Daily Practice · Higher Plus
October 2005 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2005, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2005 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2005A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 2nd October 2005x = 107 and y = 90, each correct to the nearest whole number. Work out the upper bound of x - y.
- 3rd October 2005Use the iteration x(n+1) = cube root of (11x(n) + 7) with x(0) = 1. Work out x(1) to 3 decimal places.
- 4th October 2005y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 5th October 2005A cuboid measures 13 cm by 5 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th October 2005A bag holds 5 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th October 2005On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th October 2005A car covers 390 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 9th October 2005Work out the nth term of the quadratic sequence -5, -4, 1, 10, ...
- 10th October 2005y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 11th October 2005The 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.
- 12th October 2005A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 13th October 2005A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 3. How many values in total?
- 14th October 2005Rationalise the denominator of 70/sqrt(7), giving your answer in its simplest form.
- 15th October 2005The point (-1, 4) lies on y = f(x). Write down its image on y = f(x) - 1.
- 16th October 2005y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 4.
- 17th October 2005In 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.
- 18th October 2005The probability of winning a game is 4/5. A player expects 24 wins. How many games did they play?
- 19th October 2005On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 20th October 2005Simplify sqrt(48) + sqrt(48), giving your answer in the form a sqrt(b).
- 21st October 2005Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 22nd October 2005A train slows steadily from 40 m/s to rest in 4 seconds. Work out its deceleration.
- 23rd October 2005In a vector proof you find that vector PQ = 4a - 4b and vector RS = 12a - 12b. What does this show about PQ and RS?
- 24th October 2005A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 25th October 2005A histogram has two bars: one 5 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 26th October 2005A rectangle is 7 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 27th October 2005f(x) = 2x - 9 and g(x) = 5x - 5. Work out fg(2).
- 28th October 2005y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 29th October 2005A cuboid measures 9 cm by 13 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th October 2005A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 31st October 2005On 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?