Daily Practice · Higher Plus
November 2007 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2007, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2007 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2007
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2007A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 2nd November 2007On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd November 2007A car covers 400 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.
- 4th November 2007Write x^2 - 10x - 2 in the form (x + a)^2 + b.
- 5th November 2007A train slows steadily from 26 m/s to rest in 10 seconds. Work out its deceleration.
- 6th November 2007In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 7th November 2007The probability of winning a game is 5/8. A player expects 65 wins. How many games did they play?
- 8th November 2007A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 9th November 2007Rationalise the denominator of 10/sqrt(2), giving your answer in its simplest form.
- 10th November 2007Work out the coordinates of the turning point of y = x^2 - 6x - 14.
- 11th November 2007y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 12th November 2007In a vector proof you find that vector PQ = 4a + 5b and vector RS = 16a + 20b. What does this show about PQ and RS?
- 13th November 2007A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 14th November 2007On 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?
- 15th November 2007Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
- 16th November 2007Simplify (x^2 + 11x + 30)/(x + 6).
- 17th November 2007y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 18th November 2007A cuboid measures 9 cm by 10 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th November 2007A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th November 2007A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 21st November 2007A rectangle is 18 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd November 2007In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
- 23rd November 2007y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 64.
- 24th November 2007A cuboid measures 10 cm by 8 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th November 2007A bag holds 4 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th November 2007On 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?
- 27th November 2007Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 28th November 2007Make x the subject of 2x + 7 = y(x + 7).
- 29th November 2007A train slows steadily from 38 m/s to rest in 10 seconds. Work out its deceleration.
- 30th November 2007The 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.