Daily Practice · Higher Plus
August 1955 5-a-day
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The batch download puts all 5 tiers' August 1955 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1955
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1955A 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?
- 2nd August 1955Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 3rd August 1955A quadratic sequence starts 4, 21, 48, 85. Work out the second difference, and the coefficient of n^2.
- 4th August 1955y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 81.
- 5th August 1955The 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.
- 6th August 1955A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 7th August 1955On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 8th August 1955A block has mass 430 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th August 1955Solve x^2 + 9x + 14 < 0.
- 10th August 1955A train slows steadily from 40 m/s to rest in 10 seconds. Work out its deceleration.
- 11th August 1955In 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.
- 12th August 1955The probability of winning a game is 2/5. A player expects 14 wins. How many games did they play?
- 13th August 1955A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 14th August 1955x = 106 and y = 33, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th August 1955Write x^2 + 8x - 10 in the form (x + a)^2 + b.
- 16th August 1955y is inversely proportional to x^2. When x = 3, y = 108. Work out y when x = 6.
- 17th August 1955In a vector proof you find that vector PQ = 4a - 2b and vector RS = 16a - 8b. What does this show about PQ and RS?
- 18th August 1955A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 19th August 1955On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th August 1955A car covers 290 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st August 1955Work out the coordinates of the turning point of y = x^2 - 16x + 5.
- 22nd August 1955y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 23rd August 1955A cuboid measures 14 cm by 7 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th August 1955A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th August 1955A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 26th August 1955Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 27th August 1955Simplify (x^2 + 13x + 40)/(x + 8).
- 28th August 1955y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 9.
- 29th August 1955A cuboid measures 13 cm by 5 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th August 1955A bag holds 7 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st August 1955On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?