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Ass 1%2C 2016
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SCOTCH OAKBURN COLLEGE MTM315114 MATHEMATICS METHODS ASSIGNMENT 1, 2016 SET: MONDAY, FEBRUARY 1 st DUE: MONDAY, FEBRUARY 15 th Criteria assessed: 1 & 3 1. Use the Binomial Theorem to complete the following questions, showing all working: (a) Expand ( 3 x +4 y ) 6 (b) Write down the first 5 terms in the expansion of ( x 3 − 7 x 2 ) 12 (c) Find the coefficient of x 3 in the expansion of ( x + 1 x ) 7 2. Find the equation of the straight line which passes through the two points of intersection of the curves y=−x 2 −2 x +3 and y=x 2 −4. Write the equation in the form ax +by +c=0. 3. Sketch the following functions, showing all intercepts and turning points: (a) y=3 x−2 ,x∈ [ 3,5] (b) y=( x−3) 2 (c) y=−x 2 −x +6 f ( x )=x 3 −4 x 2 −7 x +15 4. Showing algebraic working, factorise the following expressions: (a) x 2 +5 x+6 (b) 2 x 2 + 11 x +12 (c) x 3 −4 x (d) 2 x 3 −5 x 2 −28 x+1 5 5. Showing algebraic working, solve the following equations:
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Assignment 1
Transcript of Ass 1%2C 2016
SCOTCH OAKBURN COLLEGEMTM315114 MATHEMATICS METHODS ASSIGNMENT 1, 2016
SET: MONDAY, FEBRUARY 1st
DUE: MONDAY, FEBRUARY 15th
Criteria assessed: 1 & 3
1. Use the Binomial Theorem to complete the following questions, showing all working:(a) Expand (3 x+4 y )6
(b) Write down the first 5 terms in the expansion of (x3− 7x2 )
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(c) Find the coefficient of x3 in the expansion of (x+ 1x )7
2. Find the equation of the straight line which passes through the two points of intersection of the curves y=−x2−2x+3 and y=x2−4. Write the equation in the form ax+by+c=0.
3. Sketch the following functions, showing all intercepts and turning points:
(a) y=3 x−2 , x∈[3,5]
(b) y= (x−3 )2(c) y=−x2−x+6
f ( x )=x3−4 x2−7 x+154. Showing algebraic working, factorise the following expressions:
(a) x2+5 x+6
(b) 2 x2+11 x+12
(c) x3−4 x
(d) 2 x3−5x2−28 x+15
5. Showing algebraic working, solve the following equations:
(a) x2+ x−6=−x2−4 x+5 (b) 6 x3+17 x2+x−10=0
