Daily Practice · Higher Plus
June 2017 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2017, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2017 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2017
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2017Simplify sqrt(27) + sqrt(27), giving your answer in the form a sqrt(b).
- 2nd June 2017Write 3/(x + 5) + 2/(x + 6) as a single fraction.
- 3rd June 2017y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 9.
- 4th June 2017A cuboid measures 4 cm by 10 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th June 2017A bag holds 3 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th June 2017On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 7th June 2017A rectangle is 13 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 8th June 2017Solve 2x^2 - 9x + 9 = 0.
- 9th June 2017A train slows steadily from 39 m/s to rest in 5 seconds. Work out its deceleration.
- 10th June 2017The 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.
- 11th June 2017A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 2/11. Work out r.
- 12th June 2017A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 3.5. How many values in total?
- 13th June 2017Expand and simplify (9 + sqrt(3))(9 - sqrt(3)).
- 14th June 2017f(x) = 6x - 7. Work out the inverse function f^-1(x).
- 15th June 2017y is inversely proportional to x^2. When x = 4, y = 27. Work out y when x = 3.
- 16th June 2017In 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.
- 17th June 2017The probability of winning a game is 5/8. A player expects 10 wins. How many games did they play?
- 18th June 2017On 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?
- 19th June 2017A block has mass 310 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 20th June 2017Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 21st June 2017y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 4.
- 22nd June 2017In a vector proof you find that vector PQ = 2a + 3b and vector RS = 8a + 12b. What does this show about PQ and RS?
- 23rd June 2017A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 24th June 2017A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.6. How many values in total?
- 25th June 2017x = 88 and y = 33, each correct to the nearest whole number. Work out the upper bound of x - y.
- 26th June 2017Use the iteration x(n+1) = cube root of (12x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.
- 27th June 2017y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 16.
- 28th June 2017A cuboid measures 4 cm by 3 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th June 2017A bag holds 4 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th June 2017On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?