Daily Practice · Higher Plus
December 1967 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1967 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1967
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1967A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 2nd December 1967On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 3rd December 1967x = 84 and y = 5, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th December 1967Work out the coordinates of the turning point of y = x^2 - 16x - 6.
- 5th December 1967y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 6th December 1967In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 7th December 1967The probability of winning a game is 4/5. A player expects 32 wins. How many games did they play?
- 8th December 1967A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 9th December 1967A car covers 430 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th December 1967Simplify (x^2 - 7x - 8)/(x + 1).
- 11th December 1967y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 64.
- 12th December 1967In a vector proof you find that vector PQ = 5a + 3b and vector RS = 10a + 6b. What does this show about PQ and RS?
- 13th December 1967A bag holds 2 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 14th December 1967On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 15th December 1967Rationalise the denominator of 99/sqrt(11), giving your answer in its simplest form.
- 16th December 1967In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 17th December 1967A train slows steadily from 14 m/s to rest in 8 seconds. Work out its deceleration.
- 18th December 1967A cuboid measures 13 cm by 7 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th December 1967A bag holds 6 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 1967A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 21st December 1967Simplify sqrt(32) + sqrt(32), giving your answer in the form a sqrt(b).
- 22nd December 1967Make x the subject of 2x + 7 = y(x + 7).
- 23rd December 1967y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 24th December 1967A cuboid measures 11 cm by 10 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th December 1967A bag holds 3 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th December 1967On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 27th December 1967A rectangle is 7 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th December 1967Write 4/(x + 1) + 7/(x + 6) as a single fraction.
- 29th December 1967y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 30th December 1967The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 31st December 1967A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/22. Work out r.