Daily Practice · Higher Plus

January 1979 5-a-day

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January 1979

31 sheets · 155 questions · Grades 8-9

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Every sheet in January 1979

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 1979The 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.
  2. 2nd January 1979A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
  3. 3rd January 1979A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
  4. 4th January 1979Simplify sqrt(72) + sqrt(72), giving your answer in the form a sqrt(b).
  5. 5th January 1979f(x) = 4x + 4 and g(x) = 2x + 3. Work out fg(6).
  6. 6th January 1979y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
  7. 7th January 1979In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
  8. 8th January 1979The probability of winning a game is 3/8. A player expects 30 wins. How many games did they play?
  9. 9th January 1979On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
  10. 10th January 1979A rectangle is 20 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
  11. 11th January 1979The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
  12. 12th January 1979y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
  13. 13th January 1979In a vector proof you find that vector PQ = a - 3b and vector RS = 2a - 6b. What does this show about PQ and RS?
  14. 14th January 1979A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
  15. 15th January 1979A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
  16. 16th January 1979Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
  17. 17th January 1979A quadratic sequence starts 11, 19, 31, 47. Work out the second difference, and the coefficient of n^2.
  18. 18th January 1979y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 81.
  19. 19th January 1979A cuboid measures 7 cm by 11 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
  20. 20th January 1979A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
  21. 21st January 1979On 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?
  22. 22nd January 1979A block has mass 730 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
  23. 23rd January 1979Solve x^2 + 12x + 32 < 0.
  24. 24th January 1979A train slows steadily from 29 m/s to rest in 4 seconds. Work out its deceleration.
  25. 25th January 1979A cuboid measures 4 cm by 4 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
  26. 26th January 1979A bag holds 7 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
  27. 27th January 1979A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
  28. 28th January 1979x = 195 and y = 163, each correct to the nearest whole number. Work out the upper bound of x - y.
  29. 29th January 1979Write x^2 - 12x - 11 in the form (x + a)^2 + b.
  30. 30th January 1979y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
  31. 31st January 1979The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.

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