Daily Practice · Higher Plus
September 2012 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2012, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2012 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2012
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2012A car covers 440 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 2nd September 2012Write 3/(x + 1) + 2/(x + 4) as a single fraction.
- 3rd September 2012y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 4th September 2012The 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.
- 5th September 2012A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 6th September 2012A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 7th September 2012Rationalise the denominator of 9/sqrt(3), giving your answer in its simplest form.
- 8th September 2012Solve 6x^2 - 11x + 4 = 0.
- 9th September 2012y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 64.
- 10th September 2012In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 11th September 2012The probability of winning a game is 5/8. A player expects 40 wins. How many games did they play?
- 12th September 2012On 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?
- 13th September 2012Simplify sqrt(48) + sqrt(12), giving your answer in the form a sqrt(b).
- 14th September 2012f(x) = 7x - 7. Work out the inverse function f^-1(x).
- 15th September 2012A train slows steadily from 17 m/s to rest in 4 seconds. Work out its deceleration.
- 16th September 2012In a vector proof you find that vector PQ = 3a + 5b and vector RS = 15a + 25b. What does this show about PQ and RS?
- 17th September 2012A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 18th September 2012A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 19th September 2012A rectangle is 4 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 20th September 2012Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 21st September 2012y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 22nd September 2012A cuboid measures 4 cm by 9 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd September 2012A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th September 2012On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th September 2012Expand and simplify (5 + sqrt(7))(5 - sqrt(7)).
- 26th September 2012Use the iteration x(n+1) = cube root of (9x(n) + 4) with x(0) = 1. Work out x(1) to 3 decimal places.
- 27th September 2012y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 28th September 2012A cuboid measures 12 cm by 9 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th September 2012A bag holds 3 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th September 2012A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?