3.1.11 determine and examine the roots of unity and their location on the unit circle Week 4 nth 3.1.12 determine and examine the nth roots of complex numbers and their location in the complex plane Week 5 3.1.13 prove and apply the factor theorem and the remainder theorem for polynomials 3.1.14 consider conjugate roots for polynomials with real coefficients 3.1.15 solve simple polynomial equations Week 6-8 3.2.1 determine when the composition of two functions is defined Response 1 (5%) 3.2.2 determine the composition of two functions 3.1.1 3.1.15 3.2.3 determine if a function is one-to-one – 3.2.4 find the inverse function of a one-to-one function 3.2.5 examine the reflection property of the graphs of a function and its inverse Week 9 -10 3.2.6 use and apply for the absolute value of the real number and the graph of Response 2 x (7%) 3.2.7 examine the relationship between the graph of 3.2.1 3.2.8 and the graphs of and – 3.2.8 sketch the graphs of simple rational functions where the numerator and denominator are polynomials of low degree Week 11 3.3.1 review the concepts of vectors from Unit 1 and extend to three dimensions, including introducing the unit vectors and i, j k 3.3.2 prove geometric results in the plane and construct simple proofs in three dimensions Week 11 3.3.3 introduce Cartesian coordinates for three-dimensional space, including plotting points and equations of spheres 3.3.4 use vector equations of curves in two or three dimensions involving a parameter and determine a Cartesian equation in the two-dimensional case ‘corresponding’ Term Two Content Resources Assessment Week 1 3.3.5 determine a vector equation of a straight line and straight line segment, the position of Investigation two points or equivalent information, in both two and three dimensions 2 (5%) 3.3.6 examine the position of two particles, each described as a vector function of time, and determine if their paths cross or if the particles meet 3.3.7 use the cross product to determine a vector normal to a given plane
Week 4 3.1.11 determine and examine the nth roots of unity and their location on the unit circle 3.1.12 determine and examine the nth roots of complex numbers and their location in the complex plane Week 5 3.1.13 prove and apply the factor theorem and the remainder theorem for polynomials 3.1.14 consider conjugate roots for polynomials with real coefficients 3.1.15 solve simple polynomial equations Week 6-8 3.2.1 determine when the composition of two functions is defined 3.2.2 determine the composition of two functions 3.2.3 determine if a function is one-to-one 3.2.4 find the inverse function of a one-to-one function 3.2.5 examine the reflection property of the graphs of a function and its inverse Response 1 (5%) 3.1.1 – 3.1.15 Week 9 -10 3.2.6 use and apply for the absolute value of the real number x and the graph of 3.2.7 examine the relationship between the graph of and the graphs of and 3.2.8 sketch the graphs of simple rational functions where the numerator and denominator are polynomials of low degree Response 2 (7%) 3.2.1 – 3.2.8 Week 11 3.3.1 review the concepts of vectors from Unit 1 and extend to three dimensions, including introducing the unit vectors i, j and k 3.3.2 prove geometric results in the plane and construct simple proofs in three dimensions Week 11 3.3.3 introduce Cartesian coordinates for three-dimensional space, including plotting points and equations of spheres 3.3.4 use vector equations of curves in two or three dimensions involving a parameter and determine a ‘corresponding’ Cartesian equation in the two-dimensional case Term Two Content Resources Assessment Week 1 3.3.5 determine a vector equation of a straight line and straight line segment, the position of two points or equivalent information, in both two and three dimensions 3.3.6 examine the position of two particles, each described as a vector function of time, and determine if their paths cross or if the particles meet 3.3.7 use the cross product to determine a vector normal to a given plane Investigation 2 (5%)