Daily Practice · Higher Plus
September 2016 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2016, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2016 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2016A cuboid measures 3 cm by 7 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd September 2016A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd September 2016On 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?
- 4th September 2016x = 153 and y = 66, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th September 2016The point (4, -4) lies on y = f(x). Write down its image on y = -f(x).
- 6th September 2016y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 7th September 2016A cuboid measures 14 cm by 12 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th September 2016A bag holds 3 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th September 2016A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 10th September 2016A car covers 350 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 11th September 2016Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 12th September 2016y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 16.
- 13th September 2016The 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.
- 14th September 2016A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
- 15th September 2016On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 16th September 2016Rationalise the denominator of 18/sqrt(6), giving your answer in its simplest form.
- 17th September 2016f(x) = 4x - 2 and g(x) = 4x + 7. Work out fg(1).
- 18th September 2016A train slows steadily from 19 m/s to rest in 4 seconds. Work out its deceleration.
- 19th September 2016In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 20th September 2016The probability of winning a game is 2/5. A player expects 4 wins. How many games did they play?
- 21st September 2016A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 22nd September 2016Simplify sqrt(80) + sqrt(5), giving your answer in the form a sqrt(b).
- 23rd September 2016The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 24th September 2016y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 25th September 2016In a vector proof you find that vector PQ = 5a - b and vector RS = 20a - 4b. What does this show about PQ and RS?
- 26th September 2016A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 27th September 2016On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th September 2016A rectangle is 24 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th September 2016A quadratic sequence starts 8, 26, 52, 86. Work out the second difference, and the coefficient of n^2.
- 30th September 2016y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.