Daily Practice · Higher Plus
December 1965 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1965 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1965
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1965A rectangle is 6 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd December 1965A quadratic sequence starts 8, 19, 36, 59. Work out the second difference, and the coefficient of n^2.
- 3rd December 1965A train slows steadily from 37 m/s to rest in 8 seconds. Work out its deceleration.
- 4th December 1965A cuboid measures 8 cm by 4 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th December 1965A 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?
- 6th December 1965A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 1.4. How many values in total?
- 7th December 1965Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 8th December 1965Solve x^2 + 15x + 56 < 0.
- 9th December 1965y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 10th December 1965The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 11th December 1965A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 12th December 1965On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 13th December 1965A block has mass 710 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th December 1965Write x^2 - 10x + 14 in the form (x + a)^2 + b.
- 15th December 1965y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 16th December 1965In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 17th December 1965The probability of winning a game is 1/4. A player expects 26 wins. How many games did they play?
- 18th December 1965A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 19th December 1965x = 47 and y = 33, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th December 1965Work out the coordinates of the turning point of y = x^2 - 2x - 13.
- 21st December 1965y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 49.
- 22nd December 1965In a vector proof you find that vector PQ = 6a + 6b and vector RS = 18a + 18b. What does this show about PQ and RS?
- 23rd December 1965A bag holds 5 red and n blue counters. The probability of taking a red is 5/9. Work out n.
- 24th December 1965On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 25th December 1965A car covers 770 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.
- 26th December 1965Simplify (x^2 + 7x + 6)/(x + 6).
- 27th December 1965A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
- 28th December 1965A cuboid measures 9 cm by 7 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th December 1965A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th December 1965A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 31st December 1965Rationalise the denominator of 33/sqrt(3), giving your answer in its simplest form.