Daily Practice · Higher Plus
February 1956 5-a-day
Printing for a group?
The batch download puts all 5 tiers' February 1956 sheets in a single PDF, each tier behind its own divider page - 145 sheets in one file.
Every sheet in February 1956
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1956The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 2nd February 1956A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 3rd February 1956On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th February 1956A car covers 810 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 5th February 1956Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 6th February 1956y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 7th February 1956In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 8th February 1956The probability of winning a game is 3/5. A player expects 78 wins. How many games did they play?
- 9th February 1956A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 10th February 1956Rationalise the denominator of 72/sqrt(6), giving your answer in its simplest form.
- 11th February 1956f(x) = 5x + 8 and g(x) = 5x - 1. Work out fg(-1).
- 12th February 1956y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 9.
- 13th February 1956In a vector proof you find that vector PQ = a - 3b and vector RS = 3a - 9b. What does this show about PQ and RS?
- 14th February 1956A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 15th February 1956On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th February 1956Simplify sqrt(72) + sqrt(32), giving your answer in the form a sqrt(b).
- 17th February 1956The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 18th February 1956A train slows steadily from 39 m/s to rest in 5 seconds. Work out its deceleration.
- 19th February 1956A cuboid measures 13 cm by 6 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th February 1956A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st February 1956A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 22nd February 1956A rectangle is 15 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd February 1956A quadratic sequence starts 8, 10, 14, 20. Work out the second difference, and the coefficient of n^2.
- 24th February 1956y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 25th February 1956A cuboid measures 10 cm by 8 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th February 1956A bag holds 4 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th February 1956On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 28th February 1956Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 29th February 1956Solve x^2 + x - 12 < 0.