Daily Practice · Higher Plus
February 1987 5-a-day
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The batch download puts all 5 tiers' February 1987 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1987A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 2nd February 1987A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 3rd February 1987Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 4th February 1987Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 5th February 1987y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 6th February 1987A cuboid measures 5 cm by 4 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th February 1987A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th February 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?
- 9th February 1987A block has mass 350 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th February 1987f(x) = 4x + 2 and g(x) = 6x - 7. Work out fg(4).
- 11th February 1987y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 12th February 1987A cuboid measures 13 cm by 6 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th February 1987A bag holds 5 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th February 1987A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 15th February 1987x = 152 and y = 55, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th February 1987The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 17th February 1987y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 25.
- 18th February 1987The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 19th February 1987A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/22. Work out r.
- 20th February 1987On 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?
- 21st February 1987A car covers 140 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd February 1987A quadratic sequence starts 3, 8, 19, 36. Work out the second difference, and the coefficient of n^2.
- 23rd February 1987A train slows steadily from 12 m/s to rest in 8 seconds. Work out its deceleration.
- 24th February 1987In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 25th February 1987The probability of winning a game is 2/5. A player expects 24 wins. How many games did they play?
- 26th February 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?
- 27th February 1987Rationalise the denominator of 22/sqrt(11), giving your answer in its simplest form.
- 28th February 1987Solve x^2 - 6x + 5 < 0.