Daily Practice · Higher Plus
June 2012 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2012, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2012 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2012
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2012A bag holds 5 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 2nd June 2012A histogram has two bars: one 20 units wide with frequency density 1.5, one 25 units wide with density 1.4. How many values in total?
- 3rd June 2012x = 44 and y = 6, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th June 2012f(x) = 4x + 7. Work out the inverse function f^-1(x).
- 5th June 2012y is directly proportional to sqrt(x). When x = 9, y = 21. Work out y when x = 49.
- 6th June 2012The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 7th June 2012A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 8th June 2012On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 9th June 2012A car covers 590 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.
- 10th June 2012Solve x^2 + y^2 = 625 and y = x - 17 simultaneously.
- 11th June 2012A train slows steadily from 19 m/s to rest in 4 seconds. Work out its deceleration.
- 12th June 2012In 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.
- 13th June 2012The probability of winning a game is 3/5. A player expects 15 wins. How many games did they play?
- 14th June 2012A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3.5. How many values in total?
- 15th June 2012Rationalise the denominator of 110/sqrt(11), giving your answer in its simplest form.
- 16th June 2012Use the iteration x(n+1) = cube root of (12x(n) + 1) with x(0) = 5. Work out x(1) to 3 decimal places.
- 17th June 2012y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 18th June 2012In a vector proof you find that vector PQ = 4a + b and vector RS = 12a + 3b. What does this show about PQ and RS?
- 19th June 2012A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 20th June 2012On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 21st June 2012Simplify sqrt(72) + sqrt(98), giving your answer in the form a sqrt(b).
- 22nd June 2012Work out the nth term of the quadratic sequence 7, 12, 21, 34, ...
- 23rd June 2012y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 5.
- 24th June 2012A cuboid measures 7 cm by 14 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 25th June 2012A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 26th June 2012A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 27th June 2012A rectangle is 29 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th June 2012The point (-6, 1) lies on y = f(x). Write down its image on y = -f(x).
- 29th June 2012y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 25.
- 30th June 2012A cuboid measures 12 cm by 7 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.