Daily Practice · Higher Plus
December 2004 - Higher Plus 5-a-day
Every Higher Plus sheet published in December 2004, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' December 2004 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in December 2004
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st December 2004Use the iteration x(n+1) = cube root of (4x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.
- 2nd December 2004y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 3rd December 2004A cuboid measures 7 cm by 4 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th December 2004A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th December 2004A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 6th December 2004A block has mass 810 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th December 2004Work out the nth term of the quadratic sequence 5, 16, 33, 56, ...
- 8th December 2004y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 4.
- 9th December 2004A cuboid measures 6 cm by 7 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th December 2004A bag holds 4 red, 4 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th December 2004On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 12th December 2004x = 199 and y = 76, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th December 2004The point (3, -2) lies on y = f(x). Write down its image on y = f(-x).
- 14th December 2004A train slows steadily from 15 m/s to rest in 4 seconds. Work out its deceleration.
- 15th December 2004The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 16th December 2004A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 17th December 2004A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 18th December 2004A car covers 410 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 19th December 2004Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 20th December 2004y is inversely proportional to x^2. When x = 3, y = 75. Work out y when x = 5.
- 21st December 2004In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 22nd December 2004The probability of winning a game is 3/4. A player expects 54 wins. How many games did they play?
- 23rd December 2004On 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?
- 24th December 2004Rationalise the denominator of 24/sqrt(2), giving your answer in its simplest form.
- 25th December 2004f(x) = 6x - 2 and g(x) = 5x + 9. Work out fg(-3).
- 26th December 2004y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 27th December 2004In a vector proof you find that vector PQ = 2a - 2b and vector RS = 6a - 6b. What does this show about PQ and RS?
- 28th December 2004A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 29th December 2004A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 30th December 2004Simplify sqrt(32) + sqrt(18), giving your answer in the form a sqrt(b).
- 31st December 2004The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.