O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2015 · Q510 Marks
Factorise completely 6x²y³ – 15x³y .
- (a)Factorise completely 6x²y³ – 15x³y .[2]
- (b)Solve (4/x) + (2/(x+2)) = 3.[3]
- (c)(i)Shade and label the region R defined by these four inequalities. x ≥ 1 y ≤ 4 x+y ≤ 6 y ≥ x[3]
- (c)(ii)The point M is the intersection of x = 1 and y=4. The point N is the intersection of x+y=6 and y=x. Find the gradient of MN.[2]
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Mark scheme
Marking points from the official mark scheme (Oct/Nov 2015). The mark or mark type is shown in brackets.
- [2] 3x²y(2y² - 5x)
- B1 for 3x²(2y³ - 5xy)
- or 3y(2x²y²-5x³)
- or x²y(6y² -15x)
- or 3xy(2xy²-5x²)
- or 3x²y(A-5x)
- or 3x²y(2y² – B)
- [3] x = ±1.63[...] or ±√8/3
- M1 for 4(x + 2) + 2x / x(x+2) = 3 soi
- M1dep for 4x + 8 + 2x = 3x² + 6x or better
- [3] Correct region shaded with 4 correct lines
- B2 for 3 or 4 correct lines
- or B1 for 2 correct lines
- [2] 1/2 oe
- B1 for (3, 3) or (1, 4) soi
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