Daily Practice · Higher Plus
August 1984 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1984 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1984
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1984A train slows steadily from 19 m/s to rest in 5 seconds. Work out its deceleration.
- 2nd August 1984The 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.
- 3rd August 1984A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 4th August 1984A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 5th August 1984x = 96 and y = 27, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th August 1984f(x) = 3x - 5 and g(x) = 5x - 2. Work out fg(4).
- 7th August 1984y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 8th August 1984In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 9th August 1984The probability of winning a game is 2/5. A player expects 4 wins. How many games did they play?
- 10th August 1984On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 11th August 1984A car covers 420 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th August 1984The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 13th August 1984y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 14th August 1984In a vector proof you find that vector PQ = 6a - 6b and vector RS = 12a - 12b. What does this show about PQ and RS?
- 15th August 1984A bag holds 5 red and n blue counters. The probability of taking a red is 5/7. Work out n.
- 16th August 1984A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 17th August 1984Rationalise the denominator of 25/sqrt(5), giving your answer in its simplest form.
- 18th August 1984A quadratic sequence starts -1, -1, 1, 5. Work out the second difference, and the coefficient of n^2.
- 19th August 1984y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 16.
- 20th August 1984A cuboid measures 9 cm by 15 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st August 1984A bag holds 4 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd August 1984On 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?
- 23rd August 1984Simplify sqrt(72) + sqrt(18), giving your answer in the form a sqrt(b).
- 24th August 1984Solve x^2 - 2x - 15 < 0.
- 25th August 1984A train slows steadily from 20 m/s to rest in 8 seconds. Work out its deceleration.
- 26th August 1984A cuboid measures 7 cm by 13 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th August 1984A bag holds 5 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th August 1984A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 29th August 1984A rectangle is 24 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th August 1984Write x^2 + 2x + 3 in the form (x + a)^2 + b.
- 31st August 1984y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.