Daily Practice · Higher Plus
July 2009 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2009, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2009 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2009
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2009A rectangle is 27 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd July 2009Solve x^2 - 4x < 0.
- 3rd July 2009y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 4th July 2009In a vector proof you find that vector PQ = 5a - b and vector RS = 20a - 4b. What does this show about PQ and RS?
- 5th July 2009A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 6th July 2009On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th July 2009Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 8th July 2009Write x^2 + 12x + 9 in the form (x + a)^2 + b.
- 9th July 2009y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 10th July 2009A cuboid measures 6 cm by 6 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th July 2009A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th July 2009A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 13th July 2009A block has mass 460 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th July 2009Work out the coordinates of the turning point of y = x^2 - 2x + 6.
- 15th July 2009y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 16.
- 16th July 2009A cuboid measures 8 cm by 14 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th July 2009A bag holds 5 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th July 2009On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 19th July 2009x = 185 and y = 23, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th July 2009Simplify (x^2 + 10x + 24)/(x + 6).
- 21st July 2009A train slows steadily from 26 m/s to rest in 8 seconds. Work out its deceleration.
- 22nd July 2009The 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.
- 23rd July 2009A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
- 24th July 2009A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 25th July 2009A car covers 450 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.
- 26th July 2009In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 27th July 2009y is inversely proportional to x^2. When x = 4, y = 9. Work out y when x = 3.
- 28th July 2009In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 29th July 2009The probability of winning a game is 7/10. A player expects 63 wins. How many games did they play?
- 30th July 2009On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 31st July 2009Rationalise the denominator of 24/sqrt(6), giving your answer in its simplest form.