Daily Practice · Higher Plus
November 2015 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2015, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2015 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2015
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2015A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
- 2nd November 2015A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 3rd November 2015Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 4th November 2015The point (-2, 6) lies on y = f(x). Write down its image on y = f(x - 2).
- 5th November 2015y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 25.
- 6th November 2015A cuboid measures 5 cm by 7 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th November 2015A bag holds 9 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th November 2015On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 9th November 2015A block has mass 320 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 10th November 2015Prove that the sum of 6 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 11th November 2015A train slows steadily from 19 m/s to rest in 8 seconds. Work out its deceleration.
- 12th November 2015A cuboid measures 11 cm by 13 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th November 2015A bag holds 7 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th November 2015A histogram has two bars: one 20 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 15th November 2015x = 176 and y = 61, each correct to the nearest whole number. Work out the upper bound of x - y.
- 16th November 2015f(x) = 3x - 5 and g(x) = 5x - 2. Work out fg(4).
- 17th November 2015y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 18th November 2015The 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.
- 19th November 2015A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 15/28. Work out r.
- 20th November 2015On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 21st November 2015A car covers 790 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 22nd November 2015The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 23rd November 2015y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 24th November 2015In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 25th November 2015The probability of winning a game is 3/8. A player expects 6 wins. How many games did they play?
- 26th November 2015A 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?
- 27th November 2015Rationalise the denominator of 14/sqrt(7), giving your answer in its simplest form.
- 28th November 2015A quadratic sequence starts 4, 18, 42, 76. Work out the second difference, and the coefficient of n^2.
- 29th November 2015y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 9.
- 30th November 2015In a vector proof you find that vector PQ = 6a - b and vector RS = 18a - 3b. What does this show about PQ and RS?