Daily Practice · Higher Plus
November 1982 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1982 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1982
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1982On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd November 1982Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 3rd November 1982Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
- 4th November 1982y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 5th November 1982A cuboid measures 4 cm by 9 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th November 1982A bag holds 4 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th November 1982A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 8th November 1982A block has mass 820 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th November 1982Use the iteration x(n+1) = cube root of (3x(n) + 2) with x(0) = 1. Work out x(1) to 3 decimal places.
- 10th November 1982y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 9.
- 11th November 1982The 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.
- 12th November 1982A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 13th November 1982On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th November 1982x = 81 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th November 1982Work out the nth term of the quadratic sequence 0, 8, 24, 48, ...
- 16th November 1982A train slows steadily from 34 m/s to rest in 4 seconds. Work out its deceleration.
- 17th November 1982In 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.
- 18th November 1982The probability of winning a game is 3/8. A player expects 21 wins. How many games did they play?
- 19th November 1982A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 20th November 1982A car covers 640 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st November 1982The point (2, -6) lies on y = f(x). Write down its image on y = f(x) - 3.
- 22nd November 1982y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
- 23rd November 1982In a vector proof you find that vector PQ = 5a - b and vector RS = 20a - 4b. What does this show about PQ and RS?
- 24th November 1982A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 25th November 1982On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 26th November 1982Rationalise the denominator of 16/sqrt(2), giving your answer in its simplest form.
- 27th November 1982Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 28th November 1982y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 29th November 1982A cuboid measures 3 cm by 10 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th November 1982A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?