Daily Practice · Higher Plus
August 1957 5-a-day
Printing for a group?
The batch download puts all 5 tiers' August 1957 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1957The probability of winning a game is 5/8. A player expects 30 wins. How many games did they play?
- 2nd August 1957A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 3rd August 1957A car covers 630 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th August 1957Work out the coordinates of the turning point of y = x^2 + 12x + 5.
- 5th August 1957y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 6th August 1957In a vector proof you find that vector PQ = 4a + 3b and vector RS = 20a + 15b. What does this show about PQ and RS?
- 7th August 1957A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 8th August 1957On 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?
- 9th August 1957Rationalise the denominator of 72/sqrt(6), giving your answer in its simplest form.
- 10th August 1957Simplify (x^2 - 11x + 30)/(x - 6).
- 11th August 1957y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 12th August 1957A cuboid measures 7 cm by 15 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th August 1957A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th August 1957A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 15th August 1957Simplify sqrt(72) + sqrt(2), giving your answer in the form a sqrt(b).
- 16th August 1957In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 17th August 1957y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 49.
- 18th August 1957A cuboid measures 8 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th August 1957A bag holds 7 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th August 1957On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 21st August 1957A rectangle is 13 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd August 1957Make x the subject of 6x + 7 = y(x + 7).
- 23rd August 1957A train slows steadily from 33 m/s to rest in 10 seconds. Work out its deceleration.
- 24th August 1957The 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.
- 25th August 1957A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 26th August 1957A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 27th August 1957Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 28th August 1957Write 7/(x + 1) + 2/(x - 3) as a single fraction.
- 29th August 1957y is inversely proportional to x^2. When x = 4, y = 9. Work out y when x = 3.
- 30th August 1957In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 31st August 1957The probability of winning a game is 3/8. A player expects 45 wins. How many games did they play?