Daily Practice · Higher Plus
July 2010 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2010, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2010 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2010
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2010On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 2nd July 2010Rationalise the denominator of 24/sqrt(2), giving your answer in its simplest form.
- 3rd July 2010Use the iteration x(n+1) = cube root of (4x(n) + 4) with x(0) = 5. Work out x(1) to 3 decimal places.
- 4th July 2010y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 5th July 2010A cuboid measures 6 cm by 6 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th July 2010A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th July 2010A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 8th July 2010Simplify sqrt(20) + sqrt(5), giving your answer in the form a sqrt(b).
- 9th July 2010Work out the nth term of the quadratic sequence 3, 11, 25, 45, ...
- 10th July 2010y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 64.
- 11th July 2010A cuboid measures 6 cm by 13 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th July 2010A bag holds 5 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th July 2010On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 14th July 2010A rectangle is 8 cm by 20 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 15th July 2010The point (-6, -5) lies on y = f(x). Write down its image on y = -f(x).
- 16th July 2010A train slows steadily from 18 m/s to rest in 8 seconds. Work out its deceleration.
- 17th July 2010The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 18th July 2010A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 19th July 2010A histogram has two bars: one 10 units wide with frequency density 2.5, one 10 units wide with density 1.4. How many values in total?
- 20th July 2010Expand and simplify (9 + sqrt(5))(9 - sqrt(5)).
- 21st July 2010Prove that the sum of 3 consecutive integers is always a multiple of 3. State the simplified sum you would use.
- 22nd July 2010y is inversely proportional to x^2. When x = 3, y = 50. Work out y when x = 5.
- 23rd July 2010In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 24th July 2010The probability of winning a game is 1/2. A player expects 65 wins. How many games did they play?
- 25th July 2010On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 26th July 2010A block has mass 880 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 27th July 2010f(x) = 6x - 4 and g(x) = 3x - 7. Work out fg(-2).
- 28th July 2010y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 29th July 2010In a vector proof you find that vector PQ = 3a - 3b and vector RS = 15a - 15b. What does this show about PQ and RS?
- 30th July 2010A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 31st July 2010A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?