Daily Practice · Higher Plus
November 2022 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2022, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2022 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2022A histogram has two bars: one 5 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 2nd November 2022A rectangle is 18 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd November 2022Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 4th November 2022y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 5th November 2022A cuboid measures 4 cm by 9 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th November 2022A bag holds 4 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th November 2022On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 8th November 2022Expand and simplify (4 + sqrt(10))(4 - sqrt(10)).
- 9th November 2022f(x) = 2x - 4 and g(x) = 4x + 4. Work out fg(-2).
- 10th November 2022y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 11th November 2022The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 12th November 2022A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/22. Work out r.
- 13th November 2022A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 14th November 2022A block has mass 710 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 15th November 2022The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 16th November 2022y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 4.
- 17th November 2022In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 18th November 2022The probability of winning a game is 1/4. A player expects 5 wins. How many games did they play?
- 19th November 2022On 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 November 2022x = 63 and y = 9, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st November 2022A quadratic sequence starts 17, 38, 69, 110. Work out the second difference, and the coefficient of n^2.
- 22nd November 2022A train slows steadily from 31 m/s to rest in 8 seconds. Work out its deceleration.
- 23rd November 2022In a vector proof you find that vector PQ = 4a + b and vector RS = 16a + 4b. What does this show about PQ and RS?
- 24th November 2022A bag holds 5 red and n blue counters. The probability of taking a red is 5/7. Work out n.
- 25th November 2022A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 26th November 2022A car covers 450 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.
- 27th November 2022Solve x^2 + 2x < 0.
- 28th November 2022y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 29th November 2022A cuboid measures 5 cm by 14 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th November 2022A 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?