Daily Practice · Higher Plus
September 2007 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2007, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2007 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2007
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2007The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 2nd September 2007A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 3rd September 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?
- 4th September 2007Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 5th September 2007f(x) = 6x - 10. Work out the inverse function f^-1(x).
- 6th September 2007y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 7th September 2007In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 8th September 2007The probability of winning a game is 7/10. A player expects 49 wins. How many games did they play?
- 9th September 2007A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 10th September 2007A block has mass 380 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th September 2007Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 12th September 2007y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 4.
- 13th September 2007In a vector proof you find that vector PQ = 4a + 4b and vector RS = 20a + 20b. What does this show about PQ and RS?
- 14th September 2007A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 15th September 2007On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th September 2007x = 135 and y = 83, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th September 2007Use the iteration x(n+1) = cube root of (3x(n) + 1) with x(0) = 1. Work out x(1) to 3 decimal places.
- 18th September 2007A train slows steadily from 36 m/s to rest in 8 seconds. Work out its deceleration.
- 19th September 2007A cuboid measures 11 cm by 8 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th September 2007A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st September 2007A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 22nd September 2007A car covers 420 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.
- 23rd September 2007Work out the nth term of the quadratic sequence 12, 26, 48, 78, ...
- 24th September 2007y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 25th September 2007A cuboid measures 7 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th September 2007A bag holds 7 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th September 2007On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th September 2007Rationalise the denominator of 14/sqrt(7), giving your answer in its simplest form.
- 29th September 2007The point (2, -1) lies on y = f(x). Write down its image on y = f(-x).
- 30th September 2007y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.