Daily Practice · Higher Plus
December 2012 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2012, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2012 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2012
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2012In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 2nd December 2012y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 3rd December 2012The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 4th December 2012A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 5th December 2012On 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?
- 6th December 2012Simplify sqrt(8) + sqrt(32), giving your answer in the form a sqrt(b).
- 7th December 2012Make x the subject of 5x + 4 = y(x + 4).
- 8th December 2012y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 9th December 2012In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 10th December 2012The probability of winning a game is 3/5. A player expects 39 wins. How many games did they play?
- 11th December 2012A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 12th December 2012A rectangle is 18 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th December 2012Write 4/(x + 3) + 7/(x - 4) as a single fraction.
- 14th December 2012y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 25.
- 15th December 2012In a vector proof you find that vector PQ = a - 2b and vector RS = 4a - 8b. What does this show about PQ and RS?
- 16th December 2012A bag holds 3 red and n blue counters. The probability of taking a red is 3/8. Work out n.
- 17th December 2012On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 18th December 2012Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 19th December 2012Solve 3x^2 - 7x - 6 = 0.
- 20th December 2012A train slows steadily from 19 m/s to rest in 4 seconds. Work out its deceleration.
- 21st December 2012A cuboid measures 3 cm by 15 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd December 2012A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd December 2012A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 24th December 2012A block has mass 770 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th December 2012f(x) = 7x - 4. Work out the inverse function f^-1(x).
- 26th December 2012y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 27th December 2012A cuboid measures 14 cm by 14 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th December 2012A bag holds 6 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th December 2012On 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 December 2012x = 48 and y = 15, each correct to the nearest whole number. Work out the upper bound of x - y.
- 31st December 2012Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.