Daily Practice · Higher Plus
August 2019 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2019, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2019 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2019A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 2nd August 2019Rationalise the denominator of 66/sqrt(6), giving your answer in its simplest form.
- 3rd August 2019Work out the coordinates of the turning point of y = x^2 - 14x + 8.
- 4th August 2019y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 64.
- 5th August 2019In 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.
- 6th August 2019The probability of winning a game is 3/5. A player expects 84 wins. How many games did they play?
- 7th August 2019On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 8th August 2019Simplify sqrt(72) + sqrt(2), giving your answer in the form a sqrt(b).
- 9th August 2019Simplify (x^2 - 15x + 56)/(x - 8).
- 10th August 2019A train slows steadily from 25 m/s to rest in 5 seconds. Work out its deceleration.
- 11th August 2019In a vector proof you find that vector PQ = 3a - 2b and vector RS = 12a - 8b. What does this show about PQ and RS?
- 12th August 2019A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 13th August 2019A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 14th August 2019A rectangle is 29 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th August 2019In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 8 in terms of an integer n?
- 16th August 2019y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
- 17th August 2019A cuboid measures 7 cm by 13 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th August 2019A 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?
- 19th August 2019On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 20th August 2019Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 21st August 2019Make x the subject of 2x + 4 = y(x + 4).
- 22nd August 2019y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 23rd August 2019A cuboid measures 4 cm by 8 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th August 2019A bag holds 4 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th August 2019A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 26th August 2019A block has mass 700 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th August 2019Write 4/(x + 5) + 2/(x - 6) as a single fraction.
- 28th August 2019y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 64.
- 29th August 2019The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 30th August 2019A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 31st August 2019On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?