Daily Practice · Higher Plus
October 2020 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2020, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2020 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2020
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2020Simplify sqrt(18) + sqrt(32), giving your answer in the form a sqrt(b).
- 2nd October 2020Make x the subject of 8x + 4 = y(x + 4).
- 3rd October 2020y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 4th October 2020In a vector proof you find that vector PQ = a + 3b and vector RS = 5a + 15b. What does this show about PQ and RS?
- 5th October 2020A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 6th October 2020A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 7th October 2020A rectangle is 11 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th October 2020Write 4/(x + 4) + 7/(x - 4) as a single fraction.
- 9th October 2020y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 9.
- 10th October 2020A cuboid measures 14 cm by 4 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th October 2020A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th October 2020On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 13th October 2020Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
- 14th October 2020Solve 6x^2 - 11x + 3 = 0.
- 15th October 2020A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
- 16th October 2020A cuboid measures 9 cm by 10 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th October 2020A bag holds 4 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th October 2020A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 19th October 2020A block has mass 720 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th October 2020f(x) = 6x - 1. Work out the inverse function f^-1(x).
- 21st October 2020y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 22nd October 2020The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 23rd October 2020A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 24th October 2020On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th October 2020x = 56 and y = 26, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th October 2020Solve x^2 + y^2 = 676 and y = x + 14 simultaneously.
- 27th October 2020y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 28th October 2020In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 29th October 2020The probability of winning a game is 7/8. A player expects 91 wins. How many games did they play?
- 30th October 2020A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 31st October 2020A car covers 440 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.