Daily Practice · Higher Plus
August 2020 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2020, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2020 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2020
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2020On 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?
- 2nd August 2020x = 134 and y = 47, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd August 2020The point (6, 1) lies on y = f(x). Write down its image on y = f(x + 1).
- 4th August 2020A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
- 5th August 2020In a vector proof you find that vector PQ = 5a + 2b and vector RS = 20a + 8b. What does this show about PQ and RS?
- 6th August 2020A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 7th August 2020A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 3.5. How many values in total?
- 8th August 2020A car covers 390 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 9th August 2020Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 10th August 2020y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 11th August 2020A cuboid measures 11 cm by 6 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th August 2020A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th August 2020On 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?
- 14th August 2020Rationalise the denominator of 12/sqrt(6), giving your answer in its simplest form.
- 15th August 2020f(x) = 4x - 4 and g(x) = 4x - 5. Work out fg(1).
- 16th August 2020y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 17th August 2020A cuboid measures 6 cm by 5 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th August 2020A bag holds 6 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th August 2020A histogram has two bars: one 10 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 20th August 2020Simplify sqrt(80) + sqrt(45), giving your answer in the form a sqrt(b).
- 21st August 2020The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 22nd August 2020y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 16.
- 23rd August 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.
- 24th August 2020A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 25th August 2020On 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?
- 26th August 2020A rectangle is 30 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th August 2020A quadratic sequence starts 13, 21, 31, 43. Work out the second difference, and the coefficient of n^2.
- 28th August 2020A train slows steadily from 16 m/s to rest in 5 seconds. Work out its deceleration.
- 29th August 2020In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 30th August 2020The probability of winning a game is 7/8. A player expects 70 wins. How many games did they play?
- 31st August 2020A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?