Daily Practice · Higher Plus
January 1957 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1957 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1957y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 2nd January 1957In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 3rd January 1957The probability of winning a game is 1/2. A player expects 60 wins. How many games did they play?
- 4th January 1957On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 5th January 1957A car covers 130 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 6th January 1957Write x^2 + 10x - 2 in the form (x + a)^2 + b.
- 7th January 1957y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 8th January 1957In a vector proof you find that vector PQ = 4a + 6b and vector RS = 12a + 18b. What does this show about PQ and RS?
- 9th January 1957A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 10th January 1957A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 0.6. How many values in total?
- 11th January 1957Rationalise the denominator of 28/sqrt(7), giving your answer in its simplest form.
- 12th January 1957Work out the coordinates of the turning point of y = x^2 + 6x + 13.
- 13th January 1957y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 16.
- 14th January 1957A cuboid measures 8 cm by 14 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th January 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?
- 16th January 1957On 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?
- 17th January 1957Simplify sqrt(72) + sqrt(32), giving your answer in the form a sqrt(b).
- 18th January 1957Simplify (x^2 + 13x + 42)/(x + 6).
- 19th January 1957A train slows steadily from 23 m/s to rest in 5 seconds. Work out its deceleration.
- 20th January 1957A cuboid measures 6 cm by 7 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st January 1957A bag holds 6 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd January 1957A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 23rd January 1957A rectangle is 19 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th January 1957In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 25th January 1957y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 26th January 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.
- 27th January 1957A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 28th January 1957On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 29th January 1957Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 30th January 1957Make x the subject of 8x + 4 = y(x + 4).
- 31st January 1957y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.