Daily Practice · Higher Plus
October 2016 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2016, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2016 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2016A cuboid measures 7 cm by 4 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd October 2016A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd October 2016A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 4th October 2016Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 5th October 2016Solve x^2 + 3x - 4 > 0.
- 6th October 2016y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 16.
- 7th October 2016A cuboid measures 14 cm by 13 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th October 2016A bag holds 3 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th October 2016On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 10th October 2016A block has mass 270 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th October 2016Write x^2 + 12x - 5 in the form (x + a)^2 + b.
- 12th October 2016A train slows steadily from 40 m/s to rest in 8 seconds. Work out its deceleration.
- 13th October 2016The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 14th October 2016A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
- 15th October 2016A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 16th October 2016x = 64 and y = 25, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th October 2016Work out the coordinates of the turning point of y = x^2 - 10x + 8.
- 18th October 2016y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 19th October 2016In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 20th October 2016The probability of winning a game is 3/4. A player expects 12 wins. How many games did they play?
- 21st October 2016On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 22nd October 2016A car covers 810 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.
- 23rd October 2016Simplify (x^2 + 9x + 20)/(x + 5).
- 24th October 2016y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 4.
- 25th October 2016In a vector proof you find that vector PQ = 6a - 5b and vector RS = 12a - 10b. What does this show about PQ and RS?
- 26th October 2016A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 27th October 2016A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 28th October 2016Rationalise the denominator of 110/sqrt(11), giving your answer in its simplest form.
- 29th October 2016In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 5 in terms of an integer n?
- 30th October 2016y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 64.
- 31st October 2016A cuboid measures 3 cm by 13 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.