Daily Practice · Higher Plus
July 2001 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2001, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2001 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2001
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2001x = 189 and y = 124, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd July 2001Write 5/(x - 6) + 3/(x - 5) as a single fraction.
- 3rd July 2001y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 4th July 2001The 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.
- 5th July 2001A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 6th July 2001A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 7th July 2001A car covers 470 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th July 2001Solve 4x^2 - 9 = 0.
- 9th July 2001y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 16.
- 10th July 2001In 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.
- 11th July 2001The probability of winning a game is 4/5. A player expects 24 wins. How many games did they play?
- 12th July 2001On 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?
- 13th July 2001Rationalise the denominator of 88/sqrt(11), giving your answer in its simplest form.
- 14th July 2001f(x) = 6x - 8. Work out the inverse function f^-1(x).
- 15th July 2001A train slows steadily from 40 m/s to rest in 8 seconds. Work out its deceleration.
- 16th July 2001In a vector proof you find that vector PQ = 3a - 3b and vector RS = 12a - 12b. What does this show about PQ and RS?
- 17th July 2001A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 18th July 2001A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 19th July 2001Simplify sqrt(32) + sqrt(18), giving your answer in the form a sqrt(b).
- 20th July 2001Solve x^2 + y^2 = 289 and y = x + 7 simultaneously.
- 21st July 2001y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 22nd July 2001A cuboid measures 14 cm by 6 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd July 2001A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th July 2001On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 25th July 2001A rectangle is 9 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th July 2001Use the iteration x(n+1) = cube root of (2x(n) + 8) with x(0) = 5. Work out x(1) to 3 decimal places.
- 27th July 2001y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 28th July 2001A cuboid measures 6 cm by 6 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th July 2001A bag holds 7 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th July 2001A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 31st July 2001Expand and simplify (6 + sqrt(2))(6 - sqrt(2)).