Daily Practice · Higher Plus
July 2011 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2011, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2011 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2011
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2011A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd July 2011A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 3rd July 2011x = 114 and y = 35, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th July 2011Simplify (x^2 - 36)/(x + 6).
- 5th July 2011y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 4.
- 6th July 2011A cuboid measures 10 cm by 11 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th July 2011A bag holds 6 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th July 2011On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th July 2011A car covers 430 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th July 2011In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 11th July 2011A train slows steadily from 29 m/s to rest in 8 seconds. Work out its deceleration.
- 12th July 2011The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 13th July 2011A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 14th July 2011A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 15th July 2011Rationalise the denominator of 15/sqrt(5), giving your answer in its simplest form.
- 16th July 2011Make x the subject of 7x + 6 = y(x + 6).
- 17th July 2011y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 18th July 2011In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 19th July 2011The probability of winning a game is 3/8. A player expects 18 wins. How many games did they play?
- 20th July 2011On 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?
- 21st July 2011Simplify sqrt(20) + sqrt(180), giving your answer in the form a sqrt(b).
- 22nd July 2011Write 7/(x - 5) + 5/(x - 4) as a single fraction.
- 23rd July 2011y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 24th July 2011In a vector proof you find that vector PQ = 6a - 4b and vector RS = 12a - 8b. What does this show about PQ and RS?
- 25th July 2011A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 26th July 2011A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 27th July 2011A rectangle is 19 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th July 2011Solve 15x^2 + 16x - 15 = 0.
- 29th July 2011y is directly proportional to sqrt(x). When x = 25, y = 15. Work out y when x = 81.
- 30th July 2011A cuboid measures 12 cm by 3 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st July 2011A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?