Daily Practice · Higher Plus
September 2000 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2000, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2000 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2000
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2000A cuboid measures 5 cm by 4 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd September 2000A bag holds 7 red, 3 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd September 2000On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th September 2000A block has mass 750 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5th September 2000Solve 5x^2 + 31x + 30 = 0.
- 6th September 2000A train slows steadily from 34 m/s to rest in 8 seconds. Work out its deceleration.
- 7th September 2000The 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.
- 8th September 2000A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 9th September 2000A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 10th September 2000x = 128 and y = 24, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th September 2000f(x) = 7x - 11. Work out the inverse function f^-1(x).
- 12th September 2000y is inversely proportional to x^2. When x = 3, y = 100. Work out y when x = 5.
- 13th September 2000In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 14th September 2000The probability of winning a game is 1/4. A player expects 10 wins. How many games did they play?
- 15th September 2000On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 16th September 2000A car covers 800 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.
- 17th September 2000Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 18th September 2000y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 19th September 2000In a vector proof you find that vector PQ = a - 2b and vector RS = 2a - 4b. What does this show about PQ and RS?
- 20th September 2000A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 21st September 2000A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3. How many values in total?
- 22nd September 2000Rationalise the denominator of 35/sqrt(7), giving your answer in its simplest form.
- 23rd September 2000Use the iteration x(n+1) = cube root of (10x(n) + 9) with x(0) = 4. Work out x(1) to 3 decimal places.
- 24th September 2000y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 16.
- 25th September 2000A cuboid measures 15 cm by 6 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th September 2000A bag holds 4 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th September 2000On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th September 2000Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 29th September 2000Work out the nth term of the quadratic sequence -5, 3, 19, 43, ...
- 30th September 2000A train slows steadily from 13 m/s to rest in 10 seconds. Work out its deceleration.