Daily Practice · Higher Plus
October 2019 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2019, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2019 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2019Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 2nd October 2019The point (-2, 1) lies on y = f(x). Write down its image on y = f(x) - 1.
- 3rd October 2019y is inversely proportional to x^2. When x = 4, y = 8. Work out y when x = 2.
- 4th October 2019In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 5th October 2019The probability of winning a game is 4/5. A player expects 56 wins. How many games did they play?
- 6th October 2019On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th October 2019A block has mass 300 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.
- 8th October 2019Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 9th October 2019y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 10th October 2019In a vector proof you find that vector PQ = 4a - 5b and vector RS = 8a - 10b. What does this show about PQ and RS?
- 11th October 2019A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 12th October 2019A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 13th October 2019x = 48 and y = 12, each correct to the nearest whole number. Work out the upper bound of x - y.
- 14th October 2019f(x) = 6x - 1 and g(x) = 5x + 9. Work out fg(0).
- 15th October 2019y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 9.
- 16th October 2019A cuboid measures 14 cm by 9 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th October 2019A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th October 2019On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th October 2019A car covers 840 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 20th October 2019The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 21st October 2019A train slows steadily from 35 m/s to rest in 5 seconds. Work out its deceleration.
- 22nd October 2019A cuboid measures 9 cm by 6 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd October 2019A bag holds 3 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th October 2019A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 25th October 2019Rationalise the denominator of 18/sqrt(2), giving your answer in its simplest form.
- 26th October 2019A quadratic sequence starts 7, 13, 23, 37. Work out the second difference, and the coefficient of n^2.
- 27th October 2019y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 28th October 2019The 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.
- 29th October 2019A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 30th October 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?
- 31st October 2019Simplify sqrt(50) + sqrt(72), giving your answer in the form a sqrt(b).