Daily Practice · Higher Plus
June 2010 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2010, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2010 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2010
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2010A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 2nd June 2010A rectangle is 22 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd June 2010Make x the subject of 2x + 4 = y(x + 4).
- 4th June 2010y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 5th June 2010A cuboid measures 14 cm by 13 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th June 2010A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th June 2010On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 8th June 2010Expand and simplify (3 + sqrt(3))(3 - sqrt(3)).
- 9th June 2010Write 4/(x + 2) + 6/(x - 6) as a single fraction.
- 10th June 2010y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 11th June 2010A cuboid measures 9 cm by 11 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th June 2010A bag holds 7 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th June 2010A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 0.8. How many values in total?
- 14th June 2010A block has mass 820 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 15th June 2010Solve 16x^2 - 8x - 3 = 0.
- 16th June 2010y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 64.
- 17th June 2010The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 18th June 2010A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 19th June 2010On 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?
- 20th June 2010x = 42 and y = 22, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st June 2010f(x) = 2x - 1. Work out the inverse function f^-1(x).
- 22nd June 2010A train slows steadily from 13 m/s to rest in 8 seconds. Work out its deceleration.
- 23rd June 2010In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 24th June 2010The probability of winning a game is 1/8. A player expects 9 wins. How many games did they play?
- 25th June 2010A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 26th June 2010A car covers 350 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 27th June 2010Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 28th June 2010y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 29th June 2010In a vector proof you find that vector PQ = 3a - 4b and vector RS = 9a - 12b. What does this show about PQ and RS?
- 30th June 2010A bag holds 6 red and n blue counters. The probability of taking a red is 3/5. Work out n.