Daily Practice · Higher Plus
December 2014 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2014, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2014 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2014
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2014A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 2nd December 2014Expand and simplify (9 + sqrt(7))(9 - sqrt(7)).
- 3rd December 2014Solve 9x^2 + 6x - 8 = 0.
- 4th December 2014y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 25.
- 5th December 2014In a vector proof you find that vector PQ = 2a + b and vector RS = 8a + 4b. What does this show about PQ and RS?
- 6th December 2014A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 7th December 2014On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 8th December 2014A block has mass 820 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.
- 9th December 2014f(x) = 7x - 4. Work out the inverse function f^-1(x).
- 10th December 2014A train slows steadily from 21 m/s to rest in 8 seconds. Work out its deceleration.
- 11th December 2014A cuboid measures 14 cm by 9 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th December 2014A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th December 2014A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 14th December 2014x = 133 and y = 116, each correct to the nearest whole number. Work out the upper bound of x - y.
- 15th December 2014Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 16th December 2014y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 17th December 2014A cuboid measures 4 cm by 4 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th December 2014A bag holds 4 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th December 2014On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 20th December 2014A car covers 350 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 21st December 2014Use the iteration x(n+1) = cube root of (5x(n) + 6) with x(0) = 1. Work out x(1) to 3 decimal places.
- 22nd December 2014y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 23rd December 2014The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 24th December 2014A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 25th December 2014A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 26th December 2014Rationalise the denominator of 99/sqrt(11), giving your answer in its simplest form.
- 27th December 2014Work out the nth term of the quadratic sequence 3, 7, 13, 21, ...
- 28th December 2014y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 81.
- 29th December 2014In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 30th December 2014The probability of winning a game is 3/5. A player expects 24 wins. How many games did they play?
- 31st December 2014On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?