Daily Practice · Higher Plus
November 2018 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2018, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2018 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2018y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 2nd November 2018The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 3rd November 2018A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 4th November 2018On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 5th November 2018A block has mass 440 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th November 2018f(x) = 3x + 6. Work out the inverse function f^-1(x).
- 7th November 2018y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 3.
- 8th November 2018In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 9th November 2018The probability of winning a game is 2/5. A player expects 26 wins. How many games did they play?
- 10th November 2018A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 11th November 2018x = 83 and y = 70, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th November 2018Solve x^2 + y^2 = 100 and y = x + 2 simultaneously.
- 13th November 2018y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 25.
- 14th November 2018In a vector proof you find that vector PQ = 5a - 2b and vector RS = 10a - 4b. What does this show about PQ and RS?
- 15th November 2018A bag holds 3 red and n blue counters. The probability of taking a red is 3/5. Work out n.
- 16th November 2018On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 17th November 2018A car covers 100 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.
- 18th November 2018Use the iteration x(n+1) = cube root of (12x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.
- 19th November 2018A train slows steadily from 38 m/s to rest in 10 seconds. Work out its deceleration.
- 20th November 2018A cuboid measures 13 cm by 3 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st November 2018A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd November 2018A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 23rd November 2018Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 24th November 2018Work out the nth term of the quadratic sequence 13, 28, 51, 82, ...
- 25th November 2018y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 26th November 2018A cuboid measures 10 cm by 10 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th November 2018A bag holds 5 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th November 2018On 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?
- 29th November 2018Simplify sqrt(8) + sqrt(98), giving your answer in the form a sqrt(b).
- 30th November 2018The point (4, 0) lies on y = f(x). Write down its image on y = -f(x).