Daily Practice · Higher Plus
August 2013 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2013, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2013 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2013
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2013A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 1/15. Work out r.
- 2nd August 2013On 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?
- 3rd August 2013A car covers 830 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.
- 4th August 2013Work out the nth term of the quadratic sequence 15, 28, 47, 72, ...
- 5th August 2013y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.
- 6th August 2013In 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.
- 7th August 2013The probability of winning a game is 3/5. A player expects 60 wins. How many games did they play?
- 8th August 2013A histogram has two bars: one 10 units wide with frequency density 0.4, one 25 units wide with density 0.8. How many values in total?
- 9th August 2013Rationalise the denominator of 10/sqrt(2), giving your answer in its simplest form.
- 10th August 2013The point (-6, -6) lies on y = f(x). Write down its image on y = f(x - 1).
- 11th August 2013y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 4.
- 12th August 2013In a vector proof you find that vector PQ = a + 5b and vector RS = 2a + 10b. What does this show about PQ and RS?
- 13th August 2013A bag holds 6 red and n blue counters. The probability of taking a red is 3/4. Work out n.
- 14th August 2013On 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?
- 15th August 2013Simplify sqrt(80) + sqrt(20), giving your answer in the form a sqrt(b).
- 16th August 2013Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 17th August 2013A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 18th August 2013A cuboid measures 6 cm by 12 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 19th August 2013A bag holds 6 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 20th August 2013A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 21st August 2013A rectangle is 9 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd August 2013f(x) = 4x - 3 and g(x) = 3x - 7. Work out fg(3).
- 23rd August 2013y is inversely proportional to x^2. When x = 4, y = 75. Work out y when x = 5.
- 24th August 2013A cuboid measures 5 cm by 5 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 25th August 2013A bag holds 6 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 26th August 2013On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 27th August 2013Expand and simplify (5 + sqrt(7))(5 - sqrt(7)).
- 28th August 2013The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 29th August 2013y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 30th August 2013The 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.
- 31st August 2013A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.