Daily Practice · Higher Plus
November 1989 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1989 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1989
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1989A rectangle is 22 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd November 1989Use the iteration x(n+1) = cube root of (7x(n) + 6) with x(0) = 2. Work out x(1) to 3 decimal places.
- 3rd November 1989A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
- 4th November 1989The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 5th November 1989A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 6th November 1989A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 7th November 1989Expand and simplify (5 + sqrt(10))(5 - sqrt(10)).
- 8th November 1989Work out the nth term of the quadratic sequence 0, 8, 20, 36, ...
- 9th November 1989y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 10th November 1989In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 11th November 1989The probability of winning a game is 3/5. A player expects 18 wins. How many games did they play?
- 12th November 1989On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th November 1989A block has mass 680 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th November 1989The point (6, -5) lies on y = f(x). Write down its image on y = -f(x).
- 15th November 1989y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 16th November 1989In a vector proof you find that vector PQ = a + 5b and vector RS = 4a + 20b. What does this show about PQ and RS?
- 17th November 1989A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 18th November 1989A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 19th November 1989x = 167 and y = 30, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th November 1989Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 21st November 1989y is directly proportional to sqrt(x). When x = 49, y = 56. Work out y when x = 36.
- 22nd November 1989A cuboid measures 14 cm by 12 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd November 1989A bag holds 9 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th November 1989On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th November 1989A car covers 650 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 26th November 1989f(x) = 4x + 2 and g(x) = 2x - 1. Work out fg(-3).
- 27th November 1989A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.
- 28th November 1989A cuboid measures 5 cm by 4 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th November 1989A bag holds 6 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th November 1989A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?