Daily Practice · Higher Plus
August 2016 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2016, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2016 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2016A train slows steadily from 36 m/s to rest in 10 seconds. Work out its deceleration.
- 2nd August 2016A cuboid measures 11 cm by 10 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd August 2016A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th August 2016A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 5th August 2016Rationalise the denominator of 18/sqrt(2), giving your answer in its simplest form.
- 6th August 2016Solve 10x^2 - x - 2 = 0.
- 7th August 2016y is inversely proportional to x^2. When x = 5, y = 8. Work out y when x = 2.
- 8th August 2016A cuboid measures 6 cm by 5 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th August 2016A bag holds 7 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th August 2016On 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?
- 11th August 2016Simplify sqrt(48) + sqrt(75), giving your answer in the form a sqrt(b).
- 12th August 2016f(x) = 8x - 11. Work out the inverse function f^-1(x).
- 13th August 2016y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 14th August 2016The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 15th August 2016A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 16th August 2016A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 17th August 2016A rectangle is 9 cm by 17 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th August 2016Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
- 19th August 2016y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 49.
- 20th August 2016In 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.
- 21st August 2016The probability of winning a game is 1/5. A player expects 3 wins. How many games did they play?
- 22nd August 2016On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 23rd August 2016Expand and simplify (6 + sqrt(7))(6 - sqrt(7)).
- 24th August 2016Use the iteration x(n+1) = cube root of (10x(n) + 7) with x(0) = 3. Work out x(1) to 3 decimal places.
- 25th August 2016A train slows steadily from 31 m/s to rest in 8 seconds. Work out its deceleration.
- 26th August 2016In a vector proof you find that vector PQ = 6a + 5b and vector RS = 24a + 20b. What does this show about PQ and RS?
- 27th August 2016A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 28th August 2016A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 29th August 2016A block has mass 460 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th August 2016Work out the nth term of the quadratic sequence 1, 11, 27, 49, ...
- 31st August 2016y is inversely proportional to x^2. When x = 2, y = 75. Work out y when x = 5.