Daily Practice · Higher Plus
July 2021 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2021, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2021 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2021
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2021In a vector proof you find that vector PQ = 5a - 5b and vector RS = 25a - 25b. What does this show about PQ and RS?
- 2nd July 2021A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 3rd July 2021On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 4th July 2021x = 111 and y = 83, each correct to the nearest whole number. Work out the upper bound of x - y.
- 5th July 2021Solve x^2 - 1 > 0.
- 6th July 2021A train slows steadily from 24 m/s to rest in 5 seconds. Work out its deceleration.
- 7th July 2021A cuboid measures 8 cm by 8 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th July 2021A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th July 2021A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 10th July 2021A car covers 350 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 11th July 2021Write x^2 + 6x - 8 in the form (x + a)^2 + b.
- 12th July 2021y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.
- 13th July 2021A cuboid measures 12 cm by 7 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th July 2021A bag holds 4 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th July 2021On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th July 2021Rationalise the denominator of 60/sqrt(5), giving your answer in its simplest form.
- 17th July 2021Work out the coordinates of the turning point of y = x^2 - 2x - 1.
- 18th July 2021y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 19th July 2021The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 20th July 2021A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
- 21st July 2021A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 22nd July 2021Simplify sqrt(50) + sqrt(98), giving your answer in the form a sqrt(b).
- 23rd July 2021Simplify (x^2 + 2x - 8)/(x - 2).
- 24th July 2021y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 36.
- 25th July 2021In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 26th July 2021The probability of winning a game is 3/5. A player expects 30 wins. How many games did they play?
- 27th July 2021On 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?
- 28th July 2021A rectangle is 16 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 29th July 2021In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 30th July 2021A train slows steadily from 20 m/s to rest in 8 seconds. Work out its deceleration.
- 31st July 2021In a vector proof you find that vector PQ = a - 3b and vector RS = 2a - 6b. What does this show about PQ and RS?