Daily Practice · Higher Plus
May 1987 5-a-day
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The batch download puts all 5 tiers' May 1987 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 1987In a vector proof you find that vector PQ = 2a - 5b and vector RS = 6a - 15b. What does this show about PQ and RS?
- 2nd May 1987A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 3rd May 1987On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th May 1987A block has mass 360 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5th May 1987Work out the nth term of the quadratic sequence 8, 12, 18, 26, ...
- 6th May 1987A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
- 7th May 1987A cuboid measures 15 cm by 8 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th May 1987A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th May 1987A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 10th May 1987x = 92 and y = 26, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th May 1987The point (6, -6) lies on y = f(x). Write down its image on y = -f(x).
- 12th May 1987y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 13th May 1987A cuboid measures 9 cm by 12 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th May 1987A bag holds 7 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th May 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?
- 16th May 1987A car covers 440 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 17th May 1987Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 18th May 1987y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 19th May 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.
- 20th May 1987A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 21st May 1987A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 22nd May 1987Rationalise the denominator of 30/sqrt(6), giving your answer in its simplest form.
- 23rd May 1987f(x) = 6x + 2 and g(x) = 4x + 9. Work out fg(4).
- 24th May 1987y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 25.
- 25th May 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.
- 26th May 1987The probability of winning a game is 3/5. A player expects 21 wins. How many games did they play?
- 27th May 1987On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th May 1987Simplify sqrt(20) + sqrt(245), giving your answer in the form a sqrt(b).
- 29th May 1987The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 30th May 1987A train slows steadily from 40 m/s to rest in 4 seconds. Work out its deceleration.
- 31st May 1987In a vector proof you find that vector PQ = 3a - 3b and vector RS = 12a - 12b. What does this show about PQ and RS?