Daily Practice · Higher Plus
February 1991 5-a-day
Printing for a group?
The batch download puts all 5 tiers' February 1991 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1991
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1991Write x^2 + 14x - 7 in the form (x + a)^2 + b.
- 2nd February 1991A train slows steadily from 23 m/s to rest in 5 seconds. Work out its deceleration.
- 3rd February 1991In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 4th February 1991The probability of winning a game is 1/2. A player expects 15 wins. How many games did they play?
- 5th February 1991A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 6th February 1991A rectangle is 23 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th February 1991Work out the coordinates of the turning point of y = x^2 - 12x - 12.
- 8th February 1991y is inversely proportional to x^2. When x = 5, y = 72. Work out y when x = 6.
- 9th February 1991In a vector proof you find that vector PQ = 4a + 2b and vector RS = 16a + 8b. What does this show about PQ and RS?
- 10th February 1991A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 11th February 1991On 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?
- 12th February 1991Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 13th February 1991Simplify (x^2 - 12x + 35)/(x - 7).
- 14th February 1991y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 15th February 1991A cuboid measures 13 cm by 13 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th February 1991A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th February 1991A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 18th February 1991A block has mass 620 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th February 1991In an algebraic proof, how would you write a multiple of 9 in terms of an integer n?
- 20th February 1991y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 81.
- 21st February 1991A cuboid measures 8 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd February 1991A bag holds 5 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd February 1991On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 24th February 1991x = 77 and y = 66, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th February 1991Make x the subject of 4x + 2 = y(x + 2).
- 26th February 1991A train slows steadily from 40 m/s to rest in 8 seconds. Work out its deceleration.
- 27th February 1991The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 28th February 1991A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.