Daily Practice · Higher Plus
December 1969 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1969 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1969
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1969In a vector proof you find that vector PQ = 2a + 6b and vector RS = 8a + 24b. What does this show about PQ and RS?
- 2nd December 1969A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 3rd December 1969On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 4th December 1969Simplify sqrt(8) + sqrt(50), giving your answer in the form a sqrt(b).
- 5th December 1969Make x the subject of 3x + 4 = y(x + 4).
- 6th December 1969A train slows steadily from 31 m/s to rest in 10 seconds. Work out its deceleration.
- 7th December 1969A cuboid measures 4 cm by 10 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th December 1969A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th December 1969A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 10th December 1969A rectangle is 22 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th December 1969Write 3/(x - 4) + 7/(x - 2) as a single fraction.
- 12th December 1969y is inversely proportional to x^2. When x = 5, y = 12. Work out y when x = 2.
- 13th December 1969A cuboid measures 9 cm by 14 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th December 1969A bag holds 5 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th December 1969On 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?
- 16th December 1969Expand and simplify (2 + sqrt(5))(2 - sqrt(5)).
- 17th December 1969Solve 10x^2 - x - 3 = 0.
- 18th December 1969y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 19th December 1969The 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.
- 20th December 1969A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 21st December 1969A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 22nd December 1969A block has mass 730 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd December 1969f(x) = 4x + 4. Work out the inverse function f^-1(x).
- 24th December 1969y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 25.
- 25th December 1969In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 26th December 1969The probability of winning a game is 1/2. A player expects 28 wins. How many games did they play?
- 27th December 1969On 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?
- 28th December 1969x = 194 and y = 58, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th December 1969Solve x^2 + y^2 = 841 and y = x + 1 simultaneously.
- 30th December 1969A train slows steadily from 36 m/s to rest in 5 seconds. Work out its deceleration.
- 31st December 1969In a vector proof you find that vector PQ = 2a - b and vector RS = 4a - 2b. What does this show about PQ and RS?