Daily Practice · Higher Plus
October 2015 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2015, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2015 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2015
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2015In a vector proof you find that vector PQ = 5a + b and vector RS = 15a + 3b. What does this show about PQ and RS?
- 2nd October 2015A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 3rd October 2015On 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?
- 4th October 2015x = 144 and y = 103, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th October 2015Solve 2x^2 + 9x + 10 = 0.
- 6th October 2015y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 5.
- 7th October 2015A cuboid measures 7 cm by 11 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th October 2015A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th October 2015A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 10th October 2015A car covers 540 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 October 2015f(x) = 6x + 10. Work out the inverse function f^-1(x).
- 12th October 2015y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 36.
- 13th October 2015A cuboid measures 6 cm by 13 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th October 2015A bag holds 3 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th October 2015On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 16th October 2015Rationalise the denominator of 70/sqrt(7), giving your answer in its simplest form.
- 17th October 2015Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 18th October 2015A train slows steadily from 27 m/s to rest in 5 seconds. Work out its deceleration.
- 19th October 2015The 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.
- 20th October 2015A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
- 21st October 2015A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 22nd October 2015Simplify sqrt(48) + sqrt(108), giving your answer in the form a sqrt(b).
- 23rd October 2015Use the iteration x(n+1) = cube root of (10x(n) + 1) with x(0) = 3. Work out x(1) to 3 decimal places.
- 24th October 2015y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 25th October 2015In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 26th October 2015The probability of winning a game is 7/8. A player expects 35 wins. How many games did they play?
- 27th October 2015On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th October 2015A rectangle is 8 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th October 2015Work out the nth term of the quadratic sequence -3, 1, 11, 27, ...
- 30th October 2015y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 4.
- 31st October 2015In a vector proof you find that vector PQ = a + 3b and vector RS = 5a + 15b. What does this show about PQ and RS?