Daily Practice · Higher Plus
July 1957 5-a-day
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The batch download puts all 5 tiers' July 1957 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1957In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 2nd July 1957The probability of winning a game is 1/5. A player expects 3 wins. How many games did they play?
- 3rd July 1957On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 4th July 1957Simplify sqrt(48) + sqrt(48), giving your answer in the form a sqrt(b).
- 5th July 1957f(x) = 4x + 5 and g(x) = 2x - 7. Work out fg(-1).
- 6th July 1957A train slows steadily from 24 m/s to rest in 8 seconds. Work out its deceleration.
- 7th July 1957In a vector proof you find that vector PQ = 6a - 6b and vector RS = 12a - 12b. What does this show about PQ and RS?
- 8th July 1957A bag holds 7 red and n blue counters. The probability of taking a red is 7/11. Work out n.
- 9th July 1957A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 10th July 1957A rectangle is 29 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th July 1957The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 12th July 1957y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 13th July 1957A cuboid measures 7 cm by 8 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th July 1957A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 15th July 1957On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 16th July 1957Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 17th July 1957A quadratic sequence starts -3, 5, 19, 39. Work out the second difference, and the coefficient of n^2.
- 18th July 1957y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 19th July 1957A cuboid measures 9 cm by 8 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th July 1957A bag holds 7 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st July 1957A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 22nd July 1957A block has mass 430 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.
- 23rd July 1957Solve x^2 + x - 12 > 0.
- 24th July 1957y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 81.
- 25th July 1957The 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.
- 26th July 1957A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 27th July 1957On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th July 1957x = 172 and y = 134, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th July 1957Write x^2 - 2x - 13 in the form (x + a)^2 + b.
- 30th July 1957A train slows steadily from 19 m/s to rest in 8 seconds. Work out its deceleration.
- 31st July 1957In 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.