Daily Practice · Higher Plus
November 1953 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1953 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1953A cuboid measures 15 cm by 8 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd November 1953A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd November 1953A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 4th November 1953A rectangle is 30 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th November 1953The point (-3, -3) lies on y = f(x). Write down its image on y = -f(x).
- 6th November 1953y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 7th November 1953A cuboid measures 14 cm by 12 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th November 1953A bag holds 6 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th November 1953On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th November 1953Expand and simplify (6 + sqrt(2))(6 - sqrt(2)).
- 11th November 1953Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 12th November 1953y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 13th November 1953The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 14th November 1953A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 15th November 1953A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 16th November 1953A block has mass 310 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th November 1953f(x) = 5x + 1 and g(x) = 5x + 3. Work out fg(3).
- 18th November 1953y is directly proportional to sqrt(x). When x = 49, y = 56. Work out y when x = 9.
- 19th November 1953In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 20th November 1953The probability of winning a game is 3/5. A player expects 15 wins. How many games did they play?
- 21st November 1953On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd November 1953x = 186 and y = 23, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd November 1953The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 24th November 1953A train slows steadily from 20 m/s to rest in 10 seconds. Work out its deceleration.
- 25th November 1953In a vector proof you find that vector PQ = 2a + 6b and vector RS = 4a + 12b. What does this show about PQ and RS?
- 26th November 1953A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 27th November 1953A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 28th November 1953A car covers 550 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th November 1953A quadratic sequence starts 4, 8, 14, 22. Work out the second difference, and the coefficient of n^2.
- 30th November 1953y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.