Daily Practice · Higher Plus
May 1991 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' May 1991 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1991A rectangle is 10 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd May 1991A quadratic sequence starts 8, 19, 36, 59. Work out the second difference, and the coefficient of n^2.
- 3rd May 1991y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 49.
- 4th May 1991In 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.
- 5th May 1991The probability of winning a game is 3/4. A player expects 39 wins. How many games did they play?
- 6th May 1991On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th May 1991Expand and simplify (5 + sqrt(7))(5 - sqrt(7)).
- 8th May 1991Solve x^2 + 14x + 48 > 0.
- 9th May 1991A train slows steadily from 35 m/s to rest in 8 seconds. Work out its deceleration.
- 10th May 1991In a vector proof you find that vector PQ = 4a - 6b and vector RS = 20a - 30b. What does this show about PQ and RS?
- 11th May 1991A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 12th May 1991A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 13th May 1991A block has mass 670 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.
- 14th May 1991Write x^2 + 4x + 4 in the form (x + a)^2 + b.
- 15th May 1991y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 16th May 1991A cuboid measures 8 cm by 8 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th May 1991A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th May 1991On 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?
- 19th May 1991x = 181 and y = 118, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th May 1991Work out the coordinates of the turning point of y = x^2 - 4x - 5.
- 21st May 1991y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 22nd May 1991A cuboid measures 6 cm by 13 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd May 1991A bag holds 3 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th May 1991A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 25th May 1991A car covers 870 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.
- 26th May 1991Simplify (x^2 + 3x - 10)/(x - 2).
- 27th May 1991y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 9.
- 28th May 1991The 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.
- 29th May 1991A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 30th May 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?
- 31st May 1991Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.