Daily Practice · Higher Plus
November 1963 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1963 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1963
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1963f(x) = 7x - 3. Work out the inverse function f^-1(x).
- 2nd November 1963y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 3rd November 1963In a vector proof you find that vector PQ = 6a + 5b and vector RS = 18a + 15b. What does this show about PQ and RS?
- 4th November 1963A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 5th November 1963On 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?
- 6th November 1963A rectangle is 29 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th November 1963Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 8th November 1963y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 9th November 1963A cuboid measures 10 cm by 6 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th November 1963A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th November 1963A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 12th November 1963Expand and simplify (5 + sqrt(3))(5 - sqrt(3)).
- 13th November 1963Use the iteration x(n+1) = cube root of (2x(n) + 4) with x(0) = 4. Work out x(1) to 3 decimal places.
- 14th November 1963y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 25.
- 15th November 1963A cuboid measures 11 cm by 9 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th November 1963A bag holds 4 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th November 1963On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th November 1963A block has mass 600 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th November 1963Work out the nth term of the quadratic sequence 4, 5, 8, 13, ...
- 20th November 1963A train slows steadily from 18 m/s to rest in 5 seconds. Work out its deceleration.
- 21st November 1963The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 22nd November 1963A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/22. Work out r.
- 23rd November 1963A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 24th November 1963x = 181 and y = 19, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th November 1963The point (-5, 0) lies on y = f(x). Write down its image on y = -f(x).
- 26th November 1963y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 27th November 1963In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 28th November 1963The probability of winning a game is 4/5. A player expects 56 wins. How many games did they play?
- 29th November 1963On 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?
- 30th November 1963A car covers 650 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.