Daily Practice · Higher Plus
February 2007 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2007, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2007 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2007
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2007Write 2/(x + 5) + 6/(x - 5) as a single fraction.
- 2nd February 2007y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 3rd February 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.
- 4th February 2007A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 5th February 2007A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 6th February 2007Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
- 7th February 2007Solve 5x^2 - 22x + 8 = 0.
- 8th February 2007y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 49.
- 9th February 2007In 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.
- 10th February 2007The probability of winning a game is 3/5. A player expects 12 wins. How many games did they play?
- 11th February 2007On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th February 2007A block has mass 480 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th February 2007f(x) = 8x + 3. Work out the inverse function f^-1(x).
- 14th February 2007A train slows steadily from 13 m/s to rest in 8 seconds. Work out its deceleration.
- 15th February 2007In a vector proof you find that vector PQ = 3a + 4b and vector RS = 6a + 8b. What does this show about PQ and RS?
- 16th February 2007A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 17th February 2007A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 18th February 2007x = 185 and y = 33, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th February 2007Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
- 20th February 2007y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 21st February 2007A cuboid measures 7 cm by 15 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd February 2007A 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?
- 23rd February 2007On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 24th February 2007A car covers 190 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.
- 25th February 2007Use the iteration x(n+1) = cube root of (3x(n) + 7) with x(0) = 5. Work out x(1) to 3 decimal places.
- 26th February 2007y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 27th February 2007A cuboid measures 12 cm by 4 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th February 2007A bag holds 6 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?