Daily Practice · Higher Plus
June 2011 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2011, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2011 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2011A bag holds 9 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd June 2011On 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?
- 3rd June 2011Rationalise the denominator of 15/sqrt(5), giving your answer in its simplest form.
- 4th June 2011The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 5th June 2011y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 6th June 2011A cuboid measures 5 cm by 6 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th June 2011A bag holds 6 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th June 2011A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 9th June 2011Simplify sqrt(72) + sqrt(8), giving your answer in the form a sqrt(b).
- 10th June 2011A quadratic sequence starts 14, 25, 40, 59. Work out the second difference, and the coefficient of n^2.
- 11th June 2011y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 16.
- 12th June 2011The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 13th June 2011A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
- 14th June 2011On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th June 2011A rectangle is 5 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th June 2011Solve x^2 - 3x < 0.
- 17th June 2011A train slows steadily from 21 m/s to rest in 4 seconds. Work out its deceleration.
- 18th June 2011In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 19th June 2011The probability of winning a game is 1/4. A player expects 14 wins. How many games did they play?
- 20th June 2011A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 21st June 2011Expand and simplify (3 + sqrt(10))(3 - sqrt(10)).
- 22nd June 2011Write x^2 - 2x + 9 in the form (x + a)^2 + b.
- 23rd June 2011y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 24th June 2011In a vector proof you find that vector PQ = 5a + 2b and vector RS = 10a + 4b. What does this show about PQ and RS?
- 25th June 2011A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 26th June 2011On 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?
- 27th June 2011A block has mass 610 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.
- 28th June 2011Work out the coordinates of the turning point of y = x^2 + 4x + 13.
- 29th June 2011y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 30th June 2011A cuboid measures 7 cm by 4 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.