Daily Practice · Higher Plus
November 2000 - Higher Plus 5-a-day
Every Higher Plus sheet published in November 2000, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' November 2000 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 2000
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 2000A bag holds 4 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd November 2000On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 3rd November 2000Rationalise the denominator of 20/sqrt(5), giving your answer in its simplest form.
- 4th November 2000Solve x^2 + 7x + 12 < 0.
- 5th November 2000y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 6th November 2000The 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.
- 7th November 2000A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 8th November 2000A 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?
- 9th November 2000Simplify sqrt(80) + sqrt(45), giving your answer in the form a sqrt(b).
- 10th November 2000Write x^2 + 14x - 13 in the form (x + a)^2 + b.
- 11th November 2000y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 64.
- 12th November 2000In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 13th November 2000The probability of winning a game is 3/4. A player expects 6 wins. How many games did they play?
- 14th November 2000On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th November 2000A rectangle is 27 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 16th November 2000Work out the coordinates of the turning point of y = x^2 - 8x - 12.
- 17th November 2000A train slows steadily from 23 m/s to rest in 8 seconds. Work out its deceleration.
- 18th November 2000In a vector proof you find that vector PQ = 3a + 6b and vector RS = 6a + 12b. What does this show about PQ and RS?
- 19th November 2000A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 20th November 2000A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 21st November 2000Expand and simplify (5 + sqrt(10))(5 - sqrt(10)).
- 22nd November 2000Simplify (x^2 + 10x + 24)/(x + 4).
- 23rd November 2000y is inversely proportional to x^2. When x = 2, y = 72. Work out y when x = 6.
- 24th November 2000A cuboid measures 7 cm by 14 cm by 11 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th November 2000A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th November 2000On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 27th November 2000A block has mass 870 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.
- 28th November 2000In an algebraic proof, how would you write the number two more than an even number in terms of an integer n?
- 29th November 2000y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 30th November 2000A cuboid measures 14 cm by 4 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.