Daily Practice · Higher Plus
February 1971 5-a-day
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The batch download puts all 5 tiers' February 1971 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1971
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1971A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd February 1971A histogram has two bars: one 5 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 3rd February 1971A rectangle is 12 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th February 1971f(x) = 2x - 7. Work out the inverse function f^-1(x).
- 5th February 1971y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 49.
- 6th February 1971A cuboid measures 4 cm by 13 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th February 1971A bag holds 6 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th February 1971On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 9th February 1971Expand and simplify (2 + sqrt(11))(2 - sqrt(11)).
- 10th February 1971Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 11th February 1971A train slows steadily from 12 m/s to rest in 4 seconds. Work out its deceleration.
- 12th February 1971The 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.
- 13th February 1971A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 14th February 1971A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 0.8. How many values in total?
- 15th February 1971A block has mass 200 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th February 1971Use the iteration x(n+1) = cube root of (10x(n) + 8) with x(0) = 3. Work out x(1) to 3 decimal places.
- 17th February 1971y is inversely proportional to x^2. When x = 4, y = 144. Work out y when x = 6.
- 18th February 1971In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 19th February 1971The probability of winning a game is 1/2. A player expects 18 wins. How many games did they play?
- 20th February 1971On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 21st February 1971x = 130 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd February 1971Work out the nth term of the quadratic sequence 6, 11, 18, 27, ...
- 23rd February 1971y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 24th February 1971In a vector proof you find that vector PQ = 4a - 4b and vector RS = 16a - 16b. What does this show about PQ and RS?
- 25th February 1971A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 26th February 1971A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 27th February 1971A car covers 580 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th February 1971The point (0, 4) lies on y = f(x). Write down its image on y = f(x - 5).