Daily Practice · Higher Plus
January 2004 - Higher Plus 5-a-day
Every Higher Plus sheet published in January 2004, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' January 2004 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 2004
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 2004y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 2nd January 2004In a vector proof you find that vector PQ = 5a - b and vector RS = 20a - 4b. What does this show about PQ and RS?
- 3rd January 2004A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 4th January 2004A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 5th January 2004A block has mass 710 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th January 2004Write 7/(x + 5) + 6/(x + 6) as a single fraction.
- 7th January 2004y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 9.
- 8th January 2004A cuboid measures 7 cm by 13 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th January 2004A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th January 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?
- 11th January 2004x = 32 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th January 2004Solve 3x^2 + 13x + 4 = 0.
- 13th January 2004A train slows steadily from 15 m/s to rest in 8 seconds. Work out its deceleration.
- 14th January 2004A cuboid measures 12 cm by 13 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th January 2004A bag holds 4 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th January 2004A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 17th January 2004A car covers 480 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 18th January 2004f(x) = 8x + 9. Work out the inverse function f^-1(x).
- 19th January 2004y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 20th January 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.
- 21st January 2004A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 22nd January 2004On 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?
- 23rd January 2004Rationalise the denominator of 77/sqrt(11), giving your answer in its simplest form.
- 24th January 2004Solve x^2 + y^2 = 169 and y = x + 7 simultaneously.
- 25th January 2004y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 26th January 2004In 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.
- 27th January 2004The probability of winning a game is 1/5. A player expects 14 wins. How many games did they play?
- 28th January 2004A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 29th January 2004Simplify sqrt(12) + sqrt(27), giving your answer in the form a sqrt(b).
- 30th January 2004Use the iteration x(n+1) = cube root of (5x(n) + 3) with x(0) = 4. Work out x(1) to 3 decimal places.
- 31st January 2004y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 16.