Daily Practice · Higher Plus
October 2000 - Higher Plus 5-a-day
Every Higher Plus sheet published in October 2000, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' October 2000 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in October 2000
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st October 2000A cuboid measures 13 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 October 2000A bag holds 7 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd October 2000A histogram has two bars: one 20 units wide with frequency density 0.4, one 25 units wide with density 3.5. How many values in total?
- 4th October 2000A rectangle is 15 cm by 30 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 5th October 2000The point (5, -3) lies on y = f(x). Write down its image on y = f(x) - 6.
- 6th October 2000y is inversely proportional to x^2. When x = 3, y = 144. Work out y when x = 6.
- 7th October 2000The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 8th October 2000A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 9th October 2000On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th October 2000Expand and simplify (4 + sqrt(11))(4 - sqrt(11)).
- 11th October 2000Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 12th October 2000y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 13th October 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.
- 14th October 2000The probability of winning a game is 1/10. A player expects 6 wins. How many games did they play?
- 15th October 2000A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 16th October 2000A block has mass 340 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.
- 17th October 2000f(x) = 5x + 4 and g(x) = 2x + 3. Work out fg(6).
- 18th October 2000y is directly proportional to sqrt(x). When x = 4, y = 16. Work out y when x = 16.
- 19th October 2000In a vector proof you find that vector PQ = 3a + 6b and vector RS = 12a + 24b. What does this show about PQ and RS?
- 20th October 2000A bag holds 4 red and n blue counters. The probability of taking a red is 4/11. Work out n.
- 21st October 2000On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 22nd October 2000x = 78 and y = 24, each correct to the nearest whole number. Work out the upper bound of x - y.
- 23rd October 2000The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 24th October 2000A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 25th October 2000A cuboid measures 5 cm by 5 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th October 2000A bag holds 4 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th October 2000A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 28th October 2000A car covers 240 m (to the nearest 10 m) in 7 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 29th October 2000A quadratic sequence starts 1, 14, 35, 64. Work out the second difference, and the coefficient of n^2.
- 30th October 2000y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 31st October 2000A cuboid measures 4 cm by 5 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.