Daily Practice · Higher Plus
December 1971 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1971 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1971
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1971Solve 6x^2 - 25x + 25 = 0.
- 2nd December 1971y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 3rd December 1971A cuboid measures 12 cm by 8 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th December 1971A bag holds 5 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th December 1971On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th December 1971A block has mass 310 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th December 1971f(x) = 6x - 5. Work out the inverse function f^-1(x).
- 8th December 1971y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 9th December 1971The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 10th December 1971A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
- 11th December 1971A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 12th December 1971x = 145 and y = 104, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th December 1971Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 14th December 1971y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 4.
- 15th December 1971In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 16th December 1971The probability of winning a game is 1/2. A player expects 14 wins. How many games did they play?
- 17th December 1971On 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?
- 18th December 1971A car covers 760 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 19th December 1971Use the iteration x(n+1) = cube root of (4x(n) + 6) with x(0) = 2. Work out x(1) to 3 decimal places.
- 20th December 1971A train slows steadily from 27 m/s to rest in 10 seconds. Work out its deceleration.
- 21st December 1971In a vector proof you find that vector PQ = a + 5b and vector RS = 2a + 10b. What does this show about PQ and RS?
- 22nd December 1971A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 23rd December 1971A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 24th December 1971Rationalise the denominator of 10/sqrt(2), giving your answer in its simplest form.
- 25th December 1971Work out the nth term of the quadratic sequence 12, 28, 52, 84, ...
- 26th December 1971y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 27th December 1971A cuboid measures 9 cm by 14 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th December 1971A bag holds 6 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th December 1971On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th December 1971Simplify sqrt(72) + sqrt(18), giving your answer in the form a sqrt(b).
- 31st December 1971The point (5, 3) lies on y = f(x). Write down its image on y = f(x) - 2.