Daily Practice · Higher Plus
November 2012 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2012, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2012 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2012
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2012A quadratic sequence starts 10, 24, 48, 82. Work out the second difference, and the coefficient of n^2.
- 2nd November 2012A train slows steadily from 16 m/s to rest in 8 seconds. Work out its deceleration.
- 3rd November 2012The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 4th November 2012A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/45. Work out r.
- 5th November 2012A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 6th November 2012Expand and simplify (3 + sqrt(11))(3 - sqrt(11)).
- 7th November 2012Solve x^2 - 6x + 5 < 0.
- 8th November 2012y is inversely proportional to x^2. When x = 2, y = 48. Work out y when x = 4.
- 9th November 2012In 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.
- 10th November 2012The probability of winning a game is 1/4. A player expects 6 wins. How many games did they play?
- 11th November 2012On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th November 2012A block has mass 870 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th November 2012Write x^2 + 8x - 1 in the form (x + a)^2 + b.
- 14th November 2012y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 15th November 2012In a vector proof you find that vector PQ = 5a + b and vector RS = 10a + 2b. What does this show about PQ and RS?
- 16th November 2012A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 17th November 2012A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 18th November 2012x = 36 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th November 2012Work out the coordinates of the turning point of y = x^2 - 2x + 15.
- 20th November 2012y is directly proportional to sqrt(x). When x = 4, y = 6. Work out y when x = 81.
- 21st November 2012A cuboid measures 5 cm by 3 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd November 2012A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd November 2012On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th November 2012A car covers 610 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 25th November 2012Simplify (x^2 + 2x - 35)/(x + 7).
- 26th November 2012A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.
- 27th November 2012A cuboid measures 8 cm by 12 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th November 2012A bag holds 7 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th November 2012A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 30th November 2012Rationalise the denominator of 24/sqrt(3), giving your answer in its simplest form.