Daily Practice · Higher Plus
January 2022 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2022, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2022 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2022Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 2nd January 2022y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 3rd January 2022A cuboid measures 4 cm by 12 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th January 2022A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th January 2022A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 3.5. How many values in total?
- 6th January 2022Simplify sqrt(50) + sqrt(18), giving your answer in the form a sqrt(b).
- 7th January 2022f(x) = 5x - 3 and g(x) = 6x - 7. Work out fg(-3).
- 8th January 2022y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 49.
- 9th January 2022A cuboid measures 5 cm by 6 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th January 2022A bag holds 3 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th January 2022On 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?
- 12th January 2022A rectangle is 27 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th January 2022The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 14th January 2022A train slows steadily from 40 m/s to rest in 8 seconds. Work out its deceleration.
- 15th January 2022The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 16th January 2022A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 17th January 2022A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 18th January 2022Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).
- 19th January 2022A quadratic sequence starts 3, 3, 5, 9. Work out the second difference, and the coefficient of n^2.
- 20th January 2022y is inversely proportional to x^2. When x = 5, y = 4. Work out y when x = 2.
- 21st January 2022In 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.
- 22nd January 2022The probability of winning a game is 1/8. A player expects 10 wins. How many games did they play?
- 23rd January 2022On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 24th January 2022A block has mass 420 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th January 2022Solve x^2 - 3x - 4 > 0.
- 26th January 2022y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 27th January 2022In a vector proof you find that vector PQ = 2a - 5b and vector RS = 8a - 20b. What does this show about PQ and RS?
- 28th January 2022A bag holds 2 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 29th January 2022A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 30th January 2022x = 147 and y = 107, each correct to the nearest whole number. Work out the upper bound of x - y.
- 31st January 2022Write x^2 + 10x - 8 in the form (x + a)^2 + b.