Daily Practice · Higher Plus
August 2010 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2010, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2010 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2010
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2010x = 118 and y = 99, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd August 2010The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 0.
- 3rd August 2010y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 4.
- 4th August 2010A cuboid measures 4 cm by 9 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th August 2010A bag holds 8 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th August 2010On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th August 2010A car covers 470 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th August 2010A quadratic sequence starts 9, 18, 31, 48. Work out the second difference, and the coefficient of n^2.
- 9th August 2010A train slows steadily from 28 m/s to rest in 4 seconds. Work out its deceleration.
- 10th August 2010A cuboid measures 10 cm by 10 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th August 2010A bag holds 7 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th August 2010A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 13th August 2010Rationalise the denominator of 9/sqrt(3), giving your answer in its simplest form.
- 14th August 2010Solve x^2 + 11x + 28 > 0.
- 15th August 2010y is inversely proportional to x^2. When x = 2, y = 50. Work out y when x = 5.
- 16th August 2010The 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.
- 17th August 2010A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 18th August 2010On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 19th August 2010Simplify sqrt(8) + sqrt(8), giving your answer in the form a sqrt(b).
- 20th August 2010Write x^2 + 4x + 3 in the form (x + a)^2 + b.
- 21st August 2010y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 5.
- 22nd August 2010In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 23rd August 2010The probability of winning a game is 1/5. A player expects 13 wins. How many games did they play?
- 24th August 2010A histogram has two bars: one 20 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 25th August 2010A rectangle is 14 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th August 2010Work out the coordinates of the turning point of y = x^2 - 8x + 5.
- 27th August 2010y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 81.
- 28th August 2010In a vector proof you find that vector PQ = 6a + 6b and vector RS = 24a + 24b. What does this show about PQ and RS?
- 29th August 2010A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 30th August 2010On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 31st August 2010Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).