Daily Practice · Higher Plus
September 1956 5-a-day
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The batch download puts all 5 tiers' September 1956 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1956
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1956A car covers 520 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 2nd September 1956f(x) = 5x + 8 and g(x) = 2x + 6. Work out fg(3).
- 3rd September 1956y is inversely proportional to x^2. When x = 5, y = 72. Work out y when x = 6.
- 4th September 1956In 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.
- 5th September 1956The probability of winning a game is 4/5. A player expects 20 wins. How many games did they play?
- 6th September 1956On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th September 1956Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.
- 8th September 1956The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 9th September 1956y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 10th September 1956In a vector proof you find that vector PQ = 4a - b and vector RS = 20a - 5b. What does this show about PQ and RS?
- 11th September 1956A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 12th September 1956A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 13th September 1956Simplify sqrt(72) + sqrt(72), giving your answer in the form a sqrt(b).
- 14th September 1956A quadratic sequence starts 10, 16, 26, 40. Work out the second difference, and the coefficient of n^2.
- 15th September 1956y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 16.
- 16th September 1956A cuboid measures 13 cm by 12 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th September 1956A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th September 1956On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 19th September 1956A rectangle is 10 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th September 1956Solve x^2 - 9 > 0.
- 21st September 1956A train slows steadily from 35 m/s to rest in 4 seconds. Work out its deceleration.
- 22nd September 1956A cuboid measures 4 cm by 6 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd September 1956A bag holds 7 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th September 1956A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 25th September 1956Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).
- 26th September 1956Write x^2 - 4x - 8 in the form (x + a)^2 + b.
- 27th September 1956y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
- 28th September 1956The 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.
- 29th September 1956A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 30th September 1956On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?