Daily Practice · Higher Plus
January 1961 5-a-day
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The batch download puts all 5 tiers' January 1961 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1961
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1961A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 2nd January 1961A block has mass 280 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 3rd January 1961Write 5/(x + 3) + 4/(x - 4) as a single fraction.
- 4th January 1961y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 5th January 1961The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 6th January 1961A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 7th January 1961On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 8th January 1961x = 111 and y = 47, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th January 1961Solve 3x^2 + 5x - 2 = 0.
- 10th January 1961y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 11th January 1961In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 12th January 1961The probability of winning a game is 1/8. A player expects 7 wins. How many games did they play?
- 13th January 1961A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 14th January 1961A car covers 440 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 15th January 1961f(x) = 3x + 11. Work out the inverse function f^-1(x).
- 16th January 1961y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 25.
- 17th January 1961In a vector proof you find that vector PQ = a - 5b and vector RS = 3a - 15b. What does this show about PQ and RS?
- 18th January 1961A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 19th January 1961On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 20th January 1961Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 21st January 1961Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 22nd January 1961A train slows steadily from 28 m/s to rest in 10 seconds. Work out its deceleration.
- 23rd January 1961A cuboid measures 11 cm by 9 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th January 1961A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th January 1961A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 26th January 1961Simplify sqrt(12) + sqrt(48), giving your answer in the form a sqrt(b).
- 27th January 1961Use the iteration x(n+1) = cube root of (9x(n) + 9) with x(0) = 3. Work out x(1) to 3 decimal places.
- 28th January 1961y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 29th January 1961A cuboid measures 7 cm by 14 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th January 1961A bag holds 5 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st January 1961On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?