Daily Practice · Higher Plus
December 2009 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2009, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2009 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2009In a vector proof you find that vector PQ = a - 2b and vector RS = 3a - 6b. What does this show about PQ and RS?
- 2nd December 2009A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 3rd December 2009A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 4th December 2009Rationalise the denominator of 56/sqrt(7), giving your answer in its simplest form.
- 5th December 2009Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 6th December 2009y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 49.
- 7th December 2009A cuboid measures 10 cm by 11 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th December 2009A bag holds 8 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th December 2009On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th December 2009Simplify sqrt(45) + sqrt(5), giving your answer in the form a sqrt(b).
- 11th December 2009Use the iteration x(n+1) = cube root of (8x(n) + 1) with x(0) = 5. Work out x(1) to 3 decimal places.
- 12th December 2009A train slows steadily from 27 m/s to rest in 10 seconds. Work out its deceleration.
- 13th December 2009A cuboid measures 4 cm by 9 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th December 2009A bag holds 4 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th December 2009A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 16th December 2009A rectangle is 13 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th December 2009Work out the nth term of the quadratic sequence 14, 30, 54, 86, ...
- 18th December 2009y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 19th December 2009The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 20th December 2009A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 21st December 2009On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd December 2009Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 23rd December 2009The point (2, 6) lies on y = f(x). Write down its image on y = f(-x).
- 24th December 2009y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 25th December 2009In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 26th December 2009The probability of winning a game is 1/10. A player expects 9 wins. How many games did they play?
- 27th December 2009A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 28th December 2009A block has mass 660 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th December 2009Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 30th December 2009y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 25.
- 31st December 2009In a vector proof you find that vector PQ = 6a + 3b and vector RS = 30a + 15b. What does this show about PQ and RS?