Daily Practice · Higher Plus
October 1986 5-a-day
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The batch download puts all 5 tiers' October 1986 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1986
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1986Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 2nd October 1986A train slows steadily from 25 m/s to rest in 4 seconds. Work out its deceleration.
- 3rd October 1986In a vector proof you find that vector PQ = a + 4b and vector RS = 4a + 16b. What does this show about PQ and RS?
- 4th October 1986A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 5th October 1986A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?
- 6th October 1986A block has mass 780 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th October 1986Use the iteration x(n+1) = cube root of (3x(n) + 3) with x(0) = 3. Work out x(1) to 3 decimal places.
- 8th October 1986y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 9th October 1986A cuboid measures 5 cm by 13 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th October 1986A bag holds 4 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th October 1986On 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?
- 12th October 1986x = 66 and y = 41, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th October 1986Work out the nth term of the quadratic sequence 2, 14, 32, 56, ...
- 14th October 1986y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 15th October 1986A cuboid measures 10 cm by 4 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th October 1986A bag holds 3 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th October 1986A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 18th October 1986A car covers 110 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.
- 19th October 1986The point (0, -5) lies on y = f(x). Write down its image on y = f(x + 3).
- 20th October 1986y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 36.
- 21st October 1986The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 22nd October 1986A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 23rd October 1986On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th October 1986Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
- 25th October 1986Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 26th October 1986A train slows steadily from 23 m/s to rest in 5 seconds. Work out its deceleration.
- 27th October 1986In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 28th October 1986The probability of winning a game is 2/5. A player expects 32 wins. How many games did they play?
- 29th October 1986A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 30th October 1986Simplify sqrt(75) + sqrt(12), giving your answer in the form a sqrt(b).
- 31st October 1986f(x) = 4x + 8 and g(x) = 5x + 3. Work out fg(0).