Daily Practice · Higher Plus

August 1970 5-a-day

← Today's Higher Plus sheet

August 1970

31 sheets · 155 questions · Grades 8-9

Printing for a group?

The batch download puts all 5 tiers' August 1970 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.

Every sheet in August 1970

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 1970A car covers 520 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  2. 2nd August 1970Work out the nth term of the quadratic sequence 4, 9, 18, 31, ...
  3. 3rd August 1970A train slows steadily from 38 m/s to rest in 10 seconds. Work out its deceleration.
  4. 4th August 1970A cuboid measures 12 cm by 4 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  5. 5th August 1970A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  6. 6th August 1970A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
  7. 7th August 1970Rationalise the denominator of 60/sqrt(5), giving your answer in its simplest form.
  8. 8th August 1970The point (-3, -6) lies on y = f(x). Write down its image on y = f(x - 4).
  9. 9th August 1970y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
  10. 10th August 1970A cuboid measures 5 cm by 8 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  11. 11th August 1970A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  12. 12th August 1970On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
  13. 13th August 1970Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
  14. 14th August 1970Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
  15. 15th August 1970y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
  16. 16th August 1970The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
  17. 17th August 1970A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
  18. 18th August 1970A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
  19. 19th August 1970A rectangle is 29 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
  20. 20th August 1970f(x) = 2x - 6 and g(x) = 5x + 7. Work out fg(2).
  21. 21st August 1970y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 64.
  22. 22nd August 1970In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
  23. 23rd August 1970The probability of winning a game is 4/5. A player expects 96 wins. How many games did they play?
  24. 24th August 1970On 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?
  25. 25th August 1970Expand and simplify (6 + sqrt(5))(6 - sqrt(5)).
  26. 26th August 1970The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
  27. 27th August 1970A train slows steadily from 26 m/s to rest in 10 seconds. Work out its deceleration.
  28. 28th August 1970In a vector proof you find that vector PQ = 6a + 2b and vector RS = 18a + 6b. What does this show about PQ and RS?
  29. 29th August 1970A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
  30. 30th August 1970A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
  31. 31st August 1970A block has mass 570 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.

The same month at another level