Daily Practice · Higher Plus
December 1968 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1968 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1968
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1968The probability of winning a game is 3/8. A player expects 24 wins. How many games did they play?
- 2nd December 1968A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 3rd December 1968Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 4th December 1968The point (-5, 6) lies on y = f(x). Write down its image on y = f(x + 4).
- 5th December 1968y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 81.
- 6th December 1968In a vector proof you find that vector PQ = 2a - 5b and vector RS = 8a - 20b. What does this show about PQ and RS?
- 7th December 1968A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 8th December 1968On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th December 1968A block has mass 330 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.
- 10th December 1968Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 11th December 1968A train slows steadily from 15 m/s to rest in 8 seconds. Work out its deceleration.
- 12th December 1968A cuboid measures 14 cm by 4 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th December 1968A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th December 1968A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 15th December 1968x = 174 and y = 148, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th December 1968f(x) = 6x - 5 and g(x) = 3x - 8. Work out fg(-3).
- 17th December 1968y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 18th December 1968A cuboid measures 4 cm by 13 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th December 1968A 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?
- 20th December 1968On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 21st December 1968A car covers 650 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd December 1968The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 23rd December 1968y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 24th December 1968The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 25th December 1968A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 21/55. Work out r.
- 26th December 1968A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 27th December 1968Rationalise the denominator of 30/sqrt(6), giving your answer in its simplest form.
- 28th December 1968A quadratic sequence starts 11, 20, 35, 56. Work out the second difference, and the coefficient of n^2.
- 29th December 1968y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 64.
- 30th December 1968In 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.
- 31st December 1968The probability of winning a game is 9/10. A player expects 45 wins. How many games did they play?