Daily Practice · Higher Plus
January 1973 5-a-day
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The batch download puts all 5 tiers' January 1973 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1973
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1973y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 4.
- 2nd January 1973The 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.
- 3rd January 1973A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 4th January 1973On 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?
- 5th January 1973Rationalise the denominator of 55/sqrt(11), giving your answer in its simplest form.
- 6th January 1973Write 2/(x - 4) + 4/(x + 3) as a single fraction.
- 7th January 1973A train slows steadily from 30 m/s to rest in 10 seconds. Work out its deceleration.
- 8th January 1973In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 9th January 1973The probability of winning a game is 1/8. A player expects 10 wins. How many games did they play?
- 10th January 1973A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 11th January 1973Simplify sqrt(72) + sqrt(2), giving your answer in the form a sqrt(b).
- 12th January 1973Solve 9x^2 - 9x - 4 = 0.
- 13th January 1973y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 14th January 1973In a vector proof you find that vector PQ = 6a - 6b and vector RS = 24a - 24b. What does this show about PQ and RS?
- 15th January 1973A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 16th January 1973On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th January 1973A rectangle is 8 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th January 1973f(x) = 6x - 10. Work out the inverse function f^-1(x).
- 19th January 1973y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 20th January 1973A cuboid measures 6 cm by 12 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st January 1973A 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?
- 22nd January 1973A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 23rd January 1973Expand and simplify (8 + sqrt(11))(8 - sqrt(11)).
- 24th January 1973Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 25th January 1973y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 4.
- 26th January 1973A cuboid measures 14 cm by 6 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th January 1973A bag holds 6 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th January 1973On 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?
- 29th January 1973A block has mass 450 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th January 1973Use the iteration x(n+1) = cube root of (8x(n) + 8) with x(0) = 1. Work out x(1) to 3 decimal places.
- 31st January 1973A train slows steadily from 15 m/s to rest in 5 seconds. Work out its deceleration.