Daily Practice · Higher Plus
July 2020 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2020, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2020 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2020
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2020The probability of winning a game is 2/5. A player expects 24 wins. How many games did they play?
- 2nd July 2020A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 3rd July 2020Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 4th July 2020Solve 2x^2 - 17x + 30 = 0.
- 5th July 2020y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 36.
- 6th July 2020In a vector proof you find that vector PQ = 4a - b and vector RS = 20a - 5b. What does this show about PQ and RS?
- 7th July 2020A bag holds 7 red and n blue counters. The probability of taking a red is 7/11. Work out n.
- 8th July 2020On 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?
- 9th July 2020Simplify sqrt(8) + sqrt(32), giving your answer in the form a sqrt(b).
- 10th July 2020f(x) = 6x + 5. Work out the inverse function f^-1(x).
- 11th July 2020A train slows steadily from 23 m/s to rest in 10 seconds. Work out its deceleration.
- 12th July 2020A cuboid measures 10 cm by 15 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th July 2020A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th July 2020A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 15th July 2020A rectangle is 24 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th July 2020Solve x^2 + y^2 = 841 and y = x + 1 simultaneously.
- 17th July 2020y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 18th July 2020A cuboid measures 6 cm by 7 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th July 2020A bag holds 5 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th July 2020On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 21st July 2020Expand and simplify (8 + sqrt(5))(8 - sqrt(5)).
- 22nd July 2020Use the iteration x(n+1) = cube root of (4x(n) + 6) with x(0) = 2. Work out x(1) to 3 decimal places.
- 23rd July 2020y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 24th July 2020The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 25th July 2020A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 26th July 2020A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 27th July 2020A block has mass 520 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.
- 28th July 2020Work out the nth term of the quadratic sequence 0, 5, 16, 33, ...
- 29th July 2020y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 64.
- 30th July 2020In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 31st July 2020The probability of winning a game is 1/2. A player expects 16 wins. How many games did they play?