Daily Practice · Higher Plus
October 2018 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2018, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2018 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2018Work out the coordinates of the turning point of y = x^2 + 2x - 5.
- 2nd October 2018A train slows steadily from 12 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd October 2018The 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.
- 4th October 2018A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 5th October 2018A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 6th October 2018A car covers 770 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.
- 7th October 2018Simplify (x^2 - 4x + 3)/(x - 3).
- 8th October 2018y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
- 9th October 2018In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 10th October 2018The probability of winning a game is 1/5. A player expects 12 wins. How many games did they play?
- 11th October 2018On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th October 2018Rationalise the denominator of 18/sqrt(2), giving your answer in its simplest form.
- 13th October 2018In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 7 in terms of an integer n?
- 14th October 2018y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 15th October 2018In a vector proof you find that vector PQ = 6a + 5b and vector RS = 30a + 25b. What does this show about PQ and RS?
- 16th October 2018A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 17th October 2018A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 18th October 2018Simplify sqrt(75) + sqrt(48), giving your answer in the form a sqrt(b).
- 19th October 2018Make x the subject of 7x + 6 = y(x + 6).
- 20th October 2018y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 25.
- 21st October 2018A cuboid measures 5 cm by 3 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd October 2018A bag holds 9 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd October 2018On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th October 2018A rectangle is 14 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th October 2018Write 7/(x + 5) + 7/(x - 6) as a single fraction.
- 26th October 2018A train slows steadily from 38 m/s to rest in 4 seconds. Work out its deceleration.
- 27th October 2018A cuboid measures 4 cm by 7 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th October 2018A bag holds 6 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th October 2018A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 30th October 2018Expand and simplify (3 + sqrt(6))(3 - sqrt(6)).
- 31st October 2018Solve 9x^2 - 21x + 10 = 0.