Daily Practice · Higher Plus
February 1954 5-a-day
Printing for a group?
The batch download puts all 5 tiers' February 1954 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1954
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1954On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 2nd February 1954Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 3rd February 1954Use the iteration x(n+1) = cube root of (8x(n) + 4) with x(0) = 5. Work out x(1) to 3 decimal places.
- 4th February 1954A train slows steadily from 19 m/s to rest in 4 seconds. Work out its deceleration.
- 5th February 1954A cuboid measures 12 cm by 13 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th February 1954A bag holds 6 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th February 1954A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 8th February 1954A block has mass 570 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th February 1954Work out the nth term of the quadratic sequence 6, 18, 36, 60, ...
- 10th February 1954y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 11th February 1954The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 12th February 1954A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
- 13th February 1954On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th February 1954x = 48 and y = 28, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th February 1954The point (4, 0) lies on y = f(x). Write down its image on y = f(x + 1).
- 16th February 1954y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 17th February 1954In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 18th February 1954The probability of winning a game is 4/5. A player expects 48 wins. How many games did they play?
- 19th February 1954A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 20th February 1954A car covers 100 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st February 1954Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 22nd February 1954y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 49.
- 23rd February 1954In a vector proof you find that vector PQ = a + 6b and vector RS = 3a + 18b. What does this show about PQ and RS?
- 24th February 1954A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 25th February 1954On 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?
- 26th February 1954Rationalise the denominator of 55/sqrt(5), giving your answer in its simplest form.
- 27th February 1954f(x) = 6x + 5 and g(x) = 5x - 9. Work out fg(2).
- 28th February 1954A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.