Daily Practice · Higher Plus
August 1985 5-a-day
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The batch download puts all 5 tiers' August 1985 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1985
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1985Write 4/(x - 3) + 6/(x + 4) as a single fraction.
- 2nd August 1985y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 3rd August 1985In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 4th August 1985The probability of winning a game is 3/5. A player expects 36 wins. How many games did they play?
- 5th August 1985On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th August 1985Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 7th August 1985Solve 9x^2 - 18x + 8 = 0.
- 8th August 1985y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 9th August 1985In a vector proof you find that vector PQ = 5a + 6b and vector RS = 20a + 24b. What does this show about PQ and RS?
- 10th August 1985A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 11th August 1985A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 12th August 1985A block has mass 550 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th August 1985f(x) = 2x - 12. Work out the inverse function f^-1(x).
- 14th August 1985y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 64.
- 15th August 1985A cuboid measures 11 cm by 9 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th August 1985A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th August 1985On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th August 1985x = 159 and y = 88, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th August 1985Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 20th August 1985A train slows steadily from 20 m/s to rest in 8 seconds. Work out its deceleration.
- 21st August 1985A cuboid measures 11 cm by 12 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd August 1985A bag holds 6 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd August 1985A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 24th August 1985A car covers 700 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.
- 25th August 1985Use the iteration x(n+1) = cube root of (9x(n) + 1) with x(0) = 4. Work out x(1) to 3 decimal places.
- 26th August 1985y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 27th August 1985The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 28th August 1985A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 29th August 1985On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th August 1985Rationalise the denominator of 21/sqrt(7), giving your answer in its simplest form.
- 31st August 1985Work out the nth term of the quadratic sequence 2, 15, 36, 65, ...