Daily Practice · Higher Plus
July 2013 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2013, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2013 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2013The 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.
- 2nd July 2013A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 3rd July 2013A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3.5. How many values in total?
- 4th July 2013Simplify sqrt(32) + sqrt(72), giving your answer in the form a sqrt(b).
- 5th July 2013Write 2/(x - 6) + 7/(x + 2) as a single fraction.
- 6th July 2013y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
- 7th July 2013In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 8th July 2013The probability of winning a game is 1/5. A player expects 6 wins. How many games did they play?
- 9th July 2013On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 10th July 2013A rectangle is 16 cm by 22 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 11th July 2013Solve 8x^2 - 10x + 3 = 0.
- 12th July 2013y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 3.
- 13th July 2013In a vector proof you find that vector PQ = a + 6b and vector RS = 4a + 24b. What does this show about PQ and RS?
- 14th July 2013A bag holds 3 red and n blue counters. The probability of taking a red is 3/11. Work out n.
- 15th July 2013A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 16th July 2013Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
- 17th July 2013f(x) = 5x - 1. Work out the inverse function f^-1(x).
- 18th July 2013y is directly proportional to sqrt(x). When x = 49, y = 49. Work out y when x = 81.
- 19th July 2013A cuboid measures 14 cm by 14 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 20th July 2013A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 21st July 2013On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 22nd July 2013A block has mass 880 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 23rd July 2013Solve x^2 + y^2 = 100 and y = x - 2 simultaneously.
- 24th July 2013A train slows steadily from 19 m/s to rest in 4 seconds. Work out its deceleration.
- 25th July 2013A cuboid measures 5 cm by 6 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 26th July 2013A bag holds 3 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 27th July 2013A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 28th July 2013x = 98 and y = 16, each correct to the nearest whole number. Work out the upper bound of x - y.
- 29th July 2013Use the iteration x(n+1) = cube root of (4x(n) + 6) with x(0) = 3. Work out x(1) to 3 decimal places.
- 30th July 2013y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 31st July 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.