Daily Practice · Higher Plus
August 2000 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2000, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2000 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2000
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2000y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 2nd August 2000A cuboid measures 7 cm by 14 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd August 2000A bag holds 5 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th August 2000A histogram has two bars: one 5 units wide with frequency density 2.5, one 20 units wide with density 3. How many values in total?
- 5th August 2000A car covers 900 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 6th August 2000Work out the coordinates of the turning point of y = x^2 + 8x + 14.
- 7th August 2000y is directly proportional to sqrt(x). When x = 9, y = 24. Work out y when x = 36.
- 8th August 2000The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 9th August 2000A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/21. Work out r.
- 10th August 2000On 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?
- 11th August 2000Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
- 12th August 2000Simplify (x^2 - 9x + 20)/(x - 5).
- 13th August 2000A train slows steadily from 36 m/s to rest in 8 seconds. Work out its deceleration.
- 14th August 2000In 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.
- 15th August 2000The probability of winning a game is 1/5. A player expects 10 wins. How many games did they play?
- 16th August 2000A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 0.8. How many values in total?
- 17th August 2000Simplify sqrt(12) + sqrt(3), giving your answer in the form a sqrt(b).
- 18th August 2000In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 19th August 2000y is inversely proportional to x^2. When x = 3, y = 32. Work out y when x = 4.
- 20th August 2000In a vector proof you find that vector PQ = 5a + b and vector RS = 20a + 4b. What does this show about PQ and RS?
- 21st August 2000A bag holds 3 red and n blue counters. The probability of taking a red is 3/7. Work out n.
- 22nd August 2000On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd August 2000A rectangle is 20 cm by 26 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 24th August 2000Make x the subject of 3x + 3 = y(x + 3).
- 25th August 2000y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 26th August 2000A cuboid measures 11 cm by 13 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th August 2000A bag holds 8 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 28th August 2000A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 29th August 2000Expand and simplify (6 + sqrt(10))(6 - sqrt(10)).
- 30th August 2000Write 3/(x + 6) + 2/(x - 3) as a single fraction.
- 31st August 2000y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 25.