Daily Practice · Higher Plus
February 2008 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2008, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2008 sheets in a single PDF, each tier behind its own divider page - 145 sheets in one file.
Every sheet in February 2008
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2008Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
- 2nd February 2008A quadratic sequence starts -3, -4, -3, 0. Work out the second difference, and the coefficient of n^2.
- 3rd February 2008y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 16.
- 4th February 2008In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 5th February 2008The probability of winning a game is 1/4. A player expects 30 wins. How many games did they play?
- 6th February 2008On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th February 2008Simplify sqrt(80) + sqrt(45), giving your answer in the form a sqrt(b).
- 8th February 2008Solve x^2 + 5x - 6 < 0.
- 9th February 2008A train slows steadily from 31 m/s to rest in 4 seconds. Work out its deceleration.
- 10th February 2008In a vector proof you find that vector PQ = 3a - 4b and vector RS = 15a - 20b. What does this show about PQ and RS?
- 11th February 2008A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 12th February 2008A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 13th February 2008A rectangle is 4 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th February 2008Write x^2 + 4x - 8 in the form (x + a)^2 + b.
- 15th February 2008y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 16th February 2008A cuboid measures 14 cm by 3 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th February 2008A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th February 2008On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th February 2008Expand and simplify (9 + sqrt(6))(9 - sqrt(6)).
- 20th February 2008Work out the coordinates of the turning point of y = x^2 - 10x + 3.
- 21st February 2008y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 5.
- 22nd February 2008A cuboid measures 7 cm by 6 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd February 2008A bag holds 6 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th February 2008A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 25th February 2008A block has mass 720 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th February 2008Simplify (x^2 - 64)/(x - 8).
- 27th February 2008y is directly proportional to sqrt(x). When x = 25, y = 10. Work out y when x = 64.
- 28th February 2008The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 29th February 2008A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.