Daily Practice · Higher Plus
October 1987 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1987 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1987Simplify sqrt(72) + sqrt(2), giving your answer in the form a sqrt(b).
- 2nd October 1987Work out the coordinates of the turning point of y = x^2 - 8x - 6.
- 3rd October 1987y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 4th October 1987A cuboid measures 11 cm by 8 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th October 1987A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th October 1987On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th October 1987A rectangle is 20 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th October 1987Simplify (x^2 + x - 6)/(x + 3).
- 9th October 1987y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 10th October 1987A cuboid measures 11 cm by 11 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th October 1987A 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?
- 12th October 1987A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 13th October 1987Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
- 14th October 1987In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 5 in terms of an integer n?
- 15th October 1987y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 81.
- 16th October 1987The 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.
- 17th October 1987A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 18th October 1987On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th October 1987A block has mass 390 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th October 1987Make x the subject of 8x + 6 = y(x + 6).
- 21st October 1987A train slows steadily from 12 m/s to rest in 4 seconds. Work out its deceleration.
- 22nd October 1987In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 23rd October 1987The probability of winning a game is 2/5. A player expects 16 wins. How many games did they play?
- 24th October 1987A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 25th October 1987x = 186 and y = 77, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th October 1987Write 2/(x - 4) + 4/(x + 2) as a single fraction.
- 27th October 1987y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 28th October 1987In a vector proof you find that vector PQ = 2a - b and vector RS = 10a - 5b. What does this show about PQ and RS?
- 29th October 1987A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 30th October 1987On 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?
- 31st October 1987A car covers 120 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.