Daily Practice · Higher Plus
December 1977 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1977 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1977
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1977A cuboid measures 13 cm by 9 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd December 1977A bag holds 5 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd December 1977A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 4th December 1977x = 129 and y = 33, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th December 1977A quadratic sequence starts 5, 7, 13, 23. Work out the second difference, and the coefficient of n^2.
- 6th December 1977y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 49.
- 7th December 1977The 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.
- 8th December 1977A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 9th December 1977On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th December 1977A car covers 740 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 11th December 1977Solve x^2 - 9x + 14 > 0.
- 12th December 1977A train slows steadily from 12 m/s to rest in 5 seconds. Work out its deceleration.
- 13th December 1977In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 14th December 1977The probability of winning a game is 3/4. A player expects 24 wins. How many games did they play?
- 15th December 1977A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 16th December 1977Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 17th December 1977Write x^2 + 16x + 15 in the form (x + a)^2 + b.
- 18th December 1977y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 19th December 1977In a vector proof you find that vector PQ = 4a - b and vector RS = 8a - 2b. What does this show about PQ and RS?
- 20th December 1977A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 21st December 1977On 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?
- 22nd December 1977Simplify sqrt(48) + sqrt(12), giving your answer in the form a sqrt(b).
- 23rd December 1977Work out the coordinates of the turning point of y = x^2 - 14x + 7.
- 24th December 1977y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 25th December 1977A cuboid measures 14 cm by 13 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th December 1977A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th December 1977A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 28th December 1977A rectangle is 23 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th December 1977Simplify (x^2 - 11x + 30)/(x - 5).
- 30th December 1977y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 4.
- 31st December 1977A cuboid measures 14 cm by 12 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.