Daily Practice · Higher Plus

January 1977 5-a-day

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January 1977

31 sheets · 155 questions · Grades 8-9

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Every sheet in January 1977

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

  1. 1st January 1977A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
  2. 2nd January 1977x = 58 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
  3. 3rd January 1977Work out the nth term of the quadratic sequence 6, 23, 48, 81, ...
  4. 4th January 1977y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 49.
  5. 5th January 1977A cuboid measures 14 cm by 4 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  6. 6th January 1977A bag holds 3 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  7. 7th January 1977On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  8. 8th January 1977A car covers 770 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
  9. 9th January 1977The point (1, -4) lies on y = f(x). Write down its image on y = f(x) - 4.
  10. 10th January 1977A train slows steadily from 31 m/s to rest in 10 seconds. Work out its deceleration.
  11. 11th January 1977The 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.
  12. 12th January 1977A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
  13. 13th January 1977A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
  14. 14th January 1977Rationalise the denominator of 72/sqrt(6), giving your answer in its simplest form.
  15. 15th January 1977Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
  16. 16th January 1977y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
  17. 17th January 1977In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
  18. 18th January 1977The probability of winning a game is 2/5. A player expects 28 wins. How many games did they play?
  19. 19th January 1977On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
  20. 20th January 1977Simplify sqrt(20) + sqrt(125), giving your answer in the form a sqrt(b).
  21. 21st January 1977f(x) = 2x - 6 and g(x) = 3x + 1. Work out fg(-2).
  22. 22nd January 1977y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
  23. 23rd January 1977In a vector proof you find that vector PQ = 4a + 4b and vector RS = 20a + 20b. What does this show about PQ and RS?
  24. 24th January 1977A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
  25. 25th January 1977A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
  26. 26th January 1977A rectangle is 24 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
  27. 27th January 1977The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
  28. 28th January 1977y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 81.
  29. 29th January 1977A cuboid measures 7 cm by 15 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  30. 30th January 1977A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  31. 31st January 1977On 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?

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