Daily Practice · Higher Plus
August 2022 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2022, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2022 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2022A cuboid measures 3 cm by 15 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd August 2022A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd August 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?
- 4th August 2022Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 5th August 2022The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 6th August 2022y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 7th August 2022A cuboid measures 13 cm by 7 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th August 2022A bag holds 6 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th August 2022A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 10th August 2022A rectangle is 17 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th August 2022A quadratic sequence starts 4, 13, 28, 49. Work out the second difference, and the coefficient of n^2.
- 12th August 2022y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 64.
- 13th August 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.
- 14th August 2022A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 15th August 2022On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th August 2022Expand and simplify (3 + sqrt(7))(3 - sqrt(7)).
- 17th August 2022Solve x^2 + 9x + 14 > 0.
- 18th August 2022A train slows steadily from 20 m/s to rest in 5 seconds. Work out its deceleration.
- 19th August 2022In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 20th August 2022The probability of winning a game is 1/2. A player expects 30 wins. How many games did they play?
- 21st August 2022A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 22nd August 2022A block has mass 390 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd August 2022Write x^2 + 12x + 6 in the form (x + a)^2 + b.
- 24th August 2022y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 25th August 2022In a vector proof you find that vector PQ = a - 3b and vector RS = 3a - 9b. What does this show about PQ and RS?
- 26th August 2022A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 27th August 2022On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th August 2022x = 118 and y = 87, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th August 2022Work out the coordinates of the turning point of y = x^2 - 8x - 14.
- 30th August 2022y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 31st August 2022A cuboid measures 7 cm by 15 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.