Daily Practice · Higher Plus
May 2008 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2008, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2008 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2008
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2008Simplify sqrt(27) + sqrt(75), giving your answer in the form a sqrt(b).
- 2nd May 2008f(x) = 2x - 1 and g(x) = 2x - 2. Work out fg(-2).
- 3rd May 2008y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 4th May 2008In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 5th May 2008The probability of winning a game is 3/5. A player expects 30 wins. How many games did they play?
- 6th May 2008A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 7th May 2008A rectangle is 16 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th May 2008The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 9th May 2008y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 49.
- 10th May 2008In a vector proof you find that vector PQ = 5a + 6b and vector RS = 20a + 24b. What does this show about PQ and RS?
- 11th May 2008A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 12th May 2008On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th May 2008Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).
- 14th May 2008A quadratic sequence starts 14, 24, 38, 56. Work out the second difference, and the coefficient of n^2.
- 15th May 2008A train slows steadily from 16 m/s to rest in 4 seconds. Work out its deceleration.
- 16th May 2008A cuboid measures 11 cm by 13 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th May 2008A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th May 2008A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 19th May 2008A block has mass 420 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th May 2008Solve x^2 - x - 2 > 0.
- 21st May 2008y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 22nd May 2008A cuboid measures 14 cm by 14 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd May 2008A bag holds 6 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th May 2008On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 25th May 2008x = 59 and y = 19, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th May 2008Write x^2 - 14x - 13 in the form (x + a)^2 + b.
- 27th May 2008y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 28th May 2008The 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.
- 29th May 2008A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 30th May 2008A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 3.5. How many values in total?
- 31st May 2008A car covers 360 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.