Daily Practice · Higher Plus
June 2022 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2022, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2022 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2022
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2022y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 25.
- 2nd June 2022A cuboid measures 3 cm by 11 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd June 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?
- 4th June 2022On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 5th June 2022x = 151 and y = 57, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th June 2022Make x the subject of 5x + 4 = y(x + 4).
- 7th June 2022A train slows steadily from 35 m/s to rest in 4 seconds. Work out its deceleration.
- 8th June 2022A cuboid measures 10 cm by 7 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th June 2022A bag holds 7 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th June 2022A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 11th June 2022A car covers 120 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.
- 12th June 2022Write 7/(x - 6) + 7/(x - 5) as a single fraction.
- 13th June 2022y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 14th June 2022The 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.
- 15th June 2022A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 16th June 2022On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th June 2022Rationalise the denominator of 45/sqrt(5), giving your answer in its simplest form.
- 18th June 2022Solve 4x^2 + 4x - 15 = 0.
- 19th June 2022y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 20th June 2022In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 21st June 2022The probability of winning a game is 1/2. A player expects 55 wins. How many games did they play?
- 22nd June 2022A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 23rd June 2022Simplify sqrt(8) + sqrt(50), giving your answer in the form a sqrt(b).
- 24th June 2022f(x) = 6x + 5. Work out the inverse function f^-1(x).
- 25th June 2022y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 49.
- 26th June 2022In a vector proof you find that vector PQ = a + 2b and vector RS = 4a + 8b. What does this show about PQ and RS?
- 27th June 2022A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 28th June 2022On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th June 2022A rectangle is 25 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th June 2022Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.