Daily Practice · Higher Plus
November 2009 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2009, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2009 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2009In a vector proof you find that vector PQ = 5a + 5b and vector RS = 10a + 10b. What does this show about PQ and RS?
- 2nd November 2009A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 3rd November 2009On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th November 2009A rectangle is 9 cm by 29 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th November 2009In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 6th November 2009y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 4.
- 7th November 2009A cuboid measures 8 cm by 10 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th November 2009A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th November 2009A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.6. How many values in total?
- 10th November 2009Expand and simplify (8 + sqrt(3))(8 - sqrt(3)).
- 11th November 2009Make x the subject of 8x + 7 = y(x + 7).
- 12th November 2009y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 4.
- 13th November 2009A cuboid measures 6 cm by 8 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th November 2009A bag holds 7 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th November 2009On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th November 2009A block has mass 700 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 17th November 2009Write 4/(x + 3) + 7/(x + 5) as a single fraction.
- 18th November 2009A train slows steadily from 23 m/s to rest in 4 seconds. Work out its deceleration.
- 19th November 2009The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 20th November 2009A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 21st November 2009A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 22nd November 2009x = 36 and y = 26, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd November 2009Solve 5x^2 - 12x - 9 = 0.
- 24th November 2009y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 25th November 2009In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 26th November 2009The probability of winning a game is 1/2. A player expects 24 wins. How many games did they play?
- 27th November 2009On 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?
- 28th November 2009A car covers 260 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th November 2009f(x) = 2x + 2. Work out the inverse function f^-1(x).
- 30th November 2009y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.