Daily Practice · Higher Plus
June 2023 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2023, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2023 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2023f(x) = 3x + 7 and g(x) = 3x + 2. Work out fg(5).
- 2nd June 2023A train slows steadily from 34 m/s to rest in 4 seconds. Work out its deceleration.
- 3rd June 2023A cuboid measures 9 cm by 13 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th June 2023A bag holds 3 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th June 2023A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 6th June 2023Expand and simplify (7 + sqrt(7))(7 - sqrt(7)).
- 7th June 2023The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 8th June 2023y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 9th June 2023The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 10th June 2023A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 11th June 2023On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 12th June 2023A block has mass 600 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th June 2023A quadratic sequence starts -3, -1, 3, 9. Work out the second difference, and the coefficient of n^2.
- 14th June 2023y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 15th June 2023In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 16th June 2023The probability of winning a game is 1/10. A player expects 14 wins. How many games did they play?
- 17th June 2023A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 18th June 2023x = 69 and y = 58, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th June 2023Solve x^2 - 8x + 15 > 0.
- 20th June 2023y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 16.
- 21st June 2023In a vector proof you find that vector PQ = 4a - 3b and vector RS = 8a - 6b. What does this show about PQ and RS?
- 22nd June 2023A bag holds 8 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 23rd June 2023On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th June 2023A car covers 570 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 25th June 2023Write x^2 + 16x - 6 in the form (x + a)^2 + b.
- 26th June 2023A train slows steadily from 13 m/s to rest in 10 seconds. Work out its deceleration.
- 27th June 2023A cuboid measures 5 cm by 14 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th June 2023A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th June 2023A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.8. How many values in total?
- 30th June 2023Rationalise the denominator of 15/sqrt(3), giving your answer in its simplest form.