Daily Practice · Higher Plus
February 2010 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2010, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2010 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2010
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2010A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.6. How many values in total?
- 2nd February 2010Expand and simplify (2 + sqrt(11))(2 - sqrt(11)).
- 3rd February 2010Work out the coordinates of the turning point of y = x^2 + 16x - 4.
- 4th February 2010y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 5th February 2010A cuboid measures 6 cm by 7 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th February 2010A bag holds 9 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th February 2010On 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?
- 8th February 2010A block has mass 520 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 9th February 2010Simplify (x^2 - 3x - 18)/(x - 6).
- 10th February 2010y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 11th February 2010A cuboid measures 12 cm by 10 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th February 2010A bag holds 4 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th February 2010A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?
- 14th February 2010x = 73 and y = 9, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th February 2010In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 16th February 2010y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 25.
- 17th February 2010The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 18th February 2010A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 19th February 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?
- 20th February 2010A car covers 270 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st February 2010Make x the subject of 3x + 3 = y(x + 3).
- 22nd February 2010A train slows steadily from 23 m/s to rest in 4 seconds. Work out its deceleration.
- 23rd February 2010In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 24th February 2010The probability of winning a game is 4/5. A player expects 48 wins. How many games did they play?
- 25th February 2010A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 26th February 2010Rationalise the denominator of 18/sqrt(6), giving your answer in its simplest form.
- 27th February 2010Write 2/(x + 2) + 3/(x + 3) as a single fraction.
- 28th February 2010y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.