Daily Practice · Higher Plus
November 1955 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1955 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1955
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1955f(x) = 3x + 3 and g(x) = 6x + 8. Work out fg(0).
- 2nd November 1955y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 3rd November 1955The 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.
- 4th November 1955A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 5th November 1955A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 6th November 1955x = 46 and y = 29, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th November 1955The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 8th November 1955y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 81.
- 9th November 1955In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 10th November 1955The probability of winning a game is 7/10. A player expects 84 wins. How many games did they play?
- 11th November 1955On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 12th November 1955A car covers 640 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.
- 13th November 1955A quadratic sequence starts 17, 29, 45, 65. Work out the second difference, and the coefficient of n^2.
- 14th November 1955A train slows steadily from 22 m/s to rest in 5 seconds. Work out its deceleration.
- 15th November 1955In a vector proof you find that vector PQ = 3a - 2b and vector RS = 12a - 8b. What does this show about PQ and RS?
- 16th November 1955A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 17th November 1955A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 18th November 1955Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 19th November 1955Solve x^2 + 8x + 15 > 0.
- 20th November 1955y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 21st November 1955A cuboid measures 5 cm by 5 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd November 1955A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd November 1955On 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?
- 24th November 1955Simplify sqrt(45) + sqrt(5), giving your answer in the form a sqrt(b).
- 25th November 1955Write x^2 + 6x - 4 in the form (x + a)^2 + b.
- 26th November 1955y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 27th November 1955A cuboid measures 12 cm by 12 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th November 1955A bag holds 3 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th November 1955A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 30th November 1955A rectangle is 22 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.