Daily Practice · Higher Plus
June 2005 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2005, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2005 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2005A cuboid measures 13 cm by 12 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 2nd June 2005A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 3rd June 2005A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 4th June 2005A car covers 600 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 5th June 2005Solve 3x^2 - 19x + 20 = 0.
- 6th June 2005y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.
- 7th June 2005A cuboid measures 10 cm by 13 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 8th June 2005A bag holds 3 red, 4 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 9th June 2005On 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?
- 10th June 2005Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 11th June 2005f(x) = 5x + 2. Work out the inverse function f^-1(x).
- 12th June 2005y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 13th June 2005The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 14th June 2005A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/6. Work out r.
- 15th June 2005A histogram has two bars: one 20 units wide with frequency density 2, one 10 units wide with density 0.6. How many values in total?
- 16th June 2005Simplify sqrt(8) + sqrt(32), giving your answer in the form a sqrt(b).
- 17th June 2005Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 18th June 2005y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 36.
- 19th June 2005In 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.
- 20th June 2005The probability of winning a game is 3/4. A player expects 15 wins. How many games did they play?
- 21st June 2005On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 22nd June 2005A rectangle is 18 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd June 2005Use the iteration x(n+1) = cube root of (7x(n) + 2) with x(0) = 2. Work out x(1) to 3 decimal places.
- 24th June 2005A train slows steadily from 18 m/s to rest in 5 seconds. Work out its deceleration.
- 25th June 2005In a vector proof you find that vector PQ = 6a + 4b and vector RS = 18a + 12b. What does this show about PQ and RS?
- 26th June 2005A bag holds 3 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 27th June 2005A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 28th June 2005Expand and simplify (3 + sqrt(5))(3 - sqrt(5)).
- 29th June 2005Work out the nth term of the quadratic sequence -5, 0, 9, 22, ...
- 30th June 2005y is inversely proportional to x^2. When x = 5, y = 64. Work out y when x = 4.