Daily Practice · Higher Plus
March 1987 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1987 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1987y is inversely proportional to x^2. When x = 2, y = 48. Work out y when x = 4.
- 2nd March 1987In a vector proof you find that vector PQ = 6a - 6b and vector RS = 18a - 18b. What does this show about PQ and RS?
- 3rd March 1987A bag holds 2 red and n blue counters. The probability of taking a red is 1/4. Work out n.
- 4th March 1987On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 5th March 1987Simplify sqrt(8) + sqrt(72), giving your answer in the form a sqrt(b).
- 6th March 1987Write x^2 - 12x + 14 in the form (x + a)^2 + b.
- 7th March 1987y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 8th March 1987A cuboid measures 8 cm by 12 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th March 1987A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th March 1987A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 11th March 1987A rectangle is 13 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th March 1987Work out the coordinates of the turning point of y = x^2 - 4x + 8.
- 13th March 1987y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 49.
- 14th March 1987A cuboid measures 13 cm by 7 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th March 1987A bag holds 7 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th March 1987On 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?
- 17th March 1987Expand and simplify (6 + sqrt(5))(6 - sqrt(5)).
- 18th March 1987Simplify (x^2 - 9x + 8)/(x - 8).
- 19th March 1987A train slows steadily from 23 m/s to rest in 5 seconds. Work out its deceleration.
- 20th March 1987The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 21st March 1987A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 22nd March 1987A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 23rd March 1987A block has mass 240 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th March 1987In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 25th March 1987y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 26th March 1987In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 27th March 1987The probability of winning a game is 9/10. A player expects 135 wins. How many games did they play?
- 28th March 1987On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 29th March 1987x = 37 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th March 1987Make x the subject of 3x + 6 = y(x + 6).
- 31st March 1987y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.