Daily Practice · Higher Plus
December 2015 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2015, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2015 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2015
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2015A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 2nd December 2015On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 3rd December 2015Simplify sqrt(20) + sqrt(80), giving your answer in the form a sqrt(b).
- 4th December 2015Solve x^2 - 11x + 24 < 0.
- 5th December 2015A train slows steadily from 17 m/s to rest in 5 seconds. Work out its deceleration.
- 6th December 2015A cuboid measures 9 cm by 14 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 7th December 2015A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 8th December 2015A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 9th December 2015A rectangle is 7 cm by 11 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 10th December 2015Write x^2 - 4x + 3 in the form (x + a)^2 + b.
- 11th December 2015y is inversely proportional to x^2. When x = 5, y = 18. Work out y when x = 3.
- 12th December 2015A cuboid measures 13 cm by 4 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 13th December 2015A bag holds 3 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 14th December 2015On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th December 2015Expand and simplify (2 + sqrt(3))(2 - sqrt(3)).
- 16th December 2015Work out the coordinates of the turning point of y = x^2 + 16x + 8.
- 17th December 2015y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 18th December 2015The 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.
- 19th December 2015A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 20th December 2015A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 1.4. How many values in total?
- 21st December 2015A 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.
- 22nd December 2015Simplify (x^2 - 8x + 15)/(x - 5).
- 23rd December 2015y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 49.
- 24th December 2015In 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.
- 25th December 2015The probability of winning a game is 3/5. A player expects 21 wins. How many games did they play?
- 26th December 2015On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 27th December 2015x = 53 and y = 26, each correct to the nearest whole number. Work out the upper bound of x - y.
- 28th December 2015In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 29th December 2015A train slows steadily from 32 m/s to rest in 5 seconds. Work out its deceleration.
- 30th December 2015In a vector proof you find that vector PQ = 4a - 3b and vector RS = 12a - 9b. What does this show about PQ and RS?
- 31st December 2015A bag holds 7 red and n blue counters. The probability of taking a red is 7/10. Work out n.