Daily Practice · Higher Plus
January 1987 5-a-day
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The batch download puts all 5 tiers' January 1987 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1987
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1987In a vector proof you find that vector PQ = 4a - 3b and vector RS = 20a - 15b. What does this show about PQ and RS?
- 2nd January 1987A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 3rd January 1987On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th January 1987x = 132 and y = 44, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th January 1987f(x) = 2x + 9. Work out the inverse function f^-1(x).
- 6th January 1987A train slows steadily from 35 m/s to rest in 8 seconds. Work out its deceleration.
- 7th January 1987A cuboid measures 12 cm by 15 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th January 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?
- 9th January 1987A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 10th January 1987A car covers 390 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 11th January 1987Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 12th January 1987y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 13th January 1987A cuboid measures 14 cm by 12 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th January 1987A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th January 1987On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th January 1987Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.
- 17th January 1987Use the iteration x(n+1) = cube root of (5x(n) + 5) with x(0) = 5. Work out x(1) to 3 decimal places.
- 18th January 1987y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 19th January 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.
- 20th January 1987A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 21st January 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 January 1987Simplify sqrt(45) + sqrt(45), giving your answer in the form a sqrt(b).
- 23rd January 1987Work out the nth term of the quadratic sequence 1, 6, 13, 22, ...
- 24th January 1987y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 36.
- 25th January 1987In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 26th January 1987The probability of winning a game is 1/10. A player expects 4 wins. How many games did they play?
- 27th January 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?
- 28th January 1987A rectangle is 13 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th January 1987The point (1, -1) lies on y = f(x). Write down its image on y = f(x) - 4.
- 30th January 1987A train slows steadily from 28 m/s to rest in 5 seconds. Work out its deceleration.
- 31st January 1987In a vector proof you find that vector PQ = 2a - 5b and vector RS = 4a - 10b. What does this show about PQ and RS?