Daily Practice · Higher Plus
December 1970 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1970 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1970
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1970A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
- 2nd December 1970A cuboid measures 5 cm by 6 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd December 1970A bag holds 8 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th December 1970A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 5th December 1970A 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.
- 6th December 1970The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 7th December 1970y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 8th December 1970A cuboid measures 4 cm by 14 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th December 1970A bag holds 3 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th December 1970On 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?
- 11th December 1970Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 12th December 1970A quadratic sequence starts 3, 8, 19, 36. Work out the second difference, and the coefficient of n^2.
- 13th December 1970y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 14th December 1970The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 15th December 1970A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 16th December 1970A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 17th December 1970Simplify sqrt(18) + sqrt(50), giving your answer in the form a sqrt(b).
- 18th December 1970Solve x^2 - 11x + 18 > 0.
- 19th December 1970y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 25.
- 20th December 1970In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 21st December 1970The probability of winning a game is 1/5. A player expects 4 wins. How many games did they play?
- 22nd December 1970On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd December 1970A rectangle is 24 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th December 1970Write x^2 - 16x - 7 in the form (x + a)^2 + b.
- 25th December 1970A train slows steadily from 19 m/s to rest in 4 seconds. Work out its deceleration.
- 26th December 1970In a vector proof you find that vector PQ = 2a + 3b and vector RS = 6a + 9b. What does this show about PQ and RS?
- 27th December 1970A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 28th December 1970A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 29th December 1970Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
- 30th December 1970Work out the coordinates of the turning point of y = x^2 + 16x - 14.
- 31st December 1970y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 2.