Daily Practice · Higher Plus
December 2005 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2005, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2005 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2005Simplify sqrt(8) + sqrt(2), giving your answer in the form a sqrt(b).
- 2nd December 2005Simplify (x^2 + 8x + 12)/(x + 6).
- 3rd December 2005y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 81.
- 4th December 2005A cuboid measures 9 cm by 13 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th December 2005A bag holds 4 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th December 2005On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th December 2005A rectangle is 14 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th December 2005In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 9th December 2005A train slows steadily from 26 m/s to rest in 8 seconds. Work out its deceleration.
- 10th December 2005The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 11th December 2005A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 12th December 2005A 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?
- 13th December 2005Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
- 14th December 2005Make x the subject of 4x + 8 = y(x + 8).
- 15th December 2005y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 16th December 2005In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 17th December 2005The probability of winning a game is 7/8. A player expects 91 wins. How many games did they play?
- 18th December 2005On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 19th December 2005A block has mass 700 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th December 2005Write 4/(x - 3) + 5/(x - 1) as a single fraction.
- 21st December 2005y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 22nd December 2005In a vector proof you find that vector PQ = 6a + 2b and vector RS = 24a + 8b. What does this show about PQ and RS?
- 23rd December 2005A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 24th December 2005A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 25th December 2005x = 171 and y = 143, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th December 2005Solve 12x^2 - 13x + 3 = 0.
- 27th December 2005y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 16.
- 28th December 2005A cuboid measures 8 cm by 15 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th December 2005A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th December 2005On 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?
- 31st December 2005A car covers 490 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.