Daily Practice · Higher Plus
February 2009 - Higher Plus 5-a-day
Every Higher Plus sheet published in February 2009, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' February 2009 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 2009x = 119 and y = 12, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd February 2009Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 3rd February 2009A train slows steadily from 17 m/s to rest in 10 seconds. Work out its deceleration.
- 4th February 2009In a vector proof you find that vector PQ = 6a - b and vector RS = 18a - 3b. What does this show about PQ and RS?
- 5th February 2009A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 6th February 2009A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 7th February 2009A car covers 880 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.
- 8th February 2009Use the iteration x(n+1) = cube root of (12x(n) + 3) with x(0) = 2. Work out x(1) to 3 decimal places.
- 9th February 2009y is inversely proportional to x^2. When x = 2, y = 64. Work out y when x = 4.
- 10th February 2009A cuboid measures 8 cm by 4 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th February 2009A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th February 2009On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th February 2009Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.
- 14th February 2009Work out the nth term of the quadratic sequence -3, 0, 7, 18, ...
- 15th February 2009y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 16th February 2009A cuboid measures 4 cm by 12 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th February 2009A bag holds 5 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th February 2009A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 19th February 2009Simplify sqrt(27) + sqrt(108), giving your answer in the form a sqrt(b).
- 20th February 2009The point (-2, -5) lies on y = f(x). Write down its image on y = f(x - 4).
- 21st February 2009y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 9.
- 22nd February 2009The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 23rd February 2009A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.
- 24th February 2009On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 25th February 2009A rectangle is 8 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th February 2009Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 27th February 2009A train slows steadily from 13 m/s to rest in 8 seconds. Work out its deceleration.
- 28th February 2009In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.