Daily Practice · Higher Plus
November 2019 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2019, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2019 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2019Solve x^2 + 8x + 15 < 0.
- 2nd November 2019y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 3rd November 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.
- 4th November 2019The probability of winning a game is 3/4. A player expects 36 wins. How many games did they play?
- 5th November 2019A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 6th November 2019A rectangle is 21 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th November 2019Write x^2 + 10x + 8 in the form (x + a)^2 + b.
- 8th November 2019y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 25.
- 9th November 2019In a vector proof you find that vector PQ = 5a + 5b and vector RS = 10a + 10b. What does this show about PQ and RS?
- 10th November 2019A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 11th November 2019On 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?
- 12th November 2019Expand and simplify (3 + sqrt(7))(3 - sqrt(7)).
- 13th November 2019Work out the coordinates of the turning point of y = x^2 - 16x + 12.
- 14th November 2019A train slows steadily from 23 m/s to rest in 4 seconds. Work out its deceleration.
- 15th November 2019A cuboid measures 10 cm by 14 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th November 2019A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th November 2019A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 18th November 2019A block has mass 620 g (to the nearest 10 g) and volume 25 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th November 2019Simplify (x^2 - 2x - 3)/(x + 1).
- 20th November 2019y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 21st November 2019A cuboid measures 5 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd November 2019A bag holds 4 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd November 2019On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th November 2019x = 94 and y = 62, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th November 2019In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 26th November 2019y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 27th November 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.
- 28th November 2019A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 29th November 2019A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 30th November 2019A car covers 510 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.