Core1 Worked solutions January 2006 paper

Link below to the worked solutions for January 2006 C1 paper.



https://docs.google.com/viewer?a=v&pid=explorer&chrome=true&srcid=0B2J1T-insOmpNDEzN2JiMTUtZGE3Ny00YTgxLWI5NzMtN2ZmMjllZjg5ZDU2&hl=en

Notes below to support the worked solutions.



1. Common factor of x factorised out first. Then factorise remaining quadratic into two brackets.



2. Substitute each term into the expression to get the next. In part (a) it is shown that all odd terms will be 1 and even terms will be 4, so 20th term will be 4.



3. (a) substituting x=3 into the equation shows that P lies on the line.

(b) gradient of -2 is just identified from the equation (the m in the form y=mx+c) - so perpendicular gradient is 1/2 - then use either straight line equation method to find the equation - finally leave in the correct form with all coefficients as integers



4. first change the second term to power of -3 then
(a) differentiate - multiply by the power (bring the power down) and reduce the power
(b) integrate - increase the power and divide by that and don't forget the +C

5. (a) split the 45 into a factor pair where one of the factors is a square number (so 9 and 5) then simplify
(b) to rationalise the denominator multiply top and bottom by the expression in the denominator but with the opposite sign - then simplify

6. (a) f(x+1) is translate one left - inside the bracket so horizontal and the opposite way to that the sign suggests
(b) 2f(x) is stretch vertically scale factor 2 - outside so vertical change
(c) f(1/2 x) is stretch horzontally scale factor 2 - inside so horiztonal and the opposite way to the coefficient suggests

7. (a) difference given so 12th birthday is just £200 more than 11th then add them up
(b) 18th birthday is 8th term so add 7 lots of the difference to the first term
(c) first term and last (8th) term are known so substitute into formula
(d) Sn,a,d are known so n is only unknown - substitute into formula and simplify

8. First separate terms of fraction, then simplify so that the expression can be integrated.
Integrate - increase power and divide by it and don't forget the +C
Use given point to substitute values for x and y to find C
Restate equation with value for C

9. second bracket is difference of two squares so factorise completely
(a) identify roots from completely factorised equation - root at x=1 is already shown on graph so P and Q are the others
(b) expand brackets and differentiate
(c) substitute x=-1 into equation for dy/dx to find gradient of tangent at that point then use either straight line equation method to find the equation
(d) make dy/dx = 1 then solve, one solution has already been used (when x=-1 so R is the other solution, find y coordinate by substituting x value in to original equation for y

10. (a) completing the square
(b) completing the square form shows translation left 1 and up 2 from basic x squared graph - substitute x=0 for point crossing y axis
(c) identify a,b,c from original equation then subsitute to find discriminant - less then zero so no real roots
(d) identify a,b,c and substitute into inequality and solve inequality