Daily Practice · Higher Plus
February 1981 5-a-day
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The batch download puts all 5 tiers' February 1981 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1981
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1981In a vector proof you find that vector PQ = 6a + 2b and vector RS = 18a + 6b. What does this show about PQ and RS?
- 2nd February 1981A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 3rd February 1981On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th February 1981A rectangle is 6 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th February 1981Make x the subject of 7x + 5 = y(x + 5).
- 6th February 1981A train slows steadily from 12 m/s to rest in 5 seconds. Work out its deceleration.
- 7th February 1981A cuboid measures 3 cm by 5 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th February 1981A 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?
- 9th February 1981A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 10th February 1981Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 11th February 1981Write 4/(x + 5) + 2/(x - 2) as a single fraction.
- 12th February 1981y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 13th February 1981A cuboid measures 14 cm by 6 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th February 1981A bag holds 4 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th February 1981On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th February 1981A block has mass 530 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.
- 17th February 1981Solve 6x^2 - 5x - 25 = 0.
- 18th February 1981y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 19th February 1981The 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.
- 20th February 1981A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/22. Work out r.
- 21st February 1981A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 22nd February 1981x = 58 and y = 48, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd February 1981f(x) = 3x - 9. Work out the inverse function f^-1(x).
- 24th February 1981y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 16.
- 25th February 1981In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 26th February 1981The probability of winning a game is 1/4. A player expects 12 wins. How many games did they play?
- 27th February 1981On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th February 1981A car covers 670 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.