Daily Practice · Higher Plus
October 2003 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2003, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2003 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2003A rectangle is 4 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd October 2003Solve 10x^2 - 37x + 30 = 0.
- 3rd October 2003y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 9.
- 4th October 2003In a vector proof you find that vector PQ = a - 5b and vector RS = 4a - 20b. What does this show about PQ and RS?
- 5th October 2003A bag holds 5 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 6th October 2003On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th October 2003Expand and simplify (8 + sqrt(10))(8 - sqrt(10)).
- 8th October 2003f(x) = 2x + 12. Work out the inverse function f^-1(x).
- 9th October 2003A train slows steadily from 18 m/s to rest in 5 seconds. Work out its deceleration.
- 10th October 2003A cuboid measures 6 cm by 11 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th October 2003A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th October 2003A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3.5. How many values in total?
- 13th October 2003A block has mass 390 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.
- 14th October 2003Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 15th October 2003y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.
- 16th October 2003A cuboid measures 8 cm by 12 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th October 2003A bag holds 3 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th October 2003On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 19th October 2003x = 70 and y = 48, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th October 2003Use the iteration x(n+1) = cube root of (5x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.
- 21st October 2003y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 22nd October 2003The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 23rd October 2003A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 28/55. Work out r.
- 24th October 2003A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 25th October 2003A car covers 600 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 26th October 2003Work out the nth term of the quadratic sequence -4, 0, 10, 26, ...
- 27th October 2003y is directly proportional to sqrt(x). When x = 16, y = 16. Work out y when x = 64.
- 28th October 2003In 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.
- 29th October 2003The probability of winning a game is 2/5. A player expects 16 wins. How many games did they play?
- 30th October 2003On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 31st October 2003Rationalise the denominator of 54/sqrt(6), giving your answer in its simplest form.