Daily Practice · Higher Plus
December 2013 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2013, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2013 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2013x = 116 and y = 89, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd December 2013f(x) = 5x - 8 and g(x) = 4x + 7. Work out fg(-2).
- 3rd December 2013y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 4th December 2013In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 5th December 2013The probability of winning a game is 4/5. A player expects 40 wins. How many games did they play?
- 6th December 2013A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 7th December 2013A car covers 130 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th December 2013The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 9th December 2013y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 16.
- 10th December 2013In a vector proof you find that vector PQ = 4a - 6b and vector RS = 20a - 30b. What does this show about PQ and RS?
- 11th December 2013A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 12th December 2013On 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?
- 13th December 2013Rationalise the denominator of 8/sqrt(2), giving your answer in its simplest form.
- 14th December 2013A quadratic sequence starts 8, 28, 58, 98. Work out the second difference, and the coefficient of n^2.
- 15th December 2013A train slows steadily from 34 m/s to rest in 4 seconds. Work out its deceleration.
- 16th December 2013A cuboid measures 9 cm by 11 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th December 2013A bag holds 7 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th December 2013A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 19th December 2013Simplify sqrt(18) + sqrt(50), giving your answer in the form a sqrt(b).
- 20th December 2013Solve x^2 - 9x + 14 < 0.
- 21st December 2013y is inversely proportional to x^2. When x = 4, y = 4. Work out y when x = 2.
- 22nd December 2013A cuboid measures 7 cm by 14 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd December 2013A bag holds 6 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th December 2013On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 25th December 2013A rectangle is 10 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th December 2013Write x^2 + 8x - 1 in the form (x + a)^2 + b.
- 27th December 2013y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 5.
- 28th December 2013The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 29th December 2013A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
- 30th December 2013A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3. How many values in total?
- 31st December 2013Expand and simplify (8 + sqrt(10))(8 - sqrt(10)).