Daily Practice · Higher Plus
March 1961 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1961 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1961
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1961A bag holds 5 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd March 1961A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
- 3rd March 1961Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
- 4th March 1961A quadratic sequence starts -5, 3, 19, 43. Work out the second difference, and the coefficient of n^2.
- 5th March 1961y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 4.
- 6th March 1961The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 7th March 1961A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 28/45. Work out r.
- 8th March 1961On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 9th March 1961Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
- 10th March 1961Solve x^2 - 8x > 0.
- 11th March 1961A train slows steadily from 23 m/s to rest in 5 seconds. Work out its deceleration.
- 12th March 1961In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 13th March 1961The probability of winning a game is 3/4. A player expects 90 wins. How many games did they play?
- 14th March 1961A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 15th March 1961A rectangle is 30 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th March 1961Write x^2 + 2x - 10 in the form (x + a)^2 + b.
- 17th March 1961y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
- 18th March 1961In a vector proof you find that vector PQ = 5a + 5b and vector RS = 10a + 10b. What does this show about PQ and RS?
- 19th March 1961A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 20th March 1961On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 21st March 1961Expand and simplify (5 + sqrt(5))(5 - sqrt(5)).
- 22nd March 1961Work out the coordinates of the turning point of y = x^2 + 8x - 11.
- 23rd March 1961y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 24th March 1961A cuboid measures 11 cm by 14 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th March 1961A 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?
- 26th March 1961A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 27th March 1961A block has mass 810 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th March 1961Simplify (x^2 - 8x + 15)/(x - 3).
- 29th March 1961y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 36.
- 30th March 1961A cuboid measures 9 cm by 12 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st March 1961A bag holds 3 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?