Daily Practice · Higher Plus
December 2017 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2017, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2017 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2017
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2017A cuboid measures 12 cm by 12 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd December 2017A bag holds 6 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd December 2017On 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?
- 4th December 2017A block has mass 400 g (to the nearest 10 g) and volume 13 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5th December 2017Simplify (x^2 - 8x + 15)/(x - 5).
- 6th December 2017y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 3.
- 7th December 2017The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 8th December 2017A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 28/45. Work out r.
- 9th December 2017A 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?
- 10th December 2017x = 89 and y = 55, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th December 2017In an algebraic proof, how would you write a multiple of 7 in terms of an integer n?
- 12th December 2017y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 49.
- 13th December 2017In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 14th December 2017The probability of winning a game is 3/10. A player expects 42 wins. How many games did they play?
- 15th December 2017On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th December 2017A car covers 900 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.
- 17th December 2017Make x the subject of 6x + 2 = y(x + 2).
- 18th December 2017A train slows steadily from 16 m/s to rest in 5 seconds. Work out its deceleration.
- 19th December 2017In a vector proof you find that vector PQ = 3a + 3b and vector RS = 9a + 9b. What does this show about PQ and RS?
- 20th December 2017A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 21st December 2017A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 22nd December 2017Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
- 23rd December 2017Write 6/(x - 1) + 5/(x + 4) as a single fraction.
- 24th December 2017y is inversely proportional to x^2. When x = 3, y = 72. Work out y when x = 6.
- 25th December 2017A cuboid measures 15 cm by 8 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th December 2017A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th December 2017On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th December 2017Simplify sqrt(18) + sqrt(32), giving your answer in the form a sqrt(b).
- 29th December 2017Solve 8x^2 + 14x - 15 = 0.
- 30th December 2017y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 31st December 2017A cuboid measures 14 cm by 12 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.