Daily Practice · Higher Plus
December 1982 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1982 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1982
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1982A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 2nd December 1982Simplify sqrt(12) + sqrt(27), giving your answer in the form a sqrt(b).
- 3rd December 1982f(x) = 6x - 1 and g(x) = 5x + 5. Work out fg(1).
- 4th December 1982y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 9.
- 5th December 1982A cuboid measures 10 cm by 8 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th December 1982A bag holds 4 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th December 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?
- 8th December 1982A rectangle is 26 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th December 1982The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 10th December 1982A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 11th December 1982The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 12th December 1982A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 13th December 1982A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 14th December 1982Expand and simplify (8 + sqrt(7))(8 - sqrt(7)).
- 15th December 1982A quadratic sequence starts 6, 15, 28, 45. Work out the second difference, and the coefficient of n^2.
- 16th December 1982y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 17th December 1982In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 18th December 1982The probability of winning a game is 1/2. A player expects 10 wins. How many games did they play?
- 19th December 1982On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th December 1982A block has mass 270 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st December 1982Solve x^2 - 8x + 7 < 0.
- 22nd December 1982y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 23rd December 1982In a vector proof you find that vector PQ = a - 5b and vector RS = 5a - 25b. What does this show about PQ and RS?
- 24th December 1982A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 25th December 1982A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 26th December 1982x = 138 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th December 1982Write x^2 - 12x + 14 in the form (x + a)^2 + b.
- 28th December 1982y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 64.
- 29th December 1982A cuboid measures 10 cm by 14 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th December 1982A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st December 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?