Daily Practice · Higher Plus
December 1986 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1986 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1986
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1986y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 2nd December 1986In a vector proof you find that vector PQ = a - b and vector RS = 4a - 4b. What does this show about PQ and RS?
- 3rd December 1986A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 4th December 1986A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 5th December 1986Rationalise the denominator of 24/sqrt(3), giving your answer in its simplest form.
- 6th December 1986Simplify (x^2 - 6x - 16)/(x + 2).
- 7th December 1986y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 9.
- 8th December 1986A cuboid measures 6 cm by 15 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th December 1986A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th December 1986On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th December 1986Simplify sqrt(8) + sqrt(50), giving your answer in the form a sqrt(b).
- 12th December 1986In an algebraic proof, how would you write a multiple of 4 in terms of an integer n?
- 13th December 1986A train slows steadily from 30 m/s to rest in 8 seconds. Work out its deceleration.
- 14th December 1986A cuboid measures 13 cm by 9 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th December 1986A bag holds 5 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th December 1986A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 17th December 1986A rectangle is 23 cm by 18 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th December 1986Make x the subject of 2x + 7 = y(x + 7).
- 19th December 1986y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
- 20th December 1986The 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.
- 21st December 1986A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
- 22nd December 1986On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd December 1986Expand and simplify (6 + sqrt(7))(6 - sqrt(7)).
- 24th December 1986Write 4/(x + 6) + 2/(x - 2) as a single fraction.
- 25th December 1986y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 26th December 1986In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 27th December 1986The probability of winning a game is 3/8. A player expects 30 wins. How many games did they play?
- 28th December 1986A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 29th December 1986A block has mass 680 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th December 1986Solve 9x^2 - 1 = 0.
- 31st December 1986y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 49.