Daily Practice · Higher Plus
May 2007 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2007, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2007 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2007
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2007Expand and simplify (8 + sqrt(2))(8 - sqrt(2)).
- 2nd May 2007In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 3rd May 2007y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 4th May 2007The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 5th May 2007A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 7/15. Work out r.
- 6th May 2007On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th May 2007A block has mass 240 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 8th May 2007Make x the subject of 6x + 4 = y(x + 4).
- 9th May 2007y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 10th May 2007In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 11th May 2007The probability of winning a game is 1/4. A player expects 22 wins. How many games did they play?
- 12th May 2007A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 13th May 2007x = 34 and y = 9, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th May 2007Write 4/(x + 2) + 4/(x + 3) as a single fraction.
- 15th May 2007y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 36.
- 16th May 2007In a vector proof you find that vector PQ = a - b and vector RS = 2a - 2b. What does this show about PQ and RS?
- 17th May 2007A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 18th May 2007On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 19th May 2007A car covers 630 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.
- 20th May 2007Solve 5x^2 - 8x - 4 = 0.
- 21st May 2007A train slows steadily from 21 m/s to rest in 8 seconds. Work out its deceleration.
- 22nd May 2007A cuboid measures 14 cm by 14 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd May 2007A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th May 2007A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 25th May 2007Rationalise the denominator of 4/sqrt(2), giving your answer in its simplest form.
- 26th May 2007f(x) = 4x - 5. Work out the inverse function f^-1(x).
- 27th May 2007y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 28th May 2007A cuboid measures 10 cm by 5 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th May 2007A bag holds 4 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th May 2007On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 31st May 2007Simplify sqrt(20) + sqrt(5), giving your answer in the form a sqrt(b).