Daily Practice · Higher Plus
May 2009 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2009, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2009 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2009A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 2nd May 2009A car covers 250 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 3rd May 2009Solve 5x^2 + 29x - 6 = 0.
- 4th May 2009y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 81.
- 5th May 2009In a vector proof you find that vector PQ = a + 3b and vector RS = 5a + 15b. What does this show about PQ and RS?
- 6th May 2009A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 7th May 2009On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 8th May 2009Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.
- 9th May 2009f(x) = 3x - 9. Work out the inverse function f^-1(x).
- 10th May 2009A train slows steadily from 37 m/s to rest in 8 seconds. Work out its deceleration.
- 11th May 2009A cuboid measures 7 cm by 14 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th May 2009A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th May 2009A 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?
- 14th May 2009Simplify sqrt(12) + sqrt(147), giving your answer in the form a sqrt(b).
- 15th May 2009Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 16th May 2009y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 17th May 2009A cuboid measures 11 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th May 2009A bag holds 6 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th May 2009On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 20th May 2009A rectangle is 30 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st May 2009Use the iteration x(n+1) = cube root of (2x(n) + 7) with x(0) = 5. Work out x(1) to 3 decimal places.
- 22nd May 2009y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 23rd May 2009The 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.
- 24th May 2009A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/45. Work out r.
- 25th May 2009A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 26th May 2009Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 27th May 2009Work out the nth term of the quadratic sequence 9, 22, 43, 72, ...
- 28th May 2009y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 9.
- 29th May 2009In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 30th May 2009The probability of winning a game is 1/2. A player expects 52 wins. How many games did they play?
- 31st May 2009On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?