Daily Practice · Higher Plus
August 1983 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1983 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1983
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1983y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 81.
- 2nd August 1983A cuboid measures 12 cm by 5 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd August 1983A bag holds 5 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th August 1983On 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?
- 5th August 1983Rationalise the denominator of 18/sqrt(2), giving your answer in its simplest form.
- 6th August 1983In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 7th August 1983A train slows steadily from 19 m/s to rest in 8 seconds. Work out its deceleration.
- 8th August 1983The 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.
- 9th August 1983A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 10th August 1983A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 11th August 1983Simplify sqrt(48) + sqrt(3), giving your answer in the form a sqrt(b).
- 12th August 1983Make x the subject of 3x + 4 = y(x + 4).
- 13th August 1983y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 14th August 1983In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 15th August 1983The probability of winning a game is 4/5. A player expects 32 wins. How many games did they play?
- 16th August 1983On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th August 1983A rectangle is 11 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th August 1983Write 3/(x + 6) + 4/(x - 5) as a single fraction.
- 19th August 1983y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 20th August 1983In a vector proof you find that vector PQ = a - b and vector RS = 5a - 5b. What does this show about PQ and RS?
- 21st August 1983A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 22nd August 1983A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 23rd August 1983Expand and simplify (9 + sqrt(2))(9 - sqrt(2)).
- 24th August 1983Solve 12x^2 + 13x + 3 = 0.
- 25th August 1983y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 16.
- 26th August 1983A cuboid measures 9 cm by 14 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th August 1983A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th August 1983On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 29th August 1983A block has mass 840 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th August 1983f(x) = 6x - 6. Work out the inverse function f^-1(x).
- 31st August 1983A train slows steadily from 14 m/s to rest in 4 seconds. Work out its deceleration.