Daily Practice · Higher Plus
February 1955 5-a-day
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The batch download puts all 5 tiers' February 1955 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1955
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1955A bag holds 3 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd February 1955A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 3rd February 1955Simplify sqrt(27) + sqrt(27), giving your answer in the form a sqrt(b).
- 4th February 1955Simplify (x^2 + 4x - 5)/(x + 5).
- 5th February 1955y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 6th February 1955The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 7th February 1955A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 8th February 1955On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 9th February 1955A rectangle is 18 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th February 1955In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 6 in terms of an integer n?
- 11th February 1955y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 12th February 1955In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 13th February 1955The probability of winning a game is 1/4. A player expects 28 wins. How many games did they play?
- 14th February 1955A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 15th February 1955Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 16th February 1955Make x the subject of 5x + 4 = y(x + 4).
- 17th February 1955y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 64.
- 18th February 1955In a vector proof you find that vector PQ = 3a - 5b and vector RS = 9a - 15b. What does this show about PQ and RS?
- 19th February 1955A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 20th February 1955On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 21st February 1955A block has mass 650 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 22nd February 1955Write 4/(x - 4) + 6/(x - 3) as a single fraction.
- 23rd February 1955A train slows steadily from 19 m/s to rest in 5 seconds. Work out its deceleration.
- 24th February 1955A cuboid measures 15 cm by 3 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th February 1955A 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?
- 26th February 1955A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 27th February 1955x = 166 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th February 1955Solve 12x^2 + 13x - 4 = 0.