Daily Practice · Higher Plus
August 1956 5-a-day
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The batch download puts all 5 tiers' August 1956 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1956
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1956On 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?
- 2nd August 1956Simplify sqrt(75) + sqrt(108), giving your answer in the form a sqrt(b).
- 3rd August 1956Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 4th August 1956A train slows steadily from 31 m/s to rest in 8 seconds. Work out its deceleration.
- 5th August 1956In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 6th August 1956The probability of winning a game is 9/10. A player expects 45 wins. How many games did they play?
- 7th August 1956A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 8th August 1956A rectangle is 25 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th August 1956Use the iteration x(n+1) = cube root of (9x(n) + 6) with x(0) = 3. Work out x(1) to 3 decimal places.
- 10th August 1956y is inversely proportional to x^2. When x = 4, y = 144. Work out y when x = 6.
- 11th August 1956In a vector proof you find that vector PQ = a + 6b and vector RS = 5a + 30b. What does this show about PQ and RS?
- 12th August 1956A bag holds 6 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 13th August 1956On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 14th August 1956Expand and simplify (8 + sqrt(2))(8 - sqrt(2)).
- 15th August 1956Work out the nth term of the quadratic sequence 3, 12, 25, 42, ...
- 16th August 1956y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 17th August 1956A cuboid measures 12 cm by 4 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th August 1956A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th August 1956A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 20th August 1956A block has mass 830 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st August 1956The point (6, -5) lies on y = f(x). Write down its image on y = f(-x).
- 22nd August 1956y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 49.
- 23rd August 1956A cuboid measures 8 cm by 7 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th August 1956A bag holds 5 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th August 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?
- 26th August 1956x = 178 and y = 69, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th August 1956Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 28th August 1956A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 29th August 1956The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 30th August 1956A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 31st August 1956A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?