Daily Practice · Higher Plus
October 2013 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2013, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2013 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2013On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd October 2013A rectangle is 22 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 3rd October 2013In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 4th October 2013A train slows steadily from 16 m/s to rest in 8 seconds. Work out its deceleration.
- 5th October 2013In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 6th October 2013The probability of winning a game is 1/4. A player expects 11 wins. How many games did they play?
- 7th October 2013A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.6. How many values in total?
- 8th October 2013Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
- 9th October 2013Make x the subject of 8x + 2 = y(x + 2).
- 10th October 2013y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.
- 11th October 2013In a vector proof you find that vector PQ = 2a - 2b and vector RS = 4a - 4b. What does this show about PQ and RS?
- 12th October 2013A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.
- 13th October 2013On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 14th October 2013A block has mass 350 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 15th October 2013Write 2/(x + 3) + 2/(x - 2) as a single fraction.
- 16th October 2013y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 17th October 2013A cuboid measures 8 cm by 9 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 18th October 2013A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 19th October 2013A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?
- 20th October 2013x = 49 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.
- 21st October 2013Solve 12x^2 - 5x - 2 = 0.
- 22nd October 2013y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 9.
- 23rd October 2013A cuboid measures 4 cm by 13 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 24th October 2013A bag holds 4 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 25th October 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?
- 26th October 2013A car covers 390 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 27th October 2013f(x) = 6x + 1. Work out the inverse function f^-1(x).
- 28th October 2013A train slows steadily from 12 m/s to rest in 5 seconds. Work out its deceleration.
- 29th October 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.
- 30th October 2013A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 31st October 2013A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?