Daily Practice · Higher Plus
March 1983 5-a-day
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The batch download puts all 5 tiers' March 1983 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1983
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1983On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd March 1983A rectangle is 10 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd March 1983The point (0, 4) lies on y = f(x). Write down its image on y = f(-x).
- 4th March 1983y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 5th March 1983A cuboid measures 11 cm by 9 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th March 1983A bag holds 7 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th March 1983A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 8th March 1983Expand and simplify (2 + sqrt(10))(2 - sqrt(10)).
- 9th March 1983Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 10th March 1983y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 64.
- 11th March 1983The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 12th March 1983A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 13th March 1983On 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?
- 14th March 1983A block has mass 740 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 15th March 1983f(x) = 3x + 2 and g(x) = 6x - 1. Work out fg(-2).
- 16th March 1983A train slows steadily from 29 m/s to rest in 5 seconds. Work out its deceleration.
- 17th March 1983In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 18th March 1983The probability of winning a game is 1/4. A player expects 28 wins. How many games did they play?
- 19th March 1983A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 20th March 1983x = 177 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st March 1983The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 22nd March 1983y is inversely proportional to x^2. When x = 2, y = 25. Work out y when x = 5.
- 23rd March 1983In a vector proof you find that vector PQ = 2a - 6b and vector RS = 4a - 12b. What does this show about PQ and RS?
- 24th March 1983A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 25th March 1983On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 26th March 1983A car covers 330 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 27th March 1983A quadratic sequence starts 0, 4, 10, 18. Work out the second difference, and the coefficient of n^2.
- 28th March 1983y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 29th March 1983A cuboid measures 4 cm by 4 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th March 1983A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st March 1983A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?