Daily Practice · Higher Plus
November 1986 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1986 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1986
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1986y is inversely proportional to x^2. When x = 4, y = 18. Work out y when x = 3.
- 2nd November 1986In a vector proof you find that vector PQ = 2a - 2b and vector RS = 4a - 4b. What does this show about PQ and RS?
- 3rd November 1986A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 4th November 1986On 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?
- 5th November 1986A rectangle is 13 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th November 1986The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 7th November 1986y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 8th November 1986A cuboid measures 8 cm by 14 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th November 1986A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th November 1986A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 11th November 1986Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).
- 12th November 1986A quadratic sequence starts -5, -1, 7, 19. Work out the second difference, and the coefficient of n^2.
- 13th November 1986y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 81.
- 14th November 1986A cuboid measures 4 cm by 8 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th November 1986A bag holds 7 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th November 1986On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 17th November 1986A block has mass 360 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th November 1986Solve x^2 - 2x - 8 < 0.
- 19th November 1986A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.
- 20th November 1986The 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.
- 21st November 1986A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/66. Work out r.
- 22nd November 1986A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 23rd November 1986x = 165 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th November 1986Write x^2 - 10x - 10 in the form (x + a)^2 + b.
- 25th November 1986y is inversely proportional to x^2. When x = 3, y = 36. Work out y when x = 6.
- 26th November 1986In 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.
- 27th November 1986The probability of winning a game is 1/5. A player expects 8 wins. How many games did they play?
- 28th November 1986On 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?
- 29th November 1986A car covers 540 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.
- 30th November 1986Work out the coordinates of the turning point of y = x^2 - 16x - 4.