Daily Practice · Higher Plus
December 2007 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2007, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2007 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2007
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2007A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 2nd December 2007A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 3rd December 2007A block has mass 260 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 4th December 2007Write 2/(x - 6) + 7/(x + 2) as a single fraction.
- 5th December 2007y is inversely proportional to x^2. When x = 4, y = 9. Work out y when x = 3.
- 6th December 2007In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 7th December 2007The probability of winning a game is 5/8. A player expects 45 wins. How many games did they play?
- 8th December 2007On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th December 2007x = 73 and y = 63, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th December 2007Solve 5x^2 - 18x - 8 = 0.
- 11th December 2007y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 12th December 2007In a vector proof you find that vector PQ = 3a + 4b and vector RS = 15a + 20b. What does this show about PQ and RS?
- 13th December 2007A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
- 14th December 2007A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 15th December 2007A car covers 510 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 16th December 2007f(x) = 3x - 8. Work out the inverse function f^-1(x).
- 17th December 2007y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 81.
- 18th December 2007A cuboid measures 15 cm by 3 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th December 2007A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th December 2007On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 21st December 2007Rationalise the denominator of 24/sqrt(2), giving your answer in its simplest form.
- 22nd December 2007Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 23rd December 2007A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.
- 24th December 2007A cuboid measures 12 cm by 6 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th December 2007A bag holds 7 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th December 2007A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 27th December 2007Simplify sqrt(27) + sqrt(3), giving your answer in the form a sqrt(b).
- 28th December 2007Use the iteration x(n+1) = cube root of (7x(n) + 7) with x(0) = 3. Work out x(1) to 3 decimal places.
- 29th December 2007y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 30th December 2007The 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.
- 31st December 2007A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/55. Work out r.