Daily Practice · Higher Plus
August 2018 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2018, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2018 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2018A rectangle is 26 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd August 2018Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 3rd August 2018y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 3.
- 4th August 2018The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 5th August 2018A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 2/7. Work out r.
- 6th August 2018A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 7th August 2018Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 8th August 2018Use the iteration x(n+1) = cube root of (10x(n) + 5) with x(0) = 5. Work out x(1) to 3 decimal places.
- 9th August 2018y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 4.
- 10th August 2018In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 11th August 2018The probability of winning a game is 1/4. A player expects 6 wins. How many games did they play?
- 12th August 2018On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th August 2018A block has mass 830 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th August 2018Work out the nth term of the quadratic sequence 1, 8, 19, 34, ...
- 15th August 2018A train slows steadily from 16 m/s to rest in 5 seconds. Work out its deceleration.
- 16th August 2018In a vector proof you find that vector PQ = 5a + b and vector RS = 20a + 4b. What does this show about PQ and RS?
- 17th August 2018A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 18th August 2018A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 19th August 2018x = 99 and y = 5, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th August 2018The point (-4, -4) lies on y = f(x). Write down its image on y = f(x - 4).
- 21st August 2018y is inversely proportional to x^2. When x = 3, y = 25. Work out y when x = 5.
- 22nd August 2018A cuboid measures 14 cm by 15 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd August 2018A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th August 2018On 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?
- 25th August 2018A car covers 190 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 26th August 2018Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 27th August 2018y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 28th August 2018A cuboid measures 11 cm by 6 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th August 2018A bag holds 6 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th August 2018A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.6. How many values in total?
- 31st August 2018Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.