Daily Practice · Higher Plus
January 1956 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1956 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1956
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1956A train slows steadily from 16 m/s to rest in 5 seconds. Work out its deceleration.
- 2nd January 1956The 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.
- 3rd January 1956A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
- 4th January 1956A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 5th January 1956Simplify sqrt(75) + sqrt(27), giving your answer in the form a sqrt(b).
- 6th January 1956f(x) = 4x + 12. Work out the inverse function f^-1(x).
- 7th January 1956y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 8th January 1956In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 9th January 1956The probability of winning a game is 3/5. A player expects 39 wins. How many games did they play?
- 10th January 1956On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th January 1956A rectangle is 4 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th January 1956Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 13th January 1956y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 14th January 1956In a vector proof you find that vector PQ = 2a - 4b and vector RS = 6a - 12b. What does this show about PQ and RS?
- 15th January 1956A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 16th January 1956A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 17th January 1956Expand and simplify (4 + sqrt(3))(4 - sqrt(3)).
- 18th January 1956Use the iteration x(n+1) = cube root of (8x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.
- 19th January 1956y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 4.
- 20th January 1956A cuboid measures 13 cm by 3 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st January 1956A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd January 1956On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd January 1956A block has mass 400 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th January 1956Work out the nth term of the quadratic sequence 13, 30, 55, 88, ...
- 25th January 1956A train slows steadily from 30 m/s to rest in 8 seconds. Work out its deceleration.
- 26th January 1956A cuboid measures 10 cm by 4 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th January 1956A bag holds 6 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th January 1956A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 29th January 1956x = 73 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th January 1956The point (6, 6) lies on y = f(x). Write down its image on y = -f(x).
- 31st January 1956y is inversely proportional to x^2. When x = 4, y = 16. Work out y when x = 2.