Daily Practice · Higher Plus
October 2021 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2021, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2021 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2021A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 2nd October 2021A car covers 320 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 3rd October 2021The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 4th October 2021y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 4.
- 5th October 2021A cuboid measures 15 cm by 8 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th October 2021A bag holds 6 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th October 2021On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 8th October 2021Rationalise the denominator of 35/sqrt(7), giving your answer in its simplest form.
- 9th October 2021A quadratic sequence starts 14, 32, 58, 92. Work out the second difference, and the coefficient of n^2.
- 10th October 2021A train slows steadily from 16 m/s to rest in 8 seconds. Work out its deceleration.
- 11th October 2021A cuboid measures 11 cm by 10 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th October 2021A bag holds 5 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th October 2021A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 14th October 2021Simplify sqrt(20) + sqrt(45), giving your answer in the form a sqrt(b).
- 15th October 2021Solve x^2 - 6x - 7 < 0.
- 16th October 2021y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 17th October 2021The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 18th October 2021A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 19th October 2021On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 20th October 2021A rectangle is 13 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st October 2021Write x^2 + 12x - 3 in the form (x + a)^2 + b.
- 22nd October 2021y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 23rd October 2021In 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.
- 24th October 2021The probability of winning a game is 3/5. A player expects 42 wins. How many games did they play?
- 25th October 2021A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 26th October 2021Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 27th October 2021Work out the coordinates of the turning point of y = x^2 - 12x - 3.
- 28th October 2021y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 25.
- 29th October 2021In a vector proof you find that vector PQ = 3a - 3b and vector RS = 9a - 9b. What does this show about PQ and RS?
- 30th October 2021A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 31st October 2021On 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?