Daily Practice · Higher Plus
September 2002 - Higher Plus 5-a-day
Every Higher Plus sheet published in September 2002, with answers. Grades 8-9 - exam-stretch algebra, geometry and reasoning.
Printing for a group?
The batch download puts all 5 tiers' September 2002 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 2002
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 2002Solve x^2 + y^2 = 25 and y = x + 1 simultaneously.
- 2nd September 2002y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 3rd September 2002In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 4th September 2002The probability of winning a game is 7/10. A player expects 28 wins. How many games did they play?
- 5th September 2002On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th September 2002Rationalise the denominator of 33/sqrt(11), giving your answer in its simplest form.
- 7th September 2002Use the iteration x(n+1) = cube root of (4x(n) + 1) with x(0) = 4. Work out x(1) to 3 decimal places.
- 8th September 2002y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 4.
- 9th September 2002In a vector proof you find that vector PQ = 6a + b and vector RS = 24a + 4b. What does this show about PQ and RS?
- 10th September 2002A bag holds 5 red and n blue counters. The probability of taking a red is 5/11. Work out n.
- 11th September 2002A histogram has two bars: one 10 units wide with frequency density 2.5, one 20 units wide with density 0.8. How many values in total?
- 12th September 2002Simplify sqrt(80) + sqrt(20), giving your answer in the form a sqrt(b).
- 13th September 2002Work out the nth term of the quadratic sequence 6, 11, 18, 27, ...
- 14th September 2002y is directly proportional to sqrt(x). When x = 49, y = 14. Work out y when x = 9.
- 15th September 2002A cuboid measures 11 cm by 11 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th September 2002A bag holds 8 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th September 2002On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 18th September 2002A rectangle is 8 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 19th September 2002The point (5, -2) lies on y = f(x). Write down its image on y = f(x) - 2.
- 20th September 2002A train slows steadily from 33 m/s to rest in 8 seconds. Work out its deceleration.
- 21st September 2002A cuboid measures 6 cm by 10 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd September 2002A bag holds 7 red, 7 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd September 2002A histogram has two bars: one 5 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 24th September 2002Expand and simplify (5 + sqrt(2))(5 - sqrt(2)).
- 25th September 2002Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 26th September 2002y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 27th September 2002The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 28th September 2002A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 2/15. Work out r.
- 29th September 2002On 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?
- 30th September 2002A block has mass 290 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.