Daily Practice · Higher Plus
December 1984 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1984 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1984
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1984A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 28/45. Work out r.
- 2nd December 1984A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 3rd December 1984A block has mass 740 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 4th December 1984Solve x^2 - 4 > 0.
- 5th December 1984y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 6th December 1984In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 7th December 1984The probability of winning a game is 1/5. A player expects 14 wins. How many games did they play?
- 8th December 1984On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 9th December 1984x = 147 and y = 15, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th December 1984Write x^2 - 4x - 13 in the form (x + a)^2 + b.
- 11th December 1984y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 12th December 1984In a vector proof you find that vector PQ = a - 5b and vector RS = 2a - 10b. What does this show about PQ and RS?
- 13th December 1984A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 14th December 1984A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 15th December 1984A car covers 110 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.
- 16th December 1984Work out the coordinates of the turning point of y = x^2 - 16x - 1.
- 17th December 1984y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 81.
- 18th December 1984A cuboid measures 15 cm by 6 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th December 1984A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th December 1984On 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?
- 21st December 1984Rationalise the denominator of 36/sqrt(6), giving your answer in its simplest form.
- 22nd December 1984Simplify (x^2 - 6x + 8)/(x - 2).
- 23rd December 1984A train slows steadily from 14 m/s to rest in 10 seconds. Work out its deceleration.
- 24th December 1984A cuboid measures 12 cm by 5 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th December 1984A bag holds 6 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th December 1984A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 27th December 1984Simplify sqrt(32) + sqrt(2), giving your answer in the form a sqrt(b).
- 28th December 1984In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 29th December 1984y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
- 30th December 1984The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 31st December 1984A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.