Daily Practice · Higher Plus
November 1987 5-a-day
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The batch download puts all 5 tiers' November 1987 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1987Solve 8x^2 - 30x + 25 = 0.
- 2nd November 1987y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 3rd November 1987A cuboid measures 14 cm by 5 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th November 1987A 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?
- 5th November 1987A 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?
- 6th November 1987Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.
- 7th November 1987f(x) = 2x + 11. Work out the inverse function f^-1(x).
- 8th November 1987y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 16.
- 9th November 1987A cuboid measures 5 cm by 5 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th November 1987A bag holds 4 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th November 1987On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 12th November 1987Simplify sqrt(27) + sqrt(48), giving your answer in the form a sqrt(b).
- 13th November 1987Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 14th November 1987A train slows steadily from 18 m/s to rest in 5 seconds. Work out its deceleration.
- 15th November 1987The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 16th November 1987A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 17th November 1987A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 18th November 1987A rectangle is 25 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th November 1987Use the iteration x(n+1) = cube root of (10x(n) + 1) with x(0) = 1. Work out x(1) to 3 decimal places.
- 20th November 1987y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 21st November 1987In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 22nd November 1987The probability of winning a game is 2/5. A player expects 24 wins. How many games did they play?
- 23rd November 1987On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th November 1987Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).
- 25th November 1987Work out the nth term of the quadratic sequence 2, 14, 34, 62, ...
- 26th November 1987y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 27th November 1987In a vector proof you find that vector PQ = 2a - 2b and vector RS = 10a - 10b. What does this show about PQ and RS?
- 28th November 1987A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 29th November 1987A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 30th November 1987A block has mass 620 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.