your answer in its simplest form.
  10. 10th April 1954In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
  11. 11th April 1954y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 49.
  12. 12th April 1954The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
  13. 13th April 1954A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
  14. 14th April 1954On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
  15. 15th April 1954Simplify sqrt(8) + sqrt(98), giving your answer in the form a sqrt(b).
  16. 16th April 1954Make x the subject of 4x + 4 = y(x + 4).
  17. 17th April 1954A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
  18. 18th April 1954In 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.
  19. 19th April 1954The probability of winning a game is 1/2. A player expects 24 wins. How many games did they play?
  20. 20th April 1954A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
  21. 21st April 1954A rectangle is 17 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
  22. 22nd April 1954Write 7/(x + 1) + 2/(x + 4) as a single fraction.
  23. 23rd April 1954y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
  24. 24th April 1954In a vector proof you find that vector PQ = 4a + 4b and vector RS = 16a + 16b. What does this show about PQ and RS?
  25. 25th April 1954A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
  26. 26th April 1954On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  27. 27th April 1954Expand and simplify (5 + sqrt(11))(5 - sqrt(11)).
  28. 28th April 1954Solve 6x^2 + x - 2 = 0.
  29. 29th April 1954y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
  30. 30th April 1954A cuboid measures 6 cm by 15 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.

The same month at another level