Daily Practice · Higher Plus
March 1954 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1954 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1954
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1954A cuboid measures 14 cm by 10 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd March 1954A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd March 1954A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 4th March 1954Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
- 5th March 1954The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 6th March 1954y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 7th March 1954A cuboid measures 10 cm by 9 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th March 1954A bag holds 7 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th March 1954On 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?
- 10th March 1954A rectangle is 18 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th March 1954A quadratic sequence starts 7, 28, 59, 100. Work out the second difference, and the coefficient of n^2.
- 12th March 1954y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 13th March 1954The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 14th March 1954A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 15th March 1954A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 16th March 1954Expand and simplify (9 + sqrt(7))(9 - sqrt(7)).
- 17th March 1954Solve x^2 - 7x + 12 < 0.
- 18th March 1954y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 25.
- 19th March 1954In 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.
- 20th March 1954The probability of winning a game is 4/5. A player expects 24 wins. How many games did they play?
- 21st March 1954On 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?
- 22nd March 1954A block has mass 520 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd March 1954Write x^2 - 6x - 7 in the form (x + a)^2 + b.
- 24th March 1954A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 25th March 1954In a vector proof you find that vector PQ = 5a - 4b and vector RS = 20a - 16b. What does this show about PQ and RS?
- 26th March 1954A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 27th March 1954A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 28th March 1954x = 88 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th March 1954Work out the coordinates of the turning point of y = x^2 - 6x + 3.
- 30th March 1954y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 31st March 1954A cuboid measures 4 cm by 15 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.