Daily Practice · Higher Plus
July 2023 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2023, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2023 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2023
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2023Work out the coordinates of the turning point of y = x^2 + 4x - 4.
- 2nd July 2023y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 3rd July 2023A cuboid measures 14 cm by 4 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th July 2023A bag holds 5 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th July 2023On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th July 2023Simplify sqrt(8) + sqrt(8), giving your answer in the form a sqrt(b).
- 7th July 2023Simplify (x^2 - 2x - 8)/(x + 2).
- 8th July 2023y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 9th July 2023The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 10th July 2023A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
- 11th July 2023A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 12th July 2023A rectangle is 15 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th July 2023In an algebraic proof, how would you write an odd number in terms of an integer n?
- 14th July 2023y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 25.
- 15th July 2023In 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.
- 16th July 2023The probability of winning a game is 1/2. A player expects 6 wins. How many games did they play?
- 17th July 2023On 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?
- 18th July 2023Expand and simplify (6 + sqrt(6))(6 - sqrt(6)).
- 19th July 2023Make x the subject of 5x + 6 = y(x + 6).
- 20th July 2023A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 21st July 2023In a vector proof you find that vector PQ = 6a - b and vector RS = 12a - 2b. What does this show about PQ and RS?
- 22nd July 2023A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 23rd July 2023A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 24th July 2023A block has mass 330 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th July 2023Write 2/(x - 2) + 4/(x - 1) as a single fraction.
- 26th July 2023y is inversely proportional to x^2. When x = 4, y = 25. Work out y when x = 5.
- 27th July 2023A cuboid measures 12 cm by 14 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th July 2023A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th July 2023On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 30th July 2023x = 77 and y = 53, each correct to the nearest whole number. Work out the upper bound of x - y.
- 31st July 2023Solve 4x^2 - 12x + 5 = 0.