Daily Practice · Higher Plus
August 2017 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2017, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2017 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2017
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2017A quadratic sequence starts 0, 1, 4, 9. Work out the second difference, and the coefficient of n^2.
- 2nd August 2017y is inversely proportional to x^2. When x = 4, y = 144. Work out y when x = 6.
- 3rd August 2017A cuboid measures 5 cm by 6 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th August 2017A bag holds 3 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th August 2017On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th August 2017x = 113 and y = 11, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th August 2017Solve x^2 + 9x + 8 < 0.
- 8th August 2017y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 9th August 2017The 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.
- 10th August 2017A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
- 11th August 2017A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 12th August 2017A car covers 320 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th August 2017Write x^2 - 2x - 12 in the form (x + a)^2 + b.
- 14th August 2017y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 16.
- 15th August 2017In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 16th August 2017The probability of winning a game is 3/4. A player expects 66 wins. How many games did they play?
- 17th August 2017On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 18th August 2017Rationalise the denominator of 132/sqrt(11), giving your answer in its simplest form.
- 19th August 2017Work out the coordinates of the turning point of y = x^2 - 16x - 5.
- 20th August 2017A train slows steadily from 37 m/s to rest in 8 seconds. Work out its deceleration.
- 21st August 2017In a vector proof you find that vector PQ = 3a - 5b and vector RS = 6a - 10b. What does this show about PQ and RS?
- 22nd August 2017A bag holds 5 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 23rd August 2017A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 24th August 2017Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
- 25th August 2017Simplify (x^2 - 2x - 48)/(x + 6).
- 26th August 2017y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 27th August 2017A cuboid measures 13 cm by 11 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th August 2017A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th August 2017On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 30th August 2017A rectangle is 21 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 31st August 2017In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?