Daily Practice · Higher Plus
May 2005 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2005, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2005 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2005
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2005y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 64.
- 2nd May 2005A cuboid measures 10 cm by 13 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd May 2005A 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?
- 4th May 2005On 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?
- 5th May 2005Simplify sqrt(32) + sqrt(32), giving your answer in the form a sqrt(b).
- 6th May 2005Work out the coordinates of the turning point of y = x^2 + 10x - 10.
- 7th May 2005A train slows steadily from 35 m/s to rest in 10 seconds. Work out its deceleration.
- 8th May 2005A cuboid measures 9 cm by 7 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th May 2005A bag holds 3 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th May 2005A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?
- 11th May 2005A rectangle is 22 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 12th May 2005Simplify (x^2 - 10x + 24)/(x - 6).
- 13th May 2005y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 14th May 2005The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 15th May 2005A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/12. Work out r.
- 16th May 2005On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 17th May 2005Expand and simplify (4 + sqrt(3))(4 - sqrt(3)).
- 18th May 2005In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 4 in terms of an integer n?
- 19th May 2005y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 3.
- 20th May 2005In 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.
- 21st May 2005The probability of winning a game is 1/2. A player expects 24 wins. How many games did they play?
- 22nd May 2005A histogram has two bars: one 5 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 23rd May 2005A block has mass 540 g (to the nearest 10 g) and volume 16 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 24th May 2005Make x the subject of 7x + 3 = y(x + 3).
- 25th May 2005y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 16.
- 26th May 2005In a vector proof you find that vector PQ = 6a - b and vector RS = 12a - 2b. What does this show about PQ and RS?
- 27th May 2005A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 28th May 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?
- 29th May 2005x = 108 and y = 38, each correct to the nearest whole number. Work out the upper bound of x - y.
- 30th May 2005Write 5/(x - 5) + 6/(x - 6) as a single fraction.
- 31st May 2005A train slows steadily from 13 m/s to rest in 10 seconds. Work out its deceleration.