Daily Practice · Higher Plus
July 2018 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2018, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2018 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2018
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2018A histogram has two bars: one 10 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 2nd July 2018A block has mass 600 g (to the nearest 10 g) and volume 3 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 3rd July 2018In an algebraic proof, how would you write a multiple of 8 in terms of an integer n?
- 4th July 2018y is inversely proportional to x^2. When x = 3, y = 75. Work out y when x = 5.
- 5th July 2018The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 6th July 2018A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 7th July 2018On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 8th July 2018x = 187 and y = 45, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th July 2018Make x the subject of 4x + 6 = y(x + 6).
- 10th July 2018y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 11th July 2018In 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.
- 12th July 2018The probability of winning a game is 1/5. A player expects 13 wins. How many games did they play?
- 13th July 2018A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 1.4. How many values in total?
- 14th July 2018A car covers 680 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 15th July 2018Write 2/(x - 3) + 7/(x + 6) as a single fraction.
- 16th July 2018y is directly proportional to sqrt(x). When x = 49, y = 42. Work out y when x = 36.
- 17th July 2018In a vector proof you find that vector PQ = a - 4b and vector RS = 5a - 20b. What does this show about PQ and RS?
- 18th July 2018A bag holds 4 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 19th July 2018On 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?
- 20th July 2018Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 21st July 2018Solve 2x^2 + 9x + 10 = 0.
- 22nd July 2018A train slows steadily from 30 m/s to rest in 10 seconds. Work out its deceleration.
- 23rd July 2018A cuboid measures 14 cm by 7 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 24th July 2018A bag holds 5 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 25th July 2018A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 3. How many values in total?
- 26th July 2018Simplify sqrt(27) + sqrt(108), giving your answer in the form a sqrt(b).
- 27th July 2018f(x) = 7x - 8. Work out the inverse function f^-1(x).
- 28th July 2018y is inversely proportional to x^2. When x = 4, y = 144. Work out y when x = 6.
- 29th July 2018A cuboid measures 5 cm by 7 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 30th July 2018A bag holds 6 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 31st July 2018On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?