Daily Practice · Higher Plus
March 1953 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1953 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1953A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 2nd March 1953On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 3rd March 1953Expand and simplify (8 + sqrt(11))(8 - sqrt(11)).
- 4th March 1953Make x the subject of 7x + 5 = y(x + 5).
- 5th March 1953A train slows steadily from 17 m/s to rest in 10 seconds. Work out its deceleration.
- 6th March 1953A cuboid measures 9 cm by 12 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th March 1953A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th March 1953A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 9th March 1953A block has mass 900 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th March 1953Write 7/(x - 2) + 2/(x - 5) as a single fraction.
- 11th March 1953y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 12th March 1953A cuboid measures 12 cm by 9 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th March 1953A bag holds 7 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th March 1953On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 15th March 1953x = 61 and y = 48, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th March 1953Solve 12x^2 - 29x + 15 = 0.
- 17th March 1953y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 18th March 1953The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 19th March 1953A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 20th March 1953A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 21st March 1953A car covers 300 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.
- 22nd March 1953f(x) = 5x + 11. Work out the inverse function f^-1(x).
- 23rd March 1953y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 64.
- 24th March 1953In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 25th March 1953The probability of winning a game is 2/5. A player expects 10 wins. How many games did they play?
- 26th March 1953On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 27th March 1953Rationalise the denominator of 30/sqrt(5), giving your answer in its simplest form.
- 28th March 1953Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.
- 29th March 1953A train slows steadily from 39 m/s to rest in 8 seconds. Work out its deceleration.
- 30th March 1953In a vector proof you find that vector PQ = 3a - 2b and vector RS = 15a - 10b. What does this show about PQ and RS?
- 31st March 1953A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.