Daily Practice · Higher Plus
December 2018 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2018, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2018 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2018y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 2nd December 2018The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 3rd December 2018A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 4th December 2018A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 5th December 2018A rectangle is 15 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th December 2018Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 7th December 2018y is directly proportional to sqrt(x). When x = 4, y = 8. Work out y when x = 64.
- 8th December 2018In 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.
- 9th December 2018The probability of winning a game is 4/5. A player expects 80 wins. How many games did they play?
- 10th December 2018On 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?
- 11th December 2018Expand and simplify (9 + sqrt(2))(9 - sqrt(2)).
- 12th December 2018f(x) = 6x - 8 and g(x) = 2x - 6. Work out fg(2).
- 13th December 2018A train slows steadily from 35 m/s to rest in 4 seconds. Work out its deceleration.
- 14th December 2018In a vector proof you find that vector PQ = 4a + 3b and vector RS = 16a + 12b. What does this show about PQ and RS?
- 15th December 2018A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 16th December 2018A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 17th December 2018A block has mass 780 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th December 2018The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 19th December 2018y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 20th December 2018A cuboid measures 8 cm by 4 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st December 2018A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd December 2018On 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?
- 23rd December 2018x = 155 and y = 96, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th December 2018A quadratic sequence starts -2, 1, 8, 19. Work out the second difference, and the coefficient of n^2.
- 25th December 2018y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 26th December 2018A cuboid measures 8 cm by 7 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th December 2018A bag holds 7 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th December 2018A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 29th December 2018A car covers 430 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.
- 30th December 2018Solve x^2 + 2x - 3 > 0.
- 31st December 2018y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 25.