Daily Practice · Higher Plus
January 2011 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2011, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2011 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2011A cuboid measures 15 cm by 8 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd January 2011A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd January 2011A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 4th January 2011Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
- 5th January 2011Solve 12x^2 + 13x + 3 = 0.
- 6th January 2011y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 7th January 2011A cuboid measures 10 cm by 7 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th January 2011A bag holds 7 red, 5 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th January 2011On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th January 2011A block has mass 260 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.
- 11th January 2011f(x) = 2x + 4. Work out the inverse function f^-1(x).
- 12th January 2011y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 13th January 2011The 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.
- 14th January 2011A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 15th January 2011A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 16th January 2011x = 64 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th January 2011Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.
- 18th January 2011y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 81.
- 19th January 2011In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 20th January 2011The probability of winning a game is 1/2. A player expects 44 wins. How many games did they play?
- 21st January 2011On 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?
- 22nd January 2011A car covers 900 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.
- 23rd January 2011Use the iteration x(n+1) = cube root of (10x(n) + 1) with x(0) = 2. Work out x(1) to 3 decimal places.
- 24th January 2011A train slows steadily from 22 m/s to rest in 5 seconds. Work out its deceleration.
- 25th January 2011In a vector proof you find that vector PQ = 5a - 5b and vector RS = 25a - 25b. What does this show about PQ and RS?
- 26th January 2011A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 27th January 2011A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 28th January 2011Rationalise the denominator of 77/sqrt(7), giving your answer in its simplest form.
- 29th January 2011Work out the nth term of the quadratic sequence 1, 12, 29, 52, ...
- 30th January 2011y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 31st January 2011A cuboid measures 10 cm by 5 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.