Daily Practice · Higher Plus
October 2017 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2017, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2017 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2017
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2017y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 4.
- 2nd October 2017A cuboid measures 11 cm by 8 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd October 2017A bag holds 6 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th October 2017On 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?
- 5th October 2017Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
- 6th October 2017Use the iteration x(n+1) = cube root of (11x(n) + 1) with x(0) = 3. Work out x(1) to 3 decimal places.
- 7th October 2017A train slows steadily from 16 m/s to rest in 10 seconds. Work out its deceleration.
- 8th October 2017The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 9th October 2017A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 10th October 2017A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 11th October 2017A rectangle is 5 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th October 2017Work out the nth term of the quadratic sequence 9, 14, 21, 30, ...
- 13th October 2017y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 14th October 2017In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 15th October 2017The probability of winning a game is 2/5. A player expects 4 wins. How many games did they play?
- 16th October 2017On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 17th October 2017Expand and simplify (4 + sqrt(6))(4 - sqrt(6)).
- 18th October 2017The point (5, -6) lies on y = f(x). Write down its image on y = f(-x).
- 19th October 2017y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 20th October 2017In a vector proof you find that vector PQ = a - 5b and vector RS = 5a - 25b. What does this show about PQ and RS?
- 21st October 2017A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 22nd October 2017A 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?
- 23rd October 2017A block has mass 590 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th October 2017Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 25th October 2017y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 9.
- 26th October 2017A cuboid measures 9 cm by 12 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th October 2017A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th October 2017On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 29th October 2017x = 127 and y = 51, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th October 2017f(x) = 5x - 7 and g(x) = 4x + 8. Work out fg(5).
- 31st October 2017A train slows steadily from 18 m/s to rest in 5 seconds. Work out its deceleration.