Daily Practice · Higher Plus
March 1991 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1991 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1991A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 2nd March 1991A car covers 620 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 3rd March 1991Write 3/(x + 1) + 4/(x - 2) as a single fraction.
- 4th March 1991y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 5th March 1991In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 6th March 1991The probability of winning a game is 4/5. A player expects 80 wins. How many games did they play?
- 7th March 1991On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th March 1991Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
- 9th March 1991Solve 10x^2 + 27x + 18 = 0.
- 10th March 1991y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 11th March 1991In a vector proof you find that vector PQ = 4a + 2b and vector RS = 12a + 6b. What does this show about PQ and RS?
- 12th March 1991A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 13th March 1991A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 14th March 1991Simplify sqrt(32) + sqrt(18), giving your answer in the form a sqrt(b).
- 15th March 1991f(x) = 4x - 11. Work out the inverse function f^-1(x).
- 16th March 1991y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 16.
- 17th March 1991A cuboid measures 6 cm by 5 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th March 1991A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th March 1991On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th March 1991A rectangle is 12 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st March 1991Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 22nd March 1991A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
- 23rd March 1991A cuboid measures 11 cm by 6 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th March 1991A bag holds 5 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th March 1991A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 26th March 1991Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).
- 27th March 1991Use the iteration x(n+1) = cube root of (11x(n) + 2) with x(0) = 5. Work out x(1) to 3 decimal places.
- 28th March 1991y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
- 29th March 1991The 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.
- 30th March 1991A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 31st March 1991On 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?