Daily Practice · Higher Plus
August 1954 5-a-day
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The batch download puts all 5 tiers' August 1954 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1954
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1954x = 125 and y = 88, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd August 1954Write 4/(x + 1) + 7/(x - 3) as a single fraction.
- 3rd August 1954y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 4th August 1954A cuboid measures 10 cm by 14 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th August 1954A bag holds 4 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th August 1954A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 7th August 1954A car covers 870 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.
- 8th August 1954Solve 10x^2 + 3x - 18 = 0.
- 9th August 1954y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 4.
- 10th August 1954The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 11th August 1954A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/22. Work out r.
- 12th August 1954On 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?
- 13th August 1954Rationalise the denominator of 49/sqrt(7), giving your answer in its simplest form.
- 14th August 1954f(x) = 7x - 9. Work out the inverse function f^-1(x).
- 15th August 1954A train slows steadily from 25 m/s to rest in 5 seconds. Work out its deceleration.
- 16th August 1954In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 17th August 1954The probability of winning a game is 1/4. A player expects 14 wins. How many games did they play?
- 18th August 1954A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 19th August 1954Simplify sqrt(32) + sqrt(50), giving your answer in the form a sqrt(b).
- 20th August 1954Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 21st August 1954y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 22nd August 1954In a vector proof you find that vector PQ = 5a + 6b and vector RS = 15a + 18b. What does this show about PQ and RS?
- 23rd August 1954A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 24th August 1954On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th August 1954A rectangle is 14 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th August 1954Use the iteration x(n+1) = cube root of (8x(n) + 4) with x(0) = 3. Work out x(1) to 3 decimal places.
- 27th August 1954y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 28th August 1954A cuboid measures 8 cm by 4 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th August 1954A bag holds 9 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th August 1954A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 31st August 1954Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).