Daily Practice · Higher Plus
October 2014 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2014, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2014 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2014
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2014The probability of winning a game is 1/5. A player expects 5 wins. How many games did they play?
- 2nd October 2014A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 3rd October 2014Rationalise the denominator of 24/sqrt(6), giving your answer in its simplest form.
- 4th October 2014f(x) = 4x - 5 and g(x) = 6x + 4. Work out fg(6).
- 5th October 2014y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 6th October 2014In a vector proof you find that vector PQ = 4a + b and vector RS = 8a + 2b. What does this show about PQ and RS?
- 7th October 2014A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 8th October 2014On 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?
- 9th October 2014Simplify sqrt(12) + sqrt(48), giving your answer in the form a sqrt(b).
- 10th October 2014The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 90.
- 11th October 2014y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 12th October 2014A cuboid measures 12 cm by 3 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th October 2014A bag holds 7 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 14th October 2014A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 0.8. How many values in total?
- 15th October 2014A rectangle is 27 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th October 2014A quadratic sequence starts 2, 17, 40, 71. Work out the second difference, and the coefficient of n^2.
- 17th October 2014y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 25.
- 18th October 2014A cuboid measures 5 cm by 11 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th October 2014A bag holds 7 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th October 2014On 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?
- 21st October 2014Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 22nd October 2014Solve x^2 + 9x + 18 < 0.
- 23rd October 2014A train slows steadily from 21 m/s to rest in 10 seconds. Work out its deceleration.
- 24th October 2014The 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.
- 25th October 2014A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 6/11. Work out r.
- 26th October 2014A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 27th October 2014A block has mass 540 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 28th October 2014Write x^2 - 2x + 1 in the form (x + a)^2 + b.
- 29th October 2014y is inversely proportional to x^2. When x = 5, y = 16. Work out y when x = 2.
- 30th October 2014In 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.
- 31st October 2014The probability of winning a game is 1/5. A player expects 26 wins. How many games did they play?