Daily Practice · Higher Plus
September 1991 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1991 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1991In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 2nd September 1991The probability of winning a game is 2/5. A player expects 28 wins. How many games did they play?
- 3rd September 1991On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 4th September 1991A rectangle is 4 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th September 1991Simplify (x^2 + x - 6)/(x - 2).
- 6th September 1991A train slows steadily from 15 m/s to rest in 10 seconds. Work out its deceleration.
- 7th September 1991In a vector proof you find that vector PQ = a + 5b and vector RS = 4a + 20b. What does this show about PQ and RS?
- 8th September 1991A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 9th September 1991A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 10th September 1991Expand and simplify (5 + sqrt(11))(5 - sqrt(11)).
- 11th September 1991In an algebraic proof, how would you write an even number in terms of an integer n?
- 12th September 1991y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 13th September 1991A cuboid measures 9 cm by 13 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th September 1991A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th September 1991On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 16th September 1991A block has mass 240 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 September 1991Make x the subject of 5x + 8 = y(x + 8).
- 18th September 1991y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 19th September 1991A cuboid measures 10 cm by 10 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th September 1991A bag holds 3 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st September 1991A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 22nd September 1991x = 60 and y = 18, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd September 1991Write 2/(x - 1) + 4/(x - 3) as a single fraction.
- 24th September 1991y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 16.
- 25th September 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.
- 26th September 1991A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 27th September 1991On 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?
- 28th September 1991A car covers 400 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th September 1991Solve 12x^2 - 11x - 15 = 0.
- 30th September 1991A train slows steadily from 33 m/s to rest in 8 seconds. Work out its deceleration.