Daily Practice · Higher Plus
July 2016 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2016, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2016 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2016
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2016Write x^2 - 2x + 1 in the form (x + a)^2 + b.
- 2nd July 2016y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 64.
- 3rd July 2016A cuboid measures 7 cm by 6 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 4th July 2016A bag holds 3 red and 11 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 5th July 2016On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 6th July 2016A rectangle is 20 cm by 7 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 7th July 2016Work out the coordinates of the turning point of y = x^2 + 2x - 3.
- 8th July 2016A train slows steadily from 34 m/s to rest in 10 seconds. Work out its deceleration.
- 9th July 2016A cuboid measures 4 cm by 7 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 10th July 2016A bag holds 4 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 11th July 2016A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 0.6. How many values in total?
- 12th July 2016Expand and simplify (3 + sqrt(2))(3 - sqrt(2)).
- 13th July 2016Simplify (x^2 + x - 2)/(x - 1).
- 14th July 2016y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 3.
- 15th July 2016The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 16th July 2016A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 17th July 2016On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 18th July 2016A block has mass 780 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 19th July 2016In an algebraic proof, how would you write a multiple of 9 in terms of an integer n?
- 20th July 2016y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 21st July 2016In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 22nd July 2016The probability of winning a game is 9/10. A player expects 45 wins. How many games did they play?
- 23rd July 2016A 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?
- 24th July 2016x = 41 and y = 5, each correct to the nearest whole number. Work out the upper bound of x - y.
- 25th July 2016Make x the subject of 7x + 2 = y(x + 2).
- 26th July 2016y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 9.
- 27th July 2016In a vector proof you find that vector PQ = a + b and vector RS = 3a + 3b. What does this show about PQ and RS?
- 28th July 2016A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 29th July 2016On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 30th July 2016A car covers 520 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 31st July 2016Write 3/(x - 6) + 6/(x - 5) as a single fraction.