Daily Practice · Higher Plus
March 1957 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1957 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1957Use the iteration x(n+1) = cube root of (7x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.
- 2nd March 1957y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 4.
- 3rd March 1957In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 4th March 1957The probability of winning a game is 5/8. A player expects 15 wins. How many games did they play?
- 5th March 1957On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 6th March 1957A rectangle is 5 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th March 1957Work out the nth term of the quadratic sequence 2, 9, 22, 41, ...
- 8th March 1957A train slows steadily from 18 m/s to rest in 8 seconds. Work out its deceleration.
- 9th March 1957In a vector proof you find that vector PQ = a - b and vector RS = 2a - 2b. What does this show about PQ and RS?
- 10th March 1957A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 11th March 1957A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 12th March 1957Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
- 13th March 1957The point (-1, 2) lies on y = f(x). Write down its image on y = f(x) + 6.
- 14th March 1957y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 15th March 1957A cuboid measures 6 cm by 5 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th March 1957A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th March 1957On 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?
- 18th March 1957A block has mass 360 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th March 1957Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 20th March 1957y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 21st March 1957A cuboid measures 7 cm by 6 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd March 1957A bag holds 6 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd March 1957A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 24th March 1957x = 33 and y = 9, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th March 1957f(x) = 3x - 7 and g(x) = 2x - 3. Work out fg(-1).
- 26th March 1957y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 4.
- 27th March 1957The 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.
- 28th March 1957A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 29th March 1957On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th March 1957A car covers 210 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.
- 31st March 1957The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.