Daily Practice · Higher Plus

August 1976 5-a-day

← Today's Higher Plus sheet

August 1976

31 sheets · 155 questions · Grades 8-9

Printing for a group?

The batch download puts all 5 tiers' August 1976 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in August 1976

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

  1. 1st August 1976y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
  2. 2nd August 1976A cuboid measures 12 cm by 12 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  3. 3rd August 1976A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  4. 4th August 1976On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
  5. 5th August 1976Simplify sqrt(80) + sqrt(80), giving your answer in the form a sqrt(b).
  6. 6th August 1976Simplify (x^2 + 10x + 24)/(x + 6).
  7. 7th August 1976y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
  8. 8th August 1976A cuboid measures 5 cm by 13 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  9. 9th August 1976A bag holds 4 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  10. 10th August 1976A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
  11. 11th August 1976A rectangle is 23 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
  12. 12th August 1976In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
  13. 13th August 1976y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 64.
  14. 14th August 1976The 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.
  15. 15th August 1976A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
  16. 16th August 1976On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
  17. 17th August 1976Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
  18. 18th August 1976Make x the subject of 2x + 8 = y(x + 8).
  19. 19th August 1976A train slows steadily from 35 m/s to rest in 8 seconds. Work out its deceleration.
  20. 20th August 1976In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
  21. 21st August 1976The probability of winning a game is 1/4. A player expects 10 wins. How many games did they play?
  22. 22nd August 1976A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
  23. 23rd August 1976A block has mass 860 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  24. 24th August 1976Write 4/(x + 1) + 6/(x + 5) as a single fraction.
  25. 25th August 1976y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.
  26. 26th August 1976In a vector proof you find that vector PQ = a + 6b and vector RS = 2a + 12b. What does this show about PQ and RS?
  27. 27th August 1976A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
  28. 28th August 1976On 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?
  29. 29th August 1976x = 41 and y = 15, each correct to the nearest whole number. Work out the upper bound of x - y.
  30. 30th August 1976Solve 5x^2 + 18x - 8 = 0.
  31. 31st August 1976y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.

The same month at another level