Daily Practice · Higher Plus
June 2001 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2001, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2001 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2001
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2001Rationalise the denominator of 25/sqrt(5), giving your answer in its simplest form.
- 2nd June 2001Write x^2 + 4x + 10 in the form (x + a)^2 + b.
- 3rd June 2001y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 3.
- 4th June 2001The 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.
- 5th June 2001A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
- 6th June 2001On 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?
- 7th June 2001Simplify sqrt(12) + sqrt(75), giving your answer in the form a sqrt(b).
- 8th June 2001Work out the coordinates of the turning point of y = x^2 - 16x - 1.
- 9th June 2001y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 10th June 2001In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 11th June 2001The probability of winning a game is 7/8. A player expects 49 wins. How many games did they play?
- 12th June 2001A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 13th June 2001A rectangle is 12 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th June 2001Simplify (x^2 + 5x - 24)/(x - 3).
- 15th June 2001y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 49.
- 16th June 2001In a vector proof you find that vector PQ = 6a + 4b and vector RS = 12a + 8b. What does this show about PQ and RS?
- 17th June 2001A bag holds 6 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 18th June 2001On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th June 2001Expand and simplify (6 + sqrt(3))(6 - sqrt(3)).
- 20th June 2001In an algebraic proof, how would you write an even number in terms of an integer n?
- 21st June 2001A train slows steadily from 12 m/s to rest in 5 seconds. Work out its deceleration.
- 22nd June 2001A cuboid measures 9 cm by 4 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 23rd June 2001A bag holds 5 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 24th June 2001A histogram has two bars: one 20 units wide with frequency density 2.5, one 20 units wide with density 3.5. How many values in total?
- 25th June 2001A block has mass 450 g (to the nearest 10 g) and volume 14 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th June 2001Make x the subject of 5x + 4 = y(x + 4).
- 27th June 2001y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.
- 28th June 2001A cuboid measures 11 cm by 8 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 29th June 2001A bag holds 6 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 30th June 2001On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?