Daily Practice · Higher Plus
May 2014 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2014, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2014 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2014
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2014Make x the subject of 2x + 7 = y(x + 7).
- 2nd May 2014y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 81.
- 3rd May 2014In 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.
- 4th May 2014The probability of winning a game is 1/10. A player expects 11 wins. How many games did they play?
- 5th May 2014On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th May 2014Expand and simplify (4 + sqrt(3))(4 - sqrt(3)).
- 7th May 2014Write 2/(x - 5) + 6/(x + 3) as a single fraction.
- 8th May 2014A train slows steadily from 22 m/s to rest in 8 seconds. Work out its deceleration.
- 9th May 2014In a vector proof you find that vector PQ = 3a - 3b and vector RS = 6a - 6b. What does this show about PQ and RS?
- 10th May 2014A bag holds 4 red and n blue counters. The probability of taking a red is 2/5. Work out n.
- 11th May 2014A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 12th May 2014A block has mass 420 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 13th May 2014Solve 9x^2 - 9x + 2 = 0.
- 14th May 2014y is inversely proportional to x^2. When x = 3, y = 36. Work out y when x = 6.
- 15th May 2014A cuboid measures 8 cm by 10 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th May 2014A 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?
- 17th May 2014On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 18th May 2014x = 46 and y = 12, each correct to the nearest whole number. Work out the upper bound of x - y.
- 19th May 2014f(x) = 4x - 11. Work out the inverse function f^-1(x).
- 20th May 2014y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 21st May 2014A cuboid measures 7 cm by 14 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd May 2014A bag holds 5 red, 7 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd May 2014A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 0.8. How many values in total?
- 24th May 2014A car covers 170 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 25th May 2014Solve x^2 + y^2 = 676 and y = x - 14 simultaneously.
- 26th May 2014y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 81.
- 27th May 2014The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 28th May 2014A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 29th May 2014On 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?
- 30th May 2014Rationalise the denominator of 24/sqrt(6), giving your answer in its simplest form.
- 31st May 2014Use the iteration x(n+1) = cube root of (4x(n) + 2) with x(0) = 4. Work out x(1) to 3 decimal places.