Daily Practice · Higher Plus
December 1995 - Higher Plus 5-a-day
Printing for a group?
The batch download puts all 5 tiers' December 1995 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 1995
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 1995Write 3/(x - 3) + 3/(x - 1) as a single fraction.
- 2nd December 1995y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 3rd December 1995The 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.
- 4th December 1995A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 5th December 1995A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 6th December 1995A rectangle is 22 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th December 1995Solve 6x^2 - 5x - 6 = 0.
- 8th December 1995y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 4.
- 9th December 1995In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 10th December 1995The probability of winning a game is 3/4. A player expects 21 wins. How many games did they play?
- 11th December 1995On 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?
- 12th December 1995Expand and simplify (9 + sqrt(6))(9 - sqrt(6)).
- 13th December 1995f(x) = 2x - 12. Work out the inverse function f^-1(x).
- 14th December 1995A train slows steadily from 24 m/s to rest in 4 seconds. Work out its deceleration.
- 15th December 1995In a vector proof you find that vector PQ = 3a - 3b and vector RS = 9a - 9b. What does this show about PQ and RS?
- 16th December 1995A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 17th December 1995A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 18th December 1995A block has mass 400 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th December 1995Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 20th December 1995y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 21st December 1995A cuboid measures 9 cm by 15 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd December 1995A bag holds 9 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd December 1995On 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?
- 24th December 1995x = 179 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th December 1995Use the iteration x(n+1) = cube root of (5x(n) + 9) with x(0) = 4. Work out x(1) to 3 decimal places.
- 26th December 1995y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 27th December 1995A cuboid measures 4 cm by 9 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th December 1995A bag holds 6 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th December 1995A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 30th December 1995A car covers 320 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 31st December 1995Work out the nth term of the quadratic sequence 6, 13, 28, 51, ...