Daily Practice · Higher Plus
September 2014 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2014, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2014 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2014
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2014The probability of winning a game is 4/5. A player expects 52 wins. How many games did they play?
- 2nd September 2014On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 3rd September 2014A rectangle is 26 cm by 28 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th September 2014Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 5th September 2014A train slows steadily from 26 m/s to rest in 10 seconds. Work out its deceleration.
- 6th September 2014In a vector proof you find that vector PQ = 5a - 2b and vector RS = 25a - 10b. What does this show about PQ and RS?
- 7th September 2014A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 8th September 2014A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 9th September 2014Expand and simplify (9 + sqrt(6))(9 - sqrt(6)).
- 10th September 2014Use the iteration x(n+1) = cube root of (7x(n) + 3) with x(0) = 4. Work out x(1) to 3 decimal places.
- 11th September 2014y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 12th September 2014A cuboid measures 14 cm by 8 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th September 2014A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th September 2014On 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?
- 15th September 2014A block has mass 860 g (to the nearest 10 g) and volume 6 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th September 2014Work out the nth term of the quadratic sequence 7, 16, 33, 58, ...
- 17th September 2014y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 18th September 2014A cuboid measures 5 cm by 7 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th September 2014A bag holds 7 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th September 2014A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 21st September 2014x = 49 and y = 11, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd September 2014The point (-6, -5) lies on y = f(x). Write down its image on y = f(x) - 6.
- 23rd September 2014y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 64.
- 24th September 2014The 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.
- 25th September 2014A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 26th September 2014On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 27th September 2014A car covers 310 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 28th September 2014Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 29th September 2014A train slows steadily from 13 m/s to rest in 8 seconds. Work out its deceleration.
- 30th September 2014In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.