Daily Practice · Higher Plus
November 1956 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1956 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1956
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1956Solve 6x^2 - 13x + 6 = 0.
- 2nd November 1956y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 4.
- 3rd November 1956In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 4th November 1956The probability of winning a game is 1/8. A player expects 4 wins. How many games did they play?
- 5th November 1956On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th November 1956Expand and simplify (2 + sqrt(2))(2 - sqrt(2)).
- 7th November 1956f(x) = 8x + 4. Work out the inverse function f^-1(x).
- 8th November 1956A train slows steadily from 39 m/s to rest in 4 seconds. Work out its deceleration.
- 9th November 1956In a vector proof you find that vector PQ = 4a - 6b and vector RS = 16a - 24b. What does this show about PQ and RS?
- 10th November 1956A bag holds 8 red and n blue counters. The probability of taking a red is 4/5. Work out n.
- 11th November 1956A 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?
- 12th November 1956A block has mass 560 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.
- 13th November 1956Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 14th November 1956y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 15th November 1956A cuboid measures 4 cm by 12 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th November 1956A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th November 1956On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 18th November 1956x = 166 and y = 150, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th November 1956Use the iteration x(n+1) = cube root of (4x(n) + 1) with x(0) = 3. Work out x(1) to 3 decimal places.
- 20th November 1956y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 21st November 1956A cuboid measures 14 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd November 1956A bag holds 4 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd November 1956A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 24th November 1956A car covers 750 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.
- 25th November 1956Work out the nth term of the quadratic sequence -2, 7, 24, 49, ...
- 26th November 1956y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 36.
- 27th November 1956The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 28th November 1956A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 29th November 1956On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th November 1956Rationalise the denominator of 12/sqrt(2), giving your answer in its simplest form.