Daily Practice · Higher Plus
October 2022 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2022, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2022 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2022A 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?
- 2nd October 2022On 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?
- 3rd October 2022A block has mass 680 g (to the nearest 10 g) and volume 8 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 4th October 2022f(x) = 3x - 9. Work out the inverse function f^-1(x).
- 5th October 2022A train slows steadily from 14 m/s to rest in 5 seconds. Work out its deceleration.
- 6th October 2022A cuboid measures 8 cm by 8 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th October 2022A bag holds 6 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th October 2022A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 9th October 2022x = 82 and y = 23, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th October 2022Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 11th October 2022y is inversely proportional to x^2. When x = 2, y = 32. Work out y when x = 4.
- 12th October 2022The 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.
- 13th October 2022A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 14th October 2022On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 15th October 2022A car covers 350 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.
- 16th October 2022Use the iteration x(n+1) = cube root of (8x(n) + 3) with x(0) = 5. Work out x(1) to 3 decimal places.
- 17th October 2022y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 18th October 2022In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 19th October 2022The probability of winning a game is 9/10. A player expects 117 wins. How many games did they play?
- 20th October 2022A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 0.8. How many values in total?
- 21st October 2022Rationalise the denominator of 14/sqrt(2), giving your answer in its simplest form.
- 22nd October 2022Work out the nth term of the quadratic sequence 0, 14, 36, 66, ...
- 23rd October 2022y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 81.
- 24th October 2022In a vector proof you find that vector PQ = 2a + 6b and vector RS = 6a + 18b. What does this show about PQ and RS?
- 25th October 2022A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 26th October 2022On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 27th October 2022Simplify sqrt(32) + sqrt(32), giving your answer in the form a sqrt(b).
- 28th October 2022The point (-2, 4) lies on y = f(x). Write down its image on y = f(x) + 5.
- 29th October 2022A train slows steadily from 17 m/s to rest in 4 seconds. Work out its deceleration.
- 30th October 2022A cuboid measures 15 cm by 5 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st October 2022A 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?