Daily Practice · Higher Plus
December 1978 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1978 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1978
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1978y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 25.
- 2nd December 1978The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 3rd December 1978A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 4th December 1978On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 5th December 1978Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).
- 6th December 1978Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 7th December 1978A train slows steadily from 21 m/s to rest in 10 seconds. Work out its deceleration.
- 8th December 1978In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 9th December 1978The probability of winning a game is 2/5. A player expects 8 wins. How many games did they play?
- 10th December 1978A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 11th December 1978A block has mass 750 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th December 1978Use the iteration x(n+1) = cube root of (11x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.
- 13th December 1978y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 14th December 1978In a vector proof you find that vector PQ = 5a + 5b and vector RS = 15a + 15b. What does this show about PQ and RS?
- 15th December 1978A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 16th December 1978On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th December 1978x = 162 and y = 108, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th December 1978Work out the nth term of the quadratic sequence -3, 2, 9, 18, ...
- 19th December 1978y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 20th December 1978A cuboid measures 8 cm by 14 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st December 1978A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd December 1978A 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?
- 23rd December 1978A car covers 870 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 24th December 1978The point (-6, 3) lies on y = f(x). Write down its image on y = f(x) + 4.
- 25th December 1978y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 16.
- 26th December 1978A cuboid measures 6 cm by 5 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th December 1978A bag holds 5 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th December 1978On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th December 1978Rationalise the denominator of 15/sqrt(3), giving your answer in its simplest form.
- 30th December 1978Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 31st December 1978A train slows steadily from 16 m/s to rest in 4 seconds. Work out its deceleration.