Daily Practice · Higher Plus
December 2008 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2008, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2008 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2008
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2008The probability of winning a game is 3/4. A player expects 90 wins. How many games did they play?
- 2nd December 2008On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 3rd December 2008A rectangle is 11 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th December 2008A quadratic sequence starts 2, 12, 28, 50. Work out the second difference, and the coefficient of n^2.
- 5th December 2008y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 6th December 2008In a vector proof you find that vector PQ = 6a - 5b and vector RS = 30a - 25b. What does this show about PQ and RS?
- 7th December 2008A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 8th December 2008A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 9th December 2008Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 10th December 2008Solve x^2 + 6x + 8 < 0.
- 11th December 2008y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 16.
- 12th December 2008A cuboid measures 7 cm by 15 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th December 2008A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th December 2008On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th December 2008A block has mass 310 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th December 2008Write x^2 + 14x - 12 in the form (x + a)^2 + b.
- 17th December 2008A train slows steadily from 40 m/s to rest in 10 seconds. Work out its deceleration.
- 18th December 2008A cuboid measures 9 cm by 10 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th December 2008A bag holds 5 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th December 2008A 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?
- 21st December 2008x = 172 and y = 150, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd December 2008Work out the coordinates of the turning point of y = x^2 - 4x + 3.
- 23rd December 2008y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 24th December 2008The 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.
- 25th December 2008A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 26th December 2008On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 27th December 2008A car covers 840 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.
- 28th December 2008Simplify (x^2 - 11x + 30)/(x - 6).
- 29th December 2008y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 30th December 2008In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 31st December 2008The probability of winning a game is 3/4. A player expects 66 wins. How many games did they play?