Daily Practice · Higher Plus
September 2018 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2018, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2018 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2018f(x) = 3x - 7 and g(x) = 6x - 9. Work out fg(6).
- 2nd September 2018y is directly proportional to sqrt(x). When x = 4, y = 4. Work out y when x = 25.
- 3rd September 2018The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 4th September 2018A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/22. Work out r.
- 5th September 2018On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th September 2018Simplify sqrt(8) + sqrt(8), giving your answer in the form a sqrt(b).
- 7th September 2018The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 8th September 2018A train slows steadily from 15 m/s to rest in 5 seconds. Work out its deceleration.
- 9th September 2018In 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.
- 10th September 2018The probability of winning a game is 7/10. A player expects 28 wins. How many games did they play?
- 11th September 2018A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
- 12th September 2018A rectangle is 12 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 13th September 2018A quadratic sequence starts 4, 15, 34, 61. Work out the second difference, and the coefficient of n^2.
- 14th September 2018y is inversely proportional to x^2. When x = 3, y = 48. Work out y when x = 4.
- 15th September 2018In a vector proof you find that vector PQ = 3a - 3b and vector RS = 15a - 15b. What does this show about PQ and RS?
- 16th September 2018A bag holds 6 red and n blue counters. The probability of taking a red is 6/13. Work out n.
- 17th September 2018On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 18th September 2018Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 19th September 2018Solve x^2 + 2x - 15 > 0.
- 20th September 2018y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 21st September 2018A cuboid measures 7 cm by 12 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd September 2018A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd September 2018A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 24th September 2018A block has mass 640 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 25th September 2018Write x^2 - 2x - 4 in the form (x + a)^2 + b.
- 26th September 2018y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 9.
- 27th September 2018A cuboid measures 6 cm by 12 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th September 2018A bag holds 3 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th September 2018On 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?
- 30th September 2018x = 79 and y = 20, each correct to the nearest whole number. Work out the upper bound of x - y.