Daily Practice · Higher Plus
September 2001 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2001, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2001 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2001
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2001A train slows steadily from 30 m/s to rest in 8 seconds. Work out its deceleration.
- 2nd September 2001The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 3rd September 2001A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 4th September 2001A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 5th September 2001A rectangle is 9 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th September 2001Solve x^2 + 7x + 10 < 0.
- 7th September 2001y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 8th September 2001In 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.
- 9th September 2001The probability of winning a game is 1/2. A player expects 25 wins. How many games did they play?
- 10th September 2001On 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?
- 11th September 2001Expand and simplify (7 + sqrt(5))(7 - sqrt(5)).
- 12th September 2001Write x^2 + 2x + 2 in the form (x + a)^2 + b.
- 13th September 2001y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 14th September 2001In a vector proof you find that vector PQ = 4a + 3b and vector RS = 8a + 6b. What does this show about PQ and RS?
- 15th September 2001A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 16th September 2001A 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?
- 17th September 2001A block has mass 430 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th September 2001Work out the coordinates of the turning point of y = x^2 + 16x + 6.
- 19th September 2001y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 4.
- 20th September 2001A cuboid measures 8 cm by 10 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st September 2001A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd September 2001On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 23rd September 2001x = 111 and y = 60, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th September 2001Simplify (x^2 + x - 2)/(x - 1).
- 25th September 2001A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
- 26th September 2001A cuboid measures 14 cm by 6 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th September 2001A bag holds 7 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th September 2001A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 1.4. How many values in total?
- 29th September 2001A car covers 380 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.
- 30th September 2001In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 3 in terms of an integer n?