Daily Practice · Higher Plus
June 2013 - Higher Plus 5-a-day
Every Higher Plus sheet published in June 2013, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' June 2013 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in June 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st June 2013The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 2nd June 2013A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 3rd June 2013On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 4th June 2013Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).
- 5th June 2013Write x^2 + 12x + 7 in the form (x + a)^2 + b.
- 6th June 2013A train slows steadily from 25 m/s to rest in 5 seconds. Work out its deceleration.
- 7th June 2013In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 8th June 2013The probability of winning a game is 1/5. A player expects 24 wins. How many games did they play?
- 9th June 2013A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 10th June 2013A block has mass 640 g (to the nearest 10 g) and volume 15 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th June 2013Work out the coordinates of the turning point of y = x^2 - 16x + 4.
- 12th June 2013y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
- 13th June 2013In a vector proof you find that vector PQ = 5a - 3b and vector RS = 20a - 12b. What does this show about PQ and RS?
- 14th June 2013A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 15th June 2013On 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?
- 16th June 2013x = 190 and y = 153, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th June 2013Simplify (x^2 - 3x - 18)/(x + 3).
- 18th June 2013y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 19th June 2013A cuboid measures 3 cm by 9 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th June 2013A bag holds 8 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st June 2013A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 3. How many values in total?
- 22nd June 2013A car covers 870 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 23rd June 2013In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 24th June 2013y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 4.
- 25th June 2013A cuboid measures 6 cm by 13 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th June 2013A bag holds 7 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th June 2013On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 28th June 2013Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 29th June 2013Make x the subject of 6x + 5 = y(x + 5).
- 30th June 2013A train slows steadily from 16 m/s to rest in 5 seconds. Work out its deceleration.