Daily Practice · Higher Plus
May 2013 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2013, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2013 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2013y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 2.
- 2nd May 2013The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 3rd May 2013A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 4th May 2013A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 5th May 2013x = 114 and y = 86, each correct to the nearest whole number. Work out the upper bound of x - y.
- 6th May 2013Prove that the sum of 9 consecutive integers is always a multiple of 9. State the simplified sum you would use.
- 7th May 2013y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 81.
- 8th May 2013In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 9th May 2013The probability of winning a game is 3/5. A player expects 30 wins. How many games did they play?
- 10th May 2013On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 11th May 2013A car covers 590 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 12th May 2013f(x) = 2x + 3 and g(x) = 2x - 5. Work out fg(3).
- 13th May 2013A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
- 14th May 2013In a vector proof you find that vector PQ = 4a + 5b and vector RS = 20a + 25b. What does this show about PQ and RS?
- 15th May 2013A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.
- 16th May 2013A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 0.8. How many values in total?
- 17th May 2013Rationalise the denominator of 66/sqrt(11), giving your answer in its simplest form.
- 18th May 2013The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 19th May 2013y is inversely proportional to x^2. When x = 3, y = 4. Work out y when x = 2.
- 20th May 2013A cuboid measures 10 cm by 12 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 21st May 2013A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 22nd May 2013On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 23rd May 2013Simplify sqrt(27) + sqrt(108), giving your answer in the form a sqrt(b).
- 24th May 2013A quadratic sequence starts 7, 15, 29, 49. Work out the second difference, and the coefficient of n^2.
- 25th May 2013y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 26th May 2013A cuboid measures 11 cm by 10 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 27th May 2013A bag holds 4 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 28th May 2013A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 29th May 2013A rectangle is 22 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 30th May 2013Solve x^2 + 6x + 5 > 0.
- 31st May 2013y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 9.