Daily Practice · Higher Plus
June 2008 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2008, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2008 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2008
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2008Work out the coordinates of the turning point of y = x^2 + 10x - 14.
- 2nd June 2008y is directly proportional to sqrt(x). When x = 9, y = 18. Work out y when x = 49.
- 3rd June 2008In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 4th June 2008The probability of winning a game is 3/5. A player expects 21 wins. How many games did they play?
- 5th June 2008On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 6th June 2008Rationalise the denominator of 50/sqrt(5), giving your answer in its simplest form.
- 7th June 2008Simplify (x^2 + 3x - 10)/(x - 2).
- 8th June 2008A train slows steadily from 26 m/s to rest in 10 seconds. Work out its deceleration.
- 9th June 2008In a vector proof you find that vector PQ = 4a + b and vector RS = 16a + 4b. What does this show about PQ and RS?
- 10th June 2008A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 11th June 2008A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 12th June 2008Simplify sqrt(8) + sqrt(72), giving your answer in the form a sqrt(b).
- 13th June 2008In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 14th June 2008y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 15th June 2008A cuboid measures 5 cm by 3 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th June 2008A bag holds 3 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th June 2008On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 18th June 2008A rectangle is 4 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th June 2008Make x the subject of 3x + 8 = y(x + 8).
- 20th June 2008y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 21st June 2008A cuboid measures 8 cm by 13 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd June 2008A bag holds 6 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd June 2008A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 24th June 2008Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 25th June 2008Write 4/(x - 5) + 2/(x - 4) as a single fraction.
- 26th June 2008y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 9.
- 27th June 2008The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 28th June 2008A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 29th June 2008On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 30th June 2008A block has mass 460 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.