Daily Practice · Higher Plus
July 2008 - Higher Plus 5-a-day
Every Higher Plus sheet published in July 2008, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' July 2008 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 2008
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 2008Solve 16x^2 - 8x - 15 = 0.
- 2nd July 2008A train slows steadily from 19 m/s to rest in 10 seconds. Work out its deceleration.
- 3rd July 2008In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 4th July 2008The probability of winning a game is 1/10. A player expects 9 wins. How many games did they play?
- 5th July 2008A histogram has two bars: one 10 units wide with frequency density 2, one 10 units wide with density 1.4. How many values in total?
- 6th July 2008x = 171 and y = 54, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th July 2008f(x) = 4x - 11. Work out the inverse function f^-1(x).
- 8th July 2008y is inversely proportional to x^2. When x = 2, y = 27. Work out y when x = 3.
- 9th July 2008In a vector proof you find that vector PQ = 5a + 2b and vector RS = 20a + 8b. What does this show about PQ and RS?
- 10th July 2008A bag holds 8 red and n blue counters. The probability of taking a red is 8/11. Work out n.
- 11th July 2008On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 12th July 2008A car covers 840 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.
- 13th July 2008Solve x^2 + y^2 = 841 and y = x - 1 simultaneously.
- 14th July 2008y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 5.
- 15th July 2008A cuboid measures 9 cm by 6 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th July 2008A bag holds 10 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th July 2008A histogram has two bars: one 10 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 18th July 2008Rationalise the denominator of 60/sqrt(6), giving your answer in its simplest form.
- 19th July 2008Use the iteration x(n+1) = cube root of (8x(n) + 8) with x(0) = 3. Work out x(1) to 3 decimal places.
- 20th July 2008y is directly proportional to sqrt(x). When x = 4, y = 14. Work out y when x = 25.
- 21st July 2008A cuboid measures 13 cm by 13 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd July 2008A bag holds 5 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd July 2008On 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?
- 24th July 2008Simplify sqrt(45) + sqrt(245), giving your answer in the form a sqrt(b).
- 25th July 2008Work out the nth term of the quadratic sequence 0, -1, 0, 3, ...
- 26th July 2008A train slows steadily from 26 m/s to rest in 5 seconds. Work out its deceleration.
- 27th July 2008The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 28th July 2008A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 1/28. Work out r.
- 29th July 2008A histogram has two bars: one 20 units wide with frequency density 1.2, one 5 units wide with density 3. How many values in total?
- 30th July 2008A rectangle is 28 cm by 14 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 31st July 2008The point (-5, -5) lies on y = f(x). Write down its image on y = f(x) + 2.