Daily Practice · Higher Plus
September 2004 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2004, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2004 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2004
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2004A rectangle is 6 cm by 4 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 2nd September 2004The point (-4, -3) lies on y = f(x). Write down its image on y = f(-x).
- 3rd September 2004y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 9.
- 4th September 2004A cuboid measures 8 cm by 4 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th September 2004A bag holds 5 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th September 2004On 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 September 2004Expand and simplify (9 + sqrt(2))(9 - sqrt(2)).
- 8th September 2004Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 9th September 2004A train slows steadily from 24 m/s to rest in 8 seconds. Work out its deceleration.
- 10th September 2004A cuboid measures 13 cm by 12 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th September 2004A bag holds 4 red, 7 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th September 2004A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 13th September 2004A block has mass 620 g (to the nearest 10 g) and volume 17 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 14th September 2004f(x) = 6x + 3 and g(x) = 3x - 1. Work out fg(3).
- 15th September 2004y is inversely proportional to x^2. When x = 5, y = 108. Work out y when x = 6.
- 16th September 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.
- 17th September 2004A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 3/11. Work out r.
- 18th September 2004On 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?
- 19th September 2004x = 80 and y = 68, each correct to the nearest whole number. Work out the upper bound of x - y.
- 20th September 2004The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 21st September 2004y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 22nd September 2004In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 23rd September 2004The probability of winning a game is 3/4. A player expects 12 wins. How many games did they play?
- 24th September 2004A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 25th September 2004A car covers 540 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.
- 26th September 2004A quadratic sequence starts 9, 14, 21, 30. Work out the second difference, and the coefficient of n^2.
- 27th September 2004y is directly proportional to sqrt(x). When x = 36, y = 18. Work out y when x = 64.
- 28th September 2004In a vector proof you find that vector PQ = 3a - 5b and vector RS = 15a - 25b. What does this show about PQ and RS?
- 29th September 2004A bag holds 4 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 30th September 2004On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?