Daily Practice · Higher Plus
September 2010 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2010, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2010 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2010
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2010Simplify (x^2 + 11x + 24)/(x + 8).
- 2nd September 2010A train slows steadily from 25 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd September 2010A cuboid measures 5 cm by 6 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th September 2010A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th September 2010A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 6th September 2010A block has mass 400 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th September 2010In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 8th September 2010y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 9th September 2010A cuboid measures 12 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th September 2010A bag holds 6 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th September 2010On 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?
- 12th September 2010x = 160 and y = 49, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th September 2010Make x the subject of 4x + 8 = y(x + 8).
- 14th September 2010y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 15th September 2010The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 16th September 2010A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 17th September 2010A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 18th September 2010A car covers 290 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 19th September 2010Write 2/(x - 1) + 4/(x + 2) as a single fraction.
- 20th September 2010y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 36.
- 21st September 2010In 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.
- 22nd September 2010The probability of winning a game is 1/2. A player expects 16 wins. How many games did they play?
- 23rd September 2010On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 24th September 2010Rationalise the denominator of 10/sqrt(2), giving your answer in its simplest form.
- 25th September 2010Solve 10x^2 - 17x + 3 = 0.
- 26th September 2010A train slows steadily from 27 m/s to rest in 10 seconds. Work out its deceleration.
- 27th September 2010In a vector proof you find that vector PQ = 5a + 3b and vector RS = 10a + 6b. What does this show about PQ and RS?
- 28th September 2010A bag holds 5 red and n blue counters. The probability of taking a red is 5/7. Work out n.
- 29th September 2010A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 30th September 2010Simplify sqrt(45) + sqrt(45), giving your answer in the form a sqrt(b).