Daily Practice · Higher Plus
May 2015 - Higher Plus 5-a-day
Every Higher Plus sheet published in May 2015, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' May 2015 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in May 2015
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st May 2015Rationalise the denominator of 84/sqrt(7), giving your answer in its simplest form.
- 2nd May 2015The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 3rd May 2015A train slows steadily from 14 m/s to rest in 5 seconds. Work out its deceleration.
- 4th May 2015In a vector proof you find that vector PQ = 4a + 6b and vector RS = 16a + 24b. What does this show about PQ and RS?
- 5th May 2015A bag holds 5 red and n blue counters. The probability of taking a red is 5/12. Work out n.
- 6th May 2015A 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?
- 7th May 2015Simplify sqrt(45) + sqrt(45), giving your answer in the form a sqrt(b).
- 8th May 2015A quadratic sequence starts 9, 15, 23, 33. Work out the second difference, and the coefficient of n^2.
- 9th May 2015y is inversely proportional to x^2. When x = 5, y = 72. Work out y when x = 6.
- 10th May 2015A cuboid measures 7 cm by 9 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th May 2015A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th May 2015On 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?
- 13th May 2015A rectangle is 8 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th May 2015Solve x^2 + 6x + 8 < 0.
- 15th May 2015y is directly proportional to x^3. When x = 4, y = 384. Work out y when x = 3.
- 16th May 2015A cuboid measures 14 cm by 14 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th May 2015A bag holds 4 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th May 2015A histogram has two bars: one 10 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 19th May 2015Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 20th May 2015Write x^2 - 6x - 6 in the form (x + a)^2 + b.
- 21st May 2015y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 49.
- 22nd May 2015The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 23rd May 2015A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 5/33. Work out r.
- 24th May 2015On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 25th May 2015A block has mass 370 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th May 2015Work out the coordinates of the turning point of y = x^2 - 14x - 2.
- 27th May 2015A train slows steadily from 29 m/s to rest in 8 seconds. Work out its deceleration.
- 28th May 2015In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 29th May 2015The probability of winning a game is 4/5. A player expects 36 wins. How many games did they play?
- 30th May 2015A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 0.6. How many values in total?
- 31st May 2015x = 129 and y = 82, each correct to the nearest whole number. Work out the upper bound of x - y.