Daily Practice · Higher Plus
August 1986 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1986 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1986
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1986Rationalise the denominator of 63/sqrt(7), giving your answer in its simplest form.
- 2nd August 1986A quadratic sequence starts 13, 19, 27, 37. Work out the second difference, and the coefficient of n^2.
- 3rd August 1986y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 4th August 1986In a vector proof you find that vector PQ = 3a + 6b and vector RS = 6a + 12b. What does this show about PQ and RS?
- 5th August 1986A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 6th August 1986A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 7th August 1986Simplify sqrt(75) + sqrt(27), giving your answer in the form a sqrt(b).
- 8th August 1986Solve x^2 + 7x > 0.
- 9th August 1986y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 4.
- 10th August 1986A cuboid measures 10 cm by 7 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th August 1986A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th August 1986On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th August 1986A rectangle is 9 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th August 1986Write x^2 - 2x - 11 in the form (x + a)^2 + b.
- 15th August 1986A train slows steadily from 18 m/s to rest in 10 seconds. Work out its deceleration.
- 16th August 1986A cuboid measures 10 cm by 14 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th August 1986A bag holds 3 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th August 1986A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
- 19th August 1986Expand and simplify (3 + sqrt(11))(3 - sqrt(11)).
- 20th August 1986Work out the coordinates of the turning point of y = x^2 + 14x + 15.
- 21st August 1986y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 22nd August 1986The 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.
- 23rd August 1986A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 24th August 1986On 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?
- 25th August 1986A block has mass 460 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th August 1986Simplify (x^2 - 5x - 24)/(x - 8).
- 27th August 1986y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 28th August 1986In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 29th August 1986The probability of winning a game is 7/10. A player expects 42 wins. How many games did they play?
- 30th August 1986A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 31st August 1986x = 167 and y = 139, each correct to the nearest whole number. Work out the upper bound of x - y.