Daily Practice · Higher Plus
August 1953 5-a-day
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The batch download puts all 5 tiers' August 1953 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1953Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 2nd August 1953y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 3rd August 1953A cuboid measures 10 cm by 5 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th August 1953A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th August 1953On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 6th August 1953Simplify sqrt(75) + sqrt(12), giving your answer in the form a sqrt(b).
- 7th August 1953f(x) = 4x - 4 and g(x) = 5x - 1. Work out fg(0).
- 8th August 1953y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 9th August 1953A cuboid measures 13 cm by 7 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th August 1953A bag holds 6 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th August 1953A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 12th August 1953A rectangle is 15 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th August 1953The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 14th August 1953y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 64.
- 15th August 1953The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 16th August 1953A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 17th August 1953On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 18th August 1953Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
- 19th August 1953A quadratic sequence starts 9, 17, 29, 45. Work out the second difference, and the coefficient of n^2.
- 20th August 1953A train slows steadily from 12 m/s to rest in 8 seconds. Work out its deceleration.
- 21st August 1953In 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.
- 22nd August 1953The probability of winning a game is 1/8. A player expects 9 wins. How many games did they play?
- 23rd August 1953A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 24th August 1953A block has mass 410 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th August 1953Solve x^2 + 4x - 12 > 0.
- 26th August 1953y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
- 27th August 1953In a vector proof you find that vector PQ = 4a - 5b and vector RS = 12a - 15b. What does this show about PQ and RS?
- 28th August 1953A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 29th August 1953On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th August 1953x = 51 and y = 29, each correct to the nearest whole number. Work out the upper bound of x - y.
- 31st August 1953Write x^2 + 8x - 8 in the form (x + a)^2 + b.