Daily Practice · Higher Plus
June 2016 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2016, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2016 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2016Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 2nd June 2016y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 3rd June 2016A cuboid measures 13 cm by 3 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th June 2016A bag holds 10 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th June 2016A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 1.4. How many values in total?
- 6th June 2016A block has mass 420 g (to the nearest 10 g) and volume 11 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 7th June 2016f(x) = 3x + 9 and g(x) = 2x + 2. Work out fg(4).
- 8th June 2016y is directly proportional to sqrt(x). When x = 16, y = 36. Work out y when x = 36.
- 9th June 2016A cuboid measures 11 cm by 4 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th June 2016A bag holds 7 red, 4 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th June 2016On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th June 2016x = 132 and y = 75, each correct to the nearest whole number. Work out the upper bound of x - y.
- 13th June 2016The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 14th June 2016A train slows steadily from 14 m/s to rest in 10 seconds. Work out its deceleration.
- 15th June 2016The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 16th June 2016A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 17th June 2016A 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?
- 18th June 2016A car covers 480 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 19th June 2016A quadratic sequence starts -2, 3, 14, 31. Work out the second difference, and the coefficient of n^2.
- 20th June 2016y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 21st June 2016In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 22nd June 2016The probability of winning a game is 2/5. A player expects 18 wins. How many games did they play?
- 23rd June 2016On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 24th June 2016Rationalise the denominator of 36/sqrt(3), giving your answer in its simplest form.
- 25th June 2016Solve x^2 - x < 0.
- 26th June 2016y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 27th June 2016In a vector proof you find that vector PQ = 3a + 3b and vector RS = 9a + 9b. What does this show about PQ and RS?
- 28th June 2016A bag holds 4 red and n blue counters. The probability of taking a red is 4/7. Work out n.
- 29th June 2016A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 30th June 2016Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).