Daily Practice · Higher Plus
October 2001 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2001, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2001 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2001
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2001y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 2nd October 2001The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 3rd October 2001A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 4th October 2001On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 5th October 2001Rationalise the denominator of 36/sqrt(3), giving your answer in its simplest form.
- 6th October 2001Make x the subject of 2x + 2 = y(x + 2).
- 7th October 2001y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.
- 8th October 2001In 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.
- 9th October 2001The probability of winning a game is 5/8. A player expects 60 wins. How many games did they play?
- 10th October 2001A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 11th October 2001Simplify sqrt(75) + sqrt(3), giving your answer in the form a sqrt(b).
- 12th October 2001Write 5/(x + 6) + 2/(x + 5) as a single fraction.
- 13th October 2001y is directly proportional to sqrt(x). When x = 25, y = 20. Work out y when x = 16.
- 14th October 2001In a vector proof you find that vector PQ = 5a + b and vector RS = 10a + 2b. What does this show about PQ and RS?
- 15th October 2001A bag holds 4 red and n blue counters. The probability of taking a red is 4/9. Work out n.
- 16th October 2001On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 17th October 2001A rectangle is 14 cm by 23 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th October 2001Solve 10x^2 + 31x + 15 = 0.
- 19th October 2001A train slows steadily from 40 m/s to rest in 8 seconds. Work out its deceleration.
- 20th October 2001A cuboid measures 3 cm by 9 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st October 2001A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd October 2001A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 3. How many values in total?
- 23rd October 2001Expand and simplify (6 + sqrt(5))(6 - sqrt(5)).
- 24th October 2001f(x) = 4x - 6. Work out the inverse function f^-1(x).
- 25th October 2001y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 26th October 2001A cuboid measures 12 cm by 12 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th October 2001A bag holds 4 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th October 2001On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 29th October 2001A block has mass 540 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th October 2001Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 31st October 2001y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 3.