Daily Practice · Higher Plus
December 1960 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1960 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1960
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1960A bag holds 3 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd December 1960On 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?
- 3rd December 1960A car covers 510 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th December 1960Write x^2 + 6x - 2 in the form (x + a)^2 + b.
- 5th December 1960A train slows steadily from 30 m/s to rest in 8 seconds. Work out its deceleration.
- 6th December 1960The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 7th December 1960A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 15/22. Work out r.
- 8th December 1960A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 9th December 1960Rationalise the denominator of 16/sqrt(2), giving your answer in its simplest form.
- 10th December 1960Work out the coordinates of the turning point of y = x^2 + 6x + 5.
- 11th December 1960y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 12th December 1960In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 13th December 1960The probability of winning a game is 3/10. A player expects 9 wins. How many games did they play?
- 14th December 1960On 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?
- 15th December 1960Simplify sqrt(72) + sqrt(8), giving your answer in the form a sqrt(b).
- 16th December 1960Simplify (x^2 + 4x - 21)/(x - 3).
- 17th December 1960y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 18th December 1960In a vector proof you find that vector PQ = 3a + 6b and vector RS = 15a + 30b. What does this show about PQ and RS?
- 19th December 1960A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 20th December 1960A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 21st December 1960A rectangle is 11 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd December 1960In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 23rd December 1960y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 36.
- 24th December 1960A cuboid measures 5 cm by 6 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th December 1960A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th December 1960On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 27th December 1960Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).
- 28th December 1960Make x the subject of 7x + 8 = y(x + 8).
- 29th December 1960A train slows steadily from 38 m/s to rest in 8 seconds. Work out its deceleration.
- 30th December 1960A cuboid measures 7 cm by 4 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st December 1960A bag holds 5 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?