Daily Practice · Higher Plus
August 2004 - Higher Plus 5-a-day
Every Higher Plus sheet published in August 2004, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' August 2004 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 2004
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 2004On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 2nd August 2004A block has mass 890 g (to the nearest 10 g) and volume 22 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 3rd August 2004Solve 12x^2 - 31x + 20 = 0.
- 4th August 2004y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 4.
- 5th August 2004A cuboid measures 14 cm by 12 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th August 2004A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 7th August 2004A 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?
- 8th August 2004x = 136 and y = 68, each correct to the nearest whole number. Work out the upper bound of x - y.
- 9th August 2004f(x) = 5x + 6. Work out the inverse function f^-1(x).
- 10th August 2004y is directly proportional to sqrt(x). When x = 16, y = 24. Work out y when x = 81.
- 11th August 2004A cuboid measures 6 cm by 12 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th August 2004A bag holds 5 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th August 2004On 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?
- 14th August 2004A car covers 320 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 15th August 2004Solve x^2 + y^2 = 169 and y = x - 7 simultaneously.
- 16th August 2004A train slows steadily from 21 m/s to rest in 8 seconds. Work out its deceleration.
- 17th August 2004The 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 August 2004A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 5/14. Work out r.
- 19th August 2004A histogram has two bars: one 10 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 20th August 2004Rationalise the denominator of 6/sqrt(3), giving your answer in its simplest form.
- 21st August 2004Use the iteration x(n+1) = cube root of (10x(n) + 7) with x(0) = 3. Work out x(1) to 3 decimal places.
- 22nd August 2004y is inversely proportional to x^2. When x = 2, y = 64. Work out y when x = 4.
- 23rd August 2004In 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.
- 24th August 2004The probability of winning a game is 2/5. A player expects 60 wins. How many games did they play?
- 25th August 2004On 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?
- 26th August 2004Simplify sqrt(48) + sqrt(12), giving your answer in the form a sqrt(b).
- 27th August 2004Work out the nth term of the quadratic sequence 11, 28, 53, 86, ...
- 28th August 2004y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 2.
- 29th August 2004In a vector proof you find that vector PQ = 6a - 2b and vector RS = 24a - 8b. What does this show about PQ and RS?
- 30th August 2004A bag holds 5 red and n blue counters. The probability of taking a red is 5/13. Work out n.
- 31st August 2004A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 0.8. How many values in total?