Daily Practice · Higher Plus
September 2013 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2013, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2013 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2013A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 2nd September 2013A block has mass 700 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 3rd September 2013A quadratic sequence starts 10, 22, 40, 64. Work out the second difference, and the coefficient of n^2.
- 4th September 2013y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 9.
- 5th September 2013In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 6th September 2013The probability of winning a game is 3/5. A player expects 42 wins. How many games did they play?
- 7th September 2013On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 8th September 2013x = 165 and y = 63, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th September 2013Solve x^2 - 12x + 20 > 0.
- 10th September 2013A train slows steadily from 22 m/s to rest in 4 seconds. Work out its deceleration.
- 11th September 2013In a vector proof you find that vector PQ = 4a + b and vector RS = 20a + 5b. What does this show about PQ and RS?
- 12th September 2013A bag holds 7 red and n blue counters. The probability of taking a red is 7/11. Work out n.
- 13th September 2013A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 14th September 2013A car covers 710 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 15th September 2013Write x^2 - 8x + 8 in the form (x + a)^2 + b.
- 16th September 2013y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 17th September 2013A cuboid measures 13 cm by 11 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th September 2013A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th September 2013On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th September 2013Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
- 21st September 2013Work out the coordinates of the turning point of y = x^2 - 4x - 14.
- 22nd September 2013y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 23rd September 2013A cuboid measures 13 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th September 2013A bag holds 4 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th September 2013A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 1.4. How many values in total?
- 26th September 2013Simplify sqrt(48) + sqrt(48), giving your answer in the form a sqrt(b).
- 27th September 2013Simplify (x^2 - 6x - 7)/(x - 7).
- 28th September 2013y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 64.
- 29th September 2013The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 30th September 2013A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/36. Work out r.