Daily Practice · Higher Plus
December 1956 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1956 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1956
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1956The point (0, 2) lies on y = f(x). Write down its image on y = f(x) - 3.
- 2nd December 1956A train slows steadily from 38 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd December 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.
- 4th December 1956The probability of winning a game is 9/10. A player expects 117 wins. How many games did they play?
- 5th December 1956A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 6th December 1956Simplify sqrt(50) + sqrt(50), giving your answer in the form a sqrt(b).
- 7th December 1956Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 8th December 1956y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
- 9th December 1956In a vector proof you find that vector PQ = 2a - 2b and vector RS = 8a - 8b. What does this show about PQ and RS?
- 10th December 1956A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 11th December 1956On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 12th December 1956A rectangle is 15 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th December 1956f(x) = 5x - 9 and g(x) = 2x - 4. Work out fg(5).
- 14th December 1956y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 15th December 1956A cuboid measures 12 cm by 5 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th December 1956A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th December 1956A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 18th December 1956Expand and simplify (7 + sqrt(10))(7 - sqrt(10)).
- 19th December 1956The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 20th December 1956y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 64.
- 21st December 1956A cuboid measures 13 cm by 4 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd December 1956A bag holds 3 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd December 1956On 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?
- 24th December 1956A block has mass 720 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th December 1956A quadratic sequence starts 16, 35, 64, 103. Work out the second difference, and the coefficient of n^2.
- 26th December 1956A train slows steadily from 25 m/s to rest in 10 seconds. Work out its deceleration.
- 27th December 1956The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 28th December 1956A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 29th December 1956A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 30th December 1956x = 197 and y = 70, each correct to the nearest whole number. Work out the upper bound of x - y.
- 31st December 1956Solve x^2 - 7x + 12 > 0.