Daily Practice · Higher Plus
July 1956 5-a-day
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The batch download puts all 5 tiers' July 1956 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1956
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1956A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/55. Work out r.
- 2nd July 1956A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
- 3rd July 1956Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
- 4th July 1956In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 5th July 1956y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 36.
- 6th July 1956In 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.
- 7th July 1956The probability of winning a game is 1/5. A player expects 12 wins. How many games did they play?
- 8th July 1956On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 9th July 1956A block has mass 570 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th July 1956Make x the subject of 3x + 3 = y(x + 3).
- 11th July 1956A train slows steadily from 26 m/s to rest in 5 seconds. Work out its deceleration.
- 12th July 1956In a vector proof you find that vector PQ = 2a + 4b and vector RS = 8a + 16b. What does this show about PQ and RS?
- 13th July 1956A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 14th July 1956A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 15th July 1956x = 126 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th July 1956Write 5/(x - 1) + 5/(x - 4) as a single fraction.
- 17th July 1956y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 18th July 1956A cuboid measures 12 cm by 4 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th July 1956A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th July 1956On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 21st July 1956A car covers 650 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.
- 22nd July 1956Solve 20x^2 - 11x - 3 = 0.
- 23rd July 1956y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 5.
- 24th July 1956A cuboid measures 12 cm by 9 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th July 1956A bag holds 3 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th July 1956A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 27th July 1956Rationalise the denominator of 49/sqrt(7), giving your answer in its simplest form.
- 28th July 1956f(x) = 4x + 7. Work out the inverse function f^-1(x).
- 29th July 1956y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 81.
- 30th July 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.
- 31st July 1956A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 6/11. Work out r.