Daily Practice · Higher Plus
August 2001 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2001, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2001 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2001
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2001Work out the nth term of the quadratic sequence -3, 5, 21, 45, ...
- 2nd August 2001y is directly proportional to sqrt(x). When x = 49, y = 21. Work out y when x = 16.
- 3rd August 2001The 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.
- 4th August 2001A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 5th August 2001On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 6th August 2001A block has mass 860 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th August 2001The point (-5, -4) lies on y = f(x). Write down its image on y = f(x) + 3.
- 8th August 2001A train slows steadily from 22 m/s to rest in 8 seconds. Work out its deceleration.
- 9th August 2001In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 10th August 2001The probability of winning a game is 2/5. A player expects 12 wins. How many games did they play?
- 11th August 2001A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 12th August 2001x = 79 and y = 15, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th August 2001Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 14th August 2001y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 15th August 2001In a vector proof you find that vector PQ = 2a + 4b and vector RS = 6a + 12b. What does this show about PQ and RS?
- 16th August 2001A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 17th August 2001On 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?
- 18th August 2001A car covers 550 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.
- 19th August 2001f(x) = 4x - 2 and g(x) = 5x - 2. Work out fg(5).
- 20th August 2001y is directly proportional to x^3. When x = 3, y = 54. Work out y when x = 2.
- 21st August 2001A cuboid measures 11 cm by 3 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 22nd August 2001A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 23rd August 2001A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 24th August 2001Rationalise the denominator of 121/sqrt(11), giving your answer in its simplest form.
- 25th August 2001The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 26th August 2001y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 4.
- 27th August 2001A cuboid measures 13 cm by 9 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 28th August 2001A bag holds 6 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 29th August 2001On 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?
- 30th August 2001Simplify sqrt(48) + sqrt(147), giving your answer in the form a sqrt(b).
- 31st August 2001A quadratic sequence starts -2, -3, -2, 1. Work out the second difference, and the coefficient of n^2.