Daily Practice · Higher Plus
August 2015 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2015, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2015 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2015
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2015y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 81.
- 2nd August 2015In a vector proof you find that vector PQ = 2a + 5b and vector RS = 6a + 15b. What does this show about PQ and RS?
- 3rd August 2015A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 4th August 2015On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 5th August 2015A rectangle is 14 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 6th August 2015f(x) = 6x + 2 and g(x) = 6x + 3. Work out fg(1).
- 7th August 2015A train slows steadily from 38 m/s to rest in 4 seconds. Work out its deceleration.
- 8th August 2015A cuboid measures 8 cm by 3 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 9th August 2015A bag holds 3 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 10th August 2015A histogram has two bars: one 5 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 11th August 2015Expand and simplify (9 + sqrt(10))(9 - sqrt(10)).
- 12th August 2015The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 13th August 2015y is inversely proportional to x^2. When x = 4, y = 72. Work out y when x = 6.
- 14th August 2015A cuboid measures 5 cm by 9 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 15th August 2015A bag holds 6 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 16th August 2015On 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?
- 17th August 2015A block has mass 460 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 18th August 2015A quadratic sequence starts 2, 12, 30, 56. Work out the second difference, and the coefficient of n^2.
- 19th August 2015y is directly proportional to x^3. When x = 2, y = 32. Work out y when x = 4.
- 20th August 2015The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 21st August 2015A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 22nd August 2015A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 23rd August 2015x = 36 and y = 17, each correct to the nearest whole number. Work out the upper bound of x - y.
- 24th August 2015Solve x^2 - 7x + 6 > 0.
- 25th August 2015y is directly proportional to sqrt(x). When x = 4, y = 12. Work out y when x = 36.
- 26th August 2015In 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.
- 27th August 2015The probability of winning a game is 1/10. A player expects 9 wins. How many games did they play?
- 28th August 2015On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 29th August 2015A car covers 450 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.
- 30th August 2015Write x^2 + 12x - 4 in the form (x + a)^2 + b.
- 31st August 2015A train slows steadily from 33 m/s to rest in 5 seconds. Work out its deceleration.