Daily Practice · Higher Plus
September 2003 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2003, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2003 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2003
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2003A block has mass 390 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd September 2003Work out the coordinates of the turning point of y = x^2 - 6x - 11.
- 3rd September 2003y is directly proportional to x^3. When x = 3, y = 135. Work out y when x = 2.
- 4th September 2003In a vector proof you find that vector PQ = 6a + 5b and vector RS = 18a + 15b. What does this show about PQ and RS?
- 5th September 2003A bag holds 2 red and n blue counters. The probability of taking a red is 2/7. Work out n.
- 6th September 2003A histogram has two bars: one 10 units wide with frequency density 1.5, one 20 units wide with density 3. How many values in total?
- 7th September 2003x = 170 and y = 145, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th September 2003Simplify (x^2 + x - 30)/(x + 6).
- 9th September 2003y is directly proportional to sqrt(x). When x = 9, y = 27. Work out y when x = 81.
- 10th September 2003A cuboid measures 4 cm by 6 cm by 8 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 11th September 2003A bag holds 4 red and 8 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 12th September 2003On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 13th September 2003A car covers 230 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 14th September 2003In an algebraic proof, how would you write a number that leaves a remainder of 1 when divided by 9 in terms of an integer n?
- 15th September 2003A train slows steadily from 17 m/s to rest in 10 seconds. Work out its deceleration.
- 16th September 2003A cuboid measures 8 cm by 4 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 17th September 2003A bag holds 3 red, 6 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 18th September 2003A histogram has two bars: one 20 units wide with frequency density 1.2, one 25 units wide with density 1.4. How many values in total?
- 19th September 2003Rationalise the denominator of 42/sqrt(6), giving your answer in its simplest form.
- 20th September 2003Make x the subject of 7x + 7 = y(x + 7).
- 21st September 2003y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 22nd September 2003The 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.
- 23rd September 2003A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 7/12. Work out r.
- 24th September 2003On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th September 2003Simplify sqrt(80) + sqrt(20), giving your answer in the form a sqrt(b).
- 26th September 2003Write 3/(x - 6) + 7/(x + 1) as a single fraction.
- 27th September 2003y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 28th September 2003In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 29th September 2003The probability of winning a game is 1/2. A player expects 20 wins. How many games did they play?
- 30th September 2003A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?