Daily Practice · Higher Plus
November 2013 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2013, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2013 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2013Rationalise the denominator of 20/sqrt(2), giving your answer in its simplest form.
- 2nd November 2013Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 3rd November 2013y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 4th November 2013In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 5th November 2013The probability of winning a game is 3/4. A player expects 21 wins. How many games did they play?
- 6th November 2013On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th November 2013Simplify sqrt(75) + sqrt(12), giving your answer in the form a sqrt(b).
- 8th November 2013Use the iteration x(n+1) = cube root of (4x(n) + 3) with x(0) = 3. Work out x(1) to 3 decimal places.
- 9th November 2013y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 10th November 2013In a vector proof you find that vector PQ = 4a - 4b and vector RS = 12a - 12b. What does this show about PQ and RS?
- 11th November 2013A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 12th November 2013A histogram has two bars: one 10 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 13th November 2013A rectangle is 25 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th November 2013Work out the nth term of the quadratic sequence 2, 4, 8, 14, ...
- 15th November 2013y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 16.
- 16th November 2013A cuboid measures 13 cm by 11 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th November 2013A bag holds 8 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th November 2013On 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?
- 19th November 2013Expand and simplify (7 + sqrt(2))(7 - sqrt(2)).
- 20th November 2013The point (5, -5) lies on y = f(x). Write down its image on y = f(x) + 6.
- 21st November 2013A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
- 22nd November 2013A cuboid measures 4 cm by 12 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd November 2013A bag holds 5 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th November 2013A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 25th November 2013A block has mass 410 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.
- 26th November 2013Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 27th November 2013y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 4.
- 28th November 2013The 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.
- 29th November 2013A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 30th November 2013On 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?