Daily Practice · Higher Plus
October 2024 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2024, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2024 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2024
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2024The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 2nd October 2024A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 3rd October 2024On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 4th October 2024Rationalise the denominator of 16/sqrt(2), giving your answer in its simplest form.
- 5th October 2024Work out the nth term of the quadratic sequence 11, 24, 45, 74, ...
- 6th October 2024y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 7th October 2024In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 8th October 2024The probability of winning a game is 2/5. A player expects 24 wins. How many games did they play?
- 9th October 2024A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 10th October 2024Simplify sqrt(18) + sqrt(50), giving your answer in the form a sqrt(b).
- 11th October 2024The point (2, 6) lies on y = f(x). Write down its image on y = f(x) - 5.
- 12th October 2024y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 16.
- 13th October 2024In a vector proof you find that vector PQ = 5a + b and vector RS = 25a + 5b. What does this show about PQ and RS?
- 14th October 2024A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 15th October 2024On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th October 2024A rectangle is 13 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th October 2024Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 18th October 2024A train slows steadily from 32 m/s to rest in 4 seconds. Work out its deceleration.
- 19th October 2024A cuboid measures 8 cm by 5 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th October 2024A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st October 2024A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 22nd October 2024Expand and simplify (8 + sqrt(7))(8 - sqrt(7)).
- 23rd October 2024f(x) = 3x - 1 and g(x) = 2x + 8. Work out fg(-2).
- 24th October 2024y is inversely proportional to x^2. When x = 5, y = 27. Work out y when x = 3.
- 25th October 2024A cuboid measures 14 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th October 2024A bag holds 6 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th October 2024On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 28th October 2024A block has mass 470 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th October 2024The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 30th October 2024y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 31st October 2024The 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.