Daily Practice · Higher Plus
June 2018 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2018, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2018 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2018On 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?
- 2nd June 2018A car covers 830 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.
- 3rd June 2018A quadratic sequence starts -1, 4, 11, 20. Work out the second difference, and the coefficient of n^2.
- 4th June 2018A train slows steadily from 21 m/s to rest in 5 seconds. Work out its deceleration.
- 5th June 2018The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 6th June 2018A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 1/7. Work out r.
- 7th June 2018A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3.5. How many values in total?
- 8th June 2018Rationalise the denominator of 24/sqrt(2), giving your answer in its simplest form.
- 9th June 2018Solve x^2 + 3x + 2 > 0.
- 10th June 2018y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 6.
- 11th June 2018In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 12th June 2018The probability of winning a game is 7/10. A player expects 21 wins. How many games did they play?
- 13th June 2018On 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?
- 14th June 2018Simplify sqrt(18) + sqrt(8), giving your answer in the form a sqrt(b).
- 15th June 2018Write x^2 + 12x + 4 in the form (x + a)^2 + b.
- 16th June 2018y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 17th June 2018In a vector proof you find that vector PQ = 3a + 3b and vector RS = 6a + 6b. What does this show about PQ and RS?
- 18th June 2018A bag holds 2 red and n blue counters. The probability of taking a red is 2/9. Work out n.
- 19th June 2018A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 20th June 2018A rectangle is 13 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 21st June 2018Work out the coordinates of the turning point of y = x^2 - 8x - 15.
- 22nd June 2018y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 4.
- 23rd June 2018A cuboid measures 10 cm by 8 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th June 2018A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th June 2018On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 26th June 2018Expand and simplify (2 + sqrt(6))(2 - sqrt(6)).
- 27th June 2018Simplify (x^2 + 9x + 20)/(x + 4).
- 28th June 2018A train slows steadily from 22 m/s to rest in 5 seconds. Work out its deceleration.
- 29th June 2018A cuboid measures 8 cm by 4 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th June 2018A bag holds 7 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?