Daily Practice · Higher Plus
December 2000 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2000, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2000 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2000
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2000A bag holds 6 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd December 2000A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 3rd December 2000x = 60 and y = 7, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th December 2000Make x the subject of 8x + 8 = y(x + 8).
- 5th December 2000y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 4.
- 6th December 2000The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 7th December 2000A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 8th December 2000On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 9th December 2000A car covers 300 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th December 2000Write 4/(x - 4) + 4/(x + 4) as a single fraction.
- 11th December 2000A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.
- 12th December 2000In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 13th December 2000The probability of winning a game is 1/5. A player expects 10 wins. How many games did they play?
- 14th December 2000A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 15th December 2000Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
- 16th December 2000Solve 9x^2 - 9x - 4 = 0.
- 17th December 2000y is inversely proportional to x^2. When x = 5, y = 27. Work out y when x = 3.
- 18th December 2000In a vector proof you find that vector PQ = 5a + 5b and vector RS = 10a + 10b. What does this show about PQ and RS?
- 19th December 2000A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 20th December 2000On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 21st December 2000Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
- 22nd December 2000f(x) = 4x - 9. Work out the inverse function f^-1(x).
- 23rd December 2000y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 24th December 2000A cuboid measures 13 cm by 15 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th December 2000A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th December 2000A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
- 27th December 2000A rectangle is 22 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th December 2000Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 29th December 2000y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 49.
- 30th December 2000A cuboid measures 14 cm by 12 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 31st December 2000A bag holds 5 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?