Daily Practice · Higher Plus
May 2012 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2012, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2012 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2012
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2012A cuboid measures 9 cm by 14 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd May 2012A bag holds 3 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd May 2012On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th May 2012Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
- 5th May 2012Simplify (x^2 - 5x + 6)/(x - 3).
- 6th May 2012y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 7th May 2012The 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.
- 8th May 2012A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 7/22. Work out r.
- 9th May 2012A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 0.8. How many values in total?
- 10th May 2012Simplify sqrt(48) + sqrt(27), giving your answer in the form a sqrt(b).
- 11th May 2012In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 9 in terms of an integer n?
- 12th May 2012y is directly proportional to sqrt(x). When x = 16, y = 20. Work out y when x = 25.
- 13th May 2012In 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.
- 14th May 2012The probability of winning a game is 1/2. A player expects 60 wins. How many games did they play?
- 15th May 2012On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 16th May 2012A rectangle is 16 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th May 2012Make x the subject of 7x + 6 = y(x + 6).
- 18th May 2012A train slows steadily from 25 m/s to rest in 8 seconds. Work out its deceleration.
- 19th May 2012In a vector proof you find that vector PQ = 2a - 6b and vector RS = 4a - 12b. What does this show about PQ and RS?
- 20th May 2012A bag holds 2 red and n blue counters. The probability of taking a red is 1/5. Work out n.
- 21st May 2012A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 22nd May 2012Expand and simplify (2 + sqrt(7))(2 - sqrt(7)).
- 23rd May 2012Write 2/(x + 5) + 5/(x + 6) as a single fraction.
- 24th May 2012y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 25th May 2012A cuboid measures 15 cm by 9 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th May 2012A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th May 2012On 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?
- 28th May 2012A block has mass 260 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th May 2012Solve 5x^2 - 11x - 12 = 0.
- 30th May 2012y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 31st May 2012A cuboid measures 13 cm by 4 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.