Daily Practice · Higher Plus
November 2011 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2011, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2011 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2011Write 7/(x + 1) + 2/(x + 5) as a single fraction.
- 2nd November 2011y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 49.
- 3rd November 2011A cuboid measures 13 cm by 4 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th November 2011A bag holds 5 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th November 2011On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 6th November 2011x = 41 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th November 2011Solve 9x^2 - 9x - 4 = 0.
- 8th November 2011A train slows steadily from 30 m/s to rest in 4 seconds. Work out its deceleration.
- 9th November 2011The 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.
- 10th November 2011A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 11th November 2011A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 12th November 2011A car covers 490 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.
- 13th November 2011f(x) = 8x - 9. Work out the inverse function f^-1(x).
- 14th November 2011y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 15th November 2011In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 16th November 2011The probability of winning a game is 1/2. A player expects 48 wins. How many games did they play?
- 17th November 2011On 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?
- 18th November 2011Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 19th November 2011Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 20th November 2011y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 21st November 2011In a vector proof you find that vector PQ = 3a + 4b and vector RS = 15a + 20b. What does this show about PQ and RS?
- 22nd November 2011A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 23rd November 2011A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 24th November 2011Simplify sqrt(8) + sqrt(98), giving your answer in the form a sqrt(b).
- 25th November 2011Use the iteration x(n+1) = cube root of (3x(n) + 1) with x(0) = 5. Work out x(1) to 3 decimal places.
- 26th November 2011y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 4.
- 27th November 2011A cuboid measures 10 cm by 12 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th November 2011A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th November 2011On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 30th November 2011A rectangle is 5 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.