Daily Practice · Higher Plus
June 2019 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2019, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2019 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2019
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2019A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 2nd June 2019A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 1.4. How many values in total?
- 3rd June 2019A block has mass 560 g (to the nearest 10 g) and volume 4 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 4th June 2019Solve x^2 + y^2 = 289 and y = x - 7 simultaneously.
- 5th June 2019y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 6th June 2019In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 7th June 2019The probability of winning a game is 1/5. A player expects 10 wins. How many games did they play?
- 8th June 2019On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th June 2019x = 62 and y = 49, each correct to the nearest whole number. Work out the upper bound of x - y.
- 10th June 2019Use the iteration x(n+1) = cube root of (5x(n) + 9) with x(0) = 1. Work out x(1) to 3 decimal places.
- 11th June 2019y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 12th June 2019In a vector proof you find that vector PQ = a + 3b and vector RS = 4a + 12b. What does this show about PQ and RS?
- 13th June 2019A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 14th June 2019A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 15th June 2019A car covers 660 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 16th June 2019Work out the nth term of the quadratic sequence 3, 19, 43, 75, ...
- 17th June 2019y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 81.
- 18th June 2019A cuboid measures 4 cm by 9 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th June 2019A bag holds 5 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th June 2019On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 21st June 2019Rationalise the denominator of 99/sqrt(11), giving your answer in its simplest form.
- 22nd June 2019The point (1, 6) lies on y = f(x). Write down its image on y = -f(x).
- 23rd June 2019A train slows steadily from 35 m/s to rest in 4 seconds. Work out its deceleration.
- 24th June 2019A cuboid measures 11 cm by 8 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th June 2019A bag holds 5 red, 3 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th June 2019A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 27th June 2019Simplify sqrt(27) + sqrt(147), giving your answer in the form a sqrt(b).
- 28th June 2019Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 29th June 2019y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 30th June 2019The 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.