Daily Practice · Higher Plus
December 1973 5-a-day
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The batch download puts all 5 tiers' December 1973 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1973
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1973A car covers 520 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.
- 2nd December 1973Use the iteration x(n+1) = cube root of (10x(n) + 3) with x(0) = 3. Work out x(1) to 3 decimal places.
- 3rd December 1973y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 9.
- 4th December 1973In 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.
- 5th December 1973The probability of winning a game is 1/4. A player expects 10 wins. How many games did they play?
- 6th December 1973On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th December 1973Rationalise the denominator of 14/sqrt(7), giving your answer in its simplest form.
- 8th December 1973Work out the nth term of the quadratic sequence 5, 7, 11, 17, ...
- 9th December 1973A train slows steadily from 20 m/s to rest in 5 seconds. Work out its deceleration.
- 10th December 1973In a vector proof you find that vector PQ = a - 4b and vector RS = 4a - 16b. What does this show about PQ and RS?
- 11th December 1973A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 12th December 1973A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 13th December 1973Simplify sqrt(32) + sqrt(72), giving your answer in the form a sqrt(b).
- 14th December 1973The point (0, 0) lies on y = f(x). Write down its image on y = f(-x).
- 15th December 1973y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 16th December 1973A cuboid measures 7 cm by 3 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th December 1973A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th December 1973On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 19th December 1973A rectangle is 9 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th December 1973Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 21st December 1973y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 22nd December 1973A cuboid measures 8 cm by 5 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd December 1973A bag holds 7 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th December 1973A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 25th December 1973Expand and simplify (2 + sqrt(5))(2 - sqrt(5)).
- 26th December 1973f(x) = 4x + 5 and g(x) = 3x - 5. Work out fg(-1).
- 27th December 1973y is directly proportional to sqrt(x). When x = 9, y = 12. Work out y when x = 4.
- 28th December 1973The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 29th December 1973A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 30th December 1973On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 31st December 1973A block has mass 450 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.