Daily Practice · Higher Plus
August 2007 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2007, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2007 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2007
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2007A train slows steadily from 22 m/s to rest in 5 seconds. Work out its deceleration.
- 2nd August 2007The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 3rd August 2007A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 21/55. Work out r.
- 4th August 2007A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 5th August 2007x = 160 and y = 132, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th August 2007Simplify (x^2 + 9x + 8)/(x + 8).
- 7th August 2007y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 8th August 2007In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 9th August 2007The probability of winning a game is 4/5. A player expects 8 wins. How many games did they play?
- 10th August 2007On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th August 2007A car covers 110 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th August 2007In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 13th August 2007y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 14th August 2007In a vector proof you find that vector PQ = 4a + 6b and vector RS = 20a + 30b. What does this show about PQ and RS?
- 15th August 2007A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 16th August 2007A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 17th August 2007Rationalise the denominator of 10/sqrt(2), giving your answer in its simplest form.
- 18th August 2007Make x the subject of 7x + 7 = y(x + 7).
- 19th August 2007y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 49.
- 20th August 2007A cuboid measures 8 cm by 12 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st August 2007A bag holds 8 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd August 2007On 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?
- 23rd August 2007Simplify sqrt(48) + sqrt(27), giving your answer in the form a sqrt(b).
- 24th August 2007Write 5/(x - 5) + 4/(x - 4) as a single fraction.
- 25th August 2007A train slows steadily from 26 m/s to rest in 5 seconds. Work out its deceleration.
- 26th August 2007A cuboid measures 5 cm by 13 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th August 2007A bag holds 6 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th August 2007A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 29th August 2007A rectangle is 15 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th August 2007Solve 12x^2 + x - 20 = 0.
- 31st August 2007y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.