Daily Practice · Higher Plus
November 1954 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1954 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1954
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1954y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 2nd November 1954A cuboid measures 13 cm by 13 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd November 1954A bag holds 3 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th November 1954On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 5th November 1954Rationalise the denominator of 88/sqrt(11), giving your answer in its simplest form.
- 6th November 1954Make x the subject of 3x + 4 = y(x + 4).
- 7th November 1954y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 8th November 1954The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 9th November 1954A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 10th November 1954A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 11th November 1954Simplify sqrt(75) + sqrt(12), giving your answer in the form a sqrt(b).
- 12th November 1954Write 4/(x + 2) + 6/(x - 1) as a single fraction.
- 13th November 1954y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 9.
- 14th November 1954In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 15th November 1954The probability of winning a game is 1/5. A player expects 5 wins. How many games did they play?
- 16th November 1954On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th November 1954A rectangle is 4 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th November 1954Solve 10x^2 - 13x + 4 = 0.
- 19th November 1954A train slows steadily from 25 m/s to rest in 8 seconds. Work out its deceleration.
- 20th November 1954In a vector proof you find that vector PQ = 4a - b and vector RS = 16a - 4b. What does this show about PQ and RS?
- 21st November 1954A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 22nd November 1954A 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 November 1954Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
- 24th November 1954f(x) = 2x - 4. Work out the inverse function f^-1(x).
- 25th November 1954y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 26th November 1954A cuboid measures 6 cm by 4 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th November 1954A bag holds 7 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th November 1954On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 29th November 1954A block has mass 680 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th November 1954Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.