Daily Practice · Higher Plus
July 2022 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2022, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2022 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2022A train slows steadily from 32 m/s to rest in 10 seconds. Work out its deceleration.
- 2nd July 2022A cuboid measures 9 cm by 4 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd July 2022A bag holds 6 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th July 2022A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 5th July 2022Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
- 6th July 2022Use the iteration x(n+1) = cube root of (2x(n) + 6) with x(0) = 3. Work out x(1) to 3 decimal places.
- 7th July 2022y is inversely proportional to x^2. When x = 2, y = 64. Work out y when x = 4.
- 8th July 2022A cuboid measures 8 cm by 11 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th July 2022A bag holds 6 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th July 2022On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 11th July 2022A block has mass 720 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th July 2022Work out the nth term of the quadratic sequence 6, 23, 48, 81, ...
- 13th July 2022y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 14th July 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.
- 15th July 2022A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 16th July 2022A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 17th July 2022x = 97 and y = 65, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th July 2022The point (-1, -6) lies on y = f(x). Write down its image on y = -f(x).
- 19th July 2022y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 16.
- 20th July 2022In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 21st July 2022The probability of winning a game is 3/8. A player expects 45 wins. How many games did they play?
- 22nd July 2022On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd July 2022A car covers 170 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 24th July 2022Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 25th July 2022A train slows steadily from 32 m/s to rest in 8 seconds. Work out its deceleration.
- 26th July 2022In a vector proof you find that vector PQ = 5a + 3b and vector RS = 10a + 6b. What does this show about PQ and RS?
- 27th July 2022A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 28th July 2022A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 29th July 2022Rationalise the denominator of 24/sqrt(6), giving your answer in its simplest form.
- 30th July 2022f(x) = 6x - 4 and g(x) = 4x - 3. Work out fg(-2).
- 31st July 2022y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.