Daily Practice · Higher Plus
December 1979 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1979 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1979
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1979Write x^2 + 12x - 1 in the form (x + a)^2 + b.
- 2nd December 1979A train slows steadily from 33 m/s to rest in 4 seconds. Work out its deceleration.
- 3rd December 1979In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 4th December 1979The probability of winning a game is 2/5. A player expects 14 wins. How many games did they play?
- 5th December 1979A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 6th December 1979Simplify sqrt(32) + sqrt(8), giving your answer in the form a sqrt(b).
- 7th December 1979Work out the coordinates of the turning point of y = x^2 + 4x + 1.
- 8th December 1979y is inversely proportional to x^2. When x = 5, y = 48. Work out y when x = 4.
- 9th December 1979In a vector proof you find that vector PQ = 4a + 2b and vector RS = 16a + 8b. What does this show about PQ and RS?
- 10th December 1979A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 11th December 1979On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 12th December 1979A rectangle is 4 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th December 1979Simplify (x^2 - 7x + 12)/(x - 4).
- 14th December 1979y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 5.
- 15th December 1979A cuboid measures 10 cm by 4 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th December 1979A 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?
- 17th December 1979A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 18th December 1979Expand and simplify (7 + sqrt(3))(7 - sqrt(3)).
- 19th December 1979In an algebraic proof, how would you write a multiple of 7 in terms of an integer n?
- 20th December 1979y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 64.
- 21st December 1979A cuboid measures 14 cm by 8 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd December 1979A bag holds 3 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd December 1979On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 24th December 1979A block has mass 240 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th December 1979Make x the subject of 6x + 2 = y(x + 2).
- 26th December 1979A train slows steadily from 19 m/s to rest in 8 seconds. Work out its deceleration.
- 27th December 1979The 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.
- 28th December 1979A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 29th December 1979A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 30th December 1979x = 65 and y = 36, each correct to the nearest whole number. Work out the upper bound of x - y.
- 31st December 1979Write 6/(x - 4) + 3/(x + 1) as a single fraction.