Daily Practice · Higher Plus
August 2014 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2014, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2014 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2014
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2014In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 2nd August 2014The probability of winning a game is 1/4. A player expects 15 wins. How many games did they play?
- 3rd August 2014A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 4th August 2014A block has mass 890 g (to the nearest 10 g) and volume 5 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5th August 2014In an algebraic proof, how would you write the next odd number after 2n + 1 in terms of an integer n?
- 6th August 2014y is directly proportional to sqrt(x). When x = 25, y = 30. Work out y when x = 64.
- 7th August 2014In a vector proof you find that vector PQ = 3a - b and vector RS = 9a - 3b. What does this show about PQ and RS?
- 8th August 2014A bag holds 8 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 9th August 2014On 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?
- 10th August 2014x = 132 and y = 47, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th August 2014Make x the subject of 7x + 6 = y(x + 6).
- 12th August 2014A train slows steadily from 29 m/s to rest in 8 seconds. Work out its deceleration.
- 13th August 2014A cuboid measures 14 cm by 5 cm by 14 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 14th August 2014A 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?
- 15th August 2014A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 0.8. How many values in total?
- 16th August 2014A car covers 720 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 17th August 2014Write 6/(x + 5) + 6/(x + 6) as a single fraction.
- 18th August 2014y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 19th August 2014A cuboid measures 9 cm by 14 cm by 4 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 20th August 2014A bag holds 6 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 21st August 2014On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd August 2014Rationalise the denominator of 20/sqrt(5), giving your answer in its simplest form.
- 23rd August 2014Solve 9x^2 + 18x + 5 = 0.
- 24th August 2014y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 25th August 2014The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 26th August 2014A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 27th August 2014A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.8. How many values in total?
- 28th August 2014Simplify sqrt(20) + sqrt(20), giving your answer in the form a sqrt(b).
- 29th August 2014f(x) = 5x - 9. Work out the inverse function f^-1(x).
- 30th August 2014y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 49.
- 31st August 2014In 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.