Daily Practice · Higher Plus
June 2021 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2021, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2021 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2021In a vector proof you find that vector PQ = 2a + 5b and vector RS = 6a + 15b. What does this show about PQ and RS?
- 2nd June 2021A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 3rd June 2021A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 4th June 2021Rationalise the denominator of 30/sqrt(6), giving your answer in its simplest form.
- 5th June 2021The point (1, 1) lies on y = f(x). Write down its image on y = f(x) - 5.
- 6th June 2021y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 4.
- 7th June 2021A cuboid measures 9 cm by 13 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th June 2021A bag holds 8 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th June 2021On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th June 2021Simplify sqrt(27) + sqrt(48), giving your answer in the form a sqrt(b).
- 11th June 2021Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 12th June 2021A train slows steadily from 23 m/s to rest in 4 seconds. Work out its deceleration.
- 13th June 2021A cuboid measures 11 cm by 6 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th June 2021A bag holds 3 red, 3 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th June 2021A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 0.8. How many values in total?
- 16th June 2021A rectangle is 27 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th June 2021f(x) = 4x + 9 and g(x) = 4x + 5. Work out fg(1).
- 18th June 2021y is inversely proportional to x^2. When x = 4, y = 18. Work out y when x = 3.
- 19th June 2021The 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.
- 20th June 2021A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 21st June 2021On 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?
- 22nd June 2021Expand and simplify (5 + sqrt(5))(5 - sqrt(5)).
- 23rd June 2021The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 24th June 2021y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 25th June 2021In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 26th June 2021The probability of winning a game is 3/8. A player expects 9 wins. How many games did they play?
- 27th June 2021A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 28th June 2021A block has mass 280 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th June 2021A quadratic sequence starts 10, 27, 52, 85. Work out the second difference, and the coefficient of n^2.
- 30th June 2021y is directly proportional to sqrt(x). When x = 49, y = 35. Work out y when x = 25.