Daily Practice · Higher Plus
March 1981 5-a-day
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The batch download puts all 5 tiers' March 1981 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1981
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1981Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 2nd March 1981A train slows steadily from 40 m/s to rest in 5 seconds. Work out its deceleration.
- 3rd March 1981In a vector proof you find that vector PQ = 4a - 3b and vector RS = 20a - 15b. What does this show about PQ and RS?
- 4th March 1981A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 5th March 1981A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 6th March 1981Rationalise the denominator of 10/sqrt(2), giving your answer in its simplest form.
- 7th March 1981Use the iteration x(n+1) = cube root of (10x(n) + 6) with x(0) = 5. Work out x(1) to 3 decimal places.
- 8th March 1981y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
- 9th March 1981A cuboid measures 8 cm by 4 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th March 1981A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th March 1981On 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?
- 12th March 1981Simplify sqrt(20) + sqrt(180), giving your answer in the form a sqrt(b).
- 13th March 1981Work out the nth term of the quadratic sequence -1, 4, 13, 26, ...
- 14th March 1981y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 15th March 1981A cuboid measures 14 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th March 1981A bag holds 3 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th March 1981A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 18th March 1981A rectangle is 18 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th March 1981The point (2, 1) lies on y = f(x). Write down its image on y = f(-x).
- 20th March 1981y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 81.
- 21st March 1981The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 22nd March 1981A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 23rd March 1981On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th March 1981Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
- 25th March 1981Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 26th March 1981A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 27th March 1981In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 28th March 1981The probability of winning a game is 3/8. A player expects 27 wins. How many games did they play?
- 29th March 1981A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 30th March 1981A block has mass 420 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.
- 31st March 1981f(x) = 2x - 3 and g(x) = 2x + 5. Work out fg(-3).