Daily Practice · Higher Plus
October 1957 5-a-day
Printing for a group?
The batch download puts all 5 tiers' October 1957 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 1957A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 2nd October 1957A rectangle is 20 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd October 1957The point (2, -4) lies on y = f(x). Write down its image on y = f(-x).
- 4th October 1957y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 81.
- 5th October 1957In a vector proof you find that vector PQ = 5a - 5b and vector RS = 10a - 10b. What does this show about PQ and RS?
- 6th October 1957A bag holds 7 red and n blue counters. The probability of taking a red is 7/13. Work out n.
- 7th October 1957On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th October 1957Expand and simplify (9 + sqrt(11))(9 - sqrt(11)).
- 9th October 1957Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 10th October 1957A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 11th October 1957A cuboid measures 9 cm by 9 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th October 1957A 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?
- 13th October 1957A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 14th October 1957A block has mass 690 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.
- 15th October 1957f(x) = 5x - 2 and g(x) = 6x - 1. Work out fg(4).
- 16th October 1957y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 17th October 1957A cuboid measures 11 cm by 11 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th October 1957A bag holds 7 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th October 1957On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th October 1957x = 78 and y = 9, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st October 1957The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 22nd October 1957y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 23rd October 1957The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 24th October 1957A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
- 25th October 1957A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 26th October 1957A car covers 680 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 27th October 1957A quadratic sequence starts 9, 20, 35, 54. Work out the second difference, and the coefficient of n^2.
- 28th October 1957y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 9.
- 29th October 1957In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 30th October 1957The probability of winning a game is 4/5. A player expects 56 wins. How many games did they play?
- 31st October 1957On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?