Daily Practice · Higher Plus
July 1961 5-a-day
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The batch download puts all 5 tiers' July 1961 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1961
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1961A car covers 600 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.
- 2nd July 1961Work out the coordinates of the turning point of y = x^2 + 14x + 7.
- 3rd July 1961y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 4.
- 4th July 1961The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 5th July 1961A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
- 6th July 1961On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th July 1961Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 8th July 1961Simplify (x^2 + 2x - 48)/(x + 8).
- 9th July 1961A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
- 10th July 1961In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 11th July 1961The probability of winning a game is 1/10. A player expects 7 wins. How many games did they play?
- 12th July 1961A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 13th July 1961Simplify sqrt(50) + sqrt(72), giving your answer in the form a sqrt(b).
- 14th July 1961In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 15th July 1961y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 16th July 1961In a vector proof you find that vector PQ = a - b and vector RS = 2a - 2b. What does this show about PQ and RS?
- 17th July 1961A bag holds 8 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 18th July 1961On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th July 1961A rectangle is 8 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th July 1961Make x the subject of 6x + 3 = y(x + 3).
- 21st July 1961y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 22nd July 1961A cuboid measures 13 cm by 12 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd July 1961A bag holds 6 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th July 1961A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 25th July 1961Expand and simplify (5 + sqrt(5))(5 - sqrt(5)).
- 26th July 1961Write 6/(x - 3) + 4/(x - 4) as a single fraction.
- 27th July 1961y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 9.
- 28th July 1961A cuboid measures 8 cm by 4 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th July 1961A bag holds 4 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th July 1961On 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?
- 31st July 1961A block has mass 810 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.