Daily Practice · Higher Plus
December 2001 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2001, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2001 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2001
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2001The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 2nd December 2001A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 3rd December 2001On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th December 2001Expand and simplify (3 + sqrt(6))(3 - sqrt(6)).
- 5th December 2001The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 6th December 2001A train slows steadily from 34 m/s to rest in 8 seconds. Work out its deceleration.
- 7th December 2001In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 8th December 2001The probability of winning a game is 1/2. A player expects 24 wins. How many games did they play?
- 9th December 2001A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 10th December 2001A block has mass 810 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th December 2001A quadratic sequence starts 4, 21, 48, 85. Work out the second difference, and the coefficient of n^2.
- 12th December 2001y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 13th December 2001In a vector proof you find that vector PQ = 5a + 5b and vector RS = 15a + 15b. What does this show about PQ and RS?
- 14th December 2001A bag holds 2 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 15th December 2001On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 16th December 2001x = 184 and y = 115, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th December 2001Solve x^2 + 10x + 16 < 0.
- 18th December 2001y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 19th December 2001A cuboid measures 5 cm by 7 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th December 2001A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st December 2001A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 3. How many values in total?
- 22nd December 2001A car covers 510 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.
- 23rd December 2001Write x^2 + 6x - 9 in the form (x + a)^2 + b.
- 24th December 2001y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 49.
- 25th December 2001A cuboid measures 13 cm by 14 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th December 2001A bag holds 7 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th December 2001On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 28th December 2001Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
- 29th December 2001Work out the coordinates of the turning point of y = x^2 - 16x - 1.
- 30th December 2001A train slows steadily from 29 m/s to rest in 4 seconds. Work out its deceleration.
- 31st December 2001The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.