Daily Practice · Higher Plus
December 2011 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2011, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2011 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2011Work out the nth term of the quadratic sequence 7, 12, 21, 34, ...
- 2nd December 2011A train slows steadily from 29 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd December 2011A cuboid measures 10 cm by 14 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th December 2011A bag holds 5 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th December 2011A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 6th December 2011Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
- 7th December 2011The point (1, -6) lies on y = f(x). Write down its image on y = f(x - 5).
- 8th December 2011y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 9th December 2011The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 10th December 2011A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 11th December 2011On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 12th December 2011A block has mass 500 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th December 2011Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 14th December 2011y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 15th December 2011In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 16th December 2011The probability of winning a game is 4/5. A player expects 96 wins. How many games did they play?
- 17th December 2011A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 18th December 2011x = 52 and y = 42, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th December 2011f(x) = 6x + 3 and g(x) = 4x - 3. Work out fg(-2).
- 20th December 2011y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 64.
- 21st December 2011In a vector proof you find that vector PQ = a + 4b and vector RS = 2a + 8b. What does this show about PQ and RS?
- 22nd December 2011A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.
- 23rd December 2011On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th December 2011A car covers 700 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 25th December 2011The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 26th December 2011A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.
- 27th December 2011A cuboid measures 5 cm by 4 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th December 2011A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th December 2011A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 30th December 2011Rationalise the denominator of 22/sqrt(2), giving your answer in its simplest form.
- 31st December 2011A quadratic sequence starts 1, 13, 35, 67. Work out the second difference, and the coefficient of n^2.