Daily Practice · Higher Plus
December 2010 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2010, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2010 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2010
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2010y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 64.
- 2nd December 2010A cuboid measures 6 cm by 4 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd December 2010A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th December 2010On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 5th December 2010x = 60 and y = 5, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th December 2010Work out the coordinates of the turning point of y = x^2 - 2x + 15.
- 7th December 2010A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 8th December 2010A cuboid measures 10 cm by 6 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th December 2010A 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?
- 10th December 2010A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 11th December 2010A car covers 620 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th December 2010Simplify (x^2 - 25)/(x - 5).
- 13th December 2010y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 14th December 2010The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 15th December 2010A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 16th December 2010On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 17th December 2010Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 18th December 2010In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 19th December 2010y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 20th December 2010In 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.
- 21st December 2010The probability of winning a game is 2/5. A player expects 22 wins. How many games did they play?
- 22nd December 2010A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 1.4. How many values in total?
- 23rd December 2010Simplify sqrt(20) + sqrt(245), giving your answer in the form a sqrt(b).
- 24th December 2010Make x the subject of 4x + 4 = y(x + 4).
- 25th December 2010y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 64.
- 26th December 2010In a vector proof you find that vector PQ = 4a - b and vector RS = 20a - 5b. What does this show about PQ and RS?
- 27th December 2010A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 28th December 2010On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th December 2010A rectangle is 12 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th December 2010Write 6/(x + 3) + 2/(x - 6) as a single fraction.
- 31st December 2010A train slows steadily from 23 m/s to rest in 8 seconds. Work out its deceleration.