Daily Practice · Higher Plus
January 1972 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1972 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1972
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1972y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 2nd January 1972A cuboid measures 9 cm by 14 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd January 1972A bag holds 4 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th January 1972A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 5th January 1972A rectangle is 11 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th January 1972Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 7th January 1972y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 4.
- 8th January 1972The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 9th January 1972A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 10th January 1972On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 11th January 1972Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
- 12th January 1972f(x) = 6x - 8 and g(x) = 5x + 3. Work out fg(4).
- 13th January 1972A train slows steadily from 13 m/s to rest in 8 seconds. Work out its deceleration.
- 14th January 1972In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 15th January 1972The probability of winning a game is 1/5. A player expects 7 wins. How many games did they play?
- 16th January 1972A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 17th January 1972A block has mass 840 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th January 1972The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 19th January 1972y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
- 20th January 1972In a vector proof you find that vector PQ = 4a + 3b and vector RS = 12a + 9b. What does this show about PQ and RS?
- 21st January 1972A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 22nd January 1972On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd January 1972x = 197 and y = 128, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th January 1972A quadratic sequence starts 10, 19, 30, 43. Work out the second difference, and the coefficient of n^2.
- 25th January 1972y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 26th January 1972A cuboid measures 14 cm by 3 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th January 1972A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th January 1972A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 29th January 1972A car covers 400 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 30th January 1972Solve x^2 - 11x + 18 < 0.
- 31st January 1972y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 36.