Higher. Expressions & Functions. Unit 2 Course Contents. Higher Higher Higher Higher Higher. Higher Higher. Higher Higher. Higher Higher.

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1 Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher Higher xpressions & unctions Unit 2 Course Contents Higher Higher

2 Polynomials A I have had experience of factorising. (common factor, difference of two squares and trinomials) Higher ook P335 x 4 Q 1 and 2 I can identify a polynomial expression. Higher ook P132 x 7A Q 1 and 2 C I can identify the coefficients of each term in a polynomial. Higher ook P132 x 7A Q 3 I have had experience of substituting and evaluating expressions. Higher ook P132 x 7A Q 6 to 8 I can use the nested form to evaluate polynomials Higher ook P133 x 7 Q 1 and 2 I can find the remainder using the remainder theorem. Higher ook P135 x 7C Q 1 to 4 Higher ook P136 x 7 Q 1 to 8 G I can factorise a polynomial expression using the factor theorem. Higher ook P137 x 7 Q 1 to 7 H I can evaluate an unknown coefficient of a polynomial given (x a) Higher ook P138 x 7 Q 1 to 5 I I can solve polynomial equations Higher ook P140 x 7G All Questions J I can find coefficients of polynomials from their graphs Higher ook P140 x 7H Q 1 to 15 K I can sketch graphs when the function is a polynomial Higher ook P143 x 7I Q 1 to 9

3 L I can find approximate roots Higher ook P144 x 7J Q 1 to 7 M Revision xercise Higher ook P145 x 7K

4 Composite and Inverse unctions A I can understand and use basic set notation. Higher ook P23 x 2A Q 1 to 3 I have investigated domain and range. Higher ook P24 x 2 Q 1 to 8 C I can determine a composite function. Higher ook P26 x 2C Q 1 to 10 I can determine the inverse of a linear function. Higher ook P28 x 2 Q 1 to 5 I understand that f(g(x)) = x implies that f(x) and g(x) are inverses. Higher ook P29 x 2 Q 1 and 2 I can sketch and draw the inverse of each function Higher ook P29 x 2 Q 1 and 2 I Revision xercise Higher ook P31 X 2I

5 xponential and Logarithmic unctions A I can investigate exponential growth and decay Higher ook P292 x 15C Q1-10 I can evaluate and for equations solve for x Higher ook P294 x 15 Q 2, 3, 4, 5 C I can identify (and sketch) the inverse function of an exponential or a logarithmic function. Higher ook P30 x 2G Q 1 Higher ook P31 x 2H Q 1 Higher ook P295 x 15 Q 1 to 3 I can use the three laws of logarithms. Higher ook P296 x 15 Q 1 to 8 I can solve logarithmic equations using the laws of logarithms. Higher ook P297 x 15G Q 1 to 4 I can solve logarithmic equations in real life contexts. Higher ook P298 x 15H Q 4 to 7 G I can solve exponential equations using natural logarithms. Higher ook P298 x 15H Q 1 to 4 H I understand formulae from experimental data. Higher ook P300 x 15I Q 1 to 2 I I understand further formulae from experimental data. Higher ook P302 x 15J Q 1 to 3 K Revision exercise Higher ook P306 x 15L

6 Graphs of functions A I can identify and sketch a function after a transformation of the form f(x) + k, f(x + k), kf(x), f(kx), -f(x), f(-x), or a combination of these. Higher ook P35 to 45 x 3 to 3M I can evaluate unknowns from exponential and logarithmic graphs Higher ook P45 x 3N Q 1 and 3 Higher ook P47 x 3O C I can use my knowledge of Graphs and unctions and graphs of y= nd y= ln x to sketch related graphs Higher ook P305 x 15K Q1 to 7 Revision Higher ook P47 x 3P

7 Trigonometric Graphs and quations A I can state the period and amplitude for a given Trigonometric Graph Higher ook P53 x 4A Q1, 3 I can sketch and annotate a basic trig graph under the transformations kf(x), f(x) + k, f(kx), f(x + k), -f(x), f(-x), or a combination of these. Higher ook P54 x 4 Q1, 2 C I can determine a trigonometric equation from the associated graph. Higher ook P54 x 4 Q 3, 4 I can convert egrees Radians and sketch and interpret Trigonometric Graphs using radians Higher ook P56 x 4C Q1, 2, 3, 4, 5 I can find exact values Higher ook P59 x 4 Q1, 2, 3 I can use graphs to solve equations Higher ook P62 x 4G Q1, 2 G I have revised solving basic trigonometric equations in degrees and radians. Higher ook P63 x 4H Q 1(a)(b), 2, 3 H I can solve a trigonometric equation involving multiple angles. Higher ook P63 x 4H Q 1(c)(d)(e)(f) 4 I I can solve a trigonometric equation involving phase angles. Higher ook P65 x 4I Q 1 to 4 J I can solve trigonometric equations which require factorisation. Higher ook P63 x 4H Q 5

8 K Revision xercise Higher ook P65 x 4J

9 Addition ormula A I understand concept of compound angles Higher ook P192 x 11A Q1 I can use addition formulae Higher ook P194 x 11 All Questions Higher ook P195 x 11C All Questions Higher ook P196 x 11 All Questions C I can use addition formula to prove trigonometric identities. Higher ook P198 x 11 Q 1 to 8 I can apply Addition ormula ormulae to problem solving context. Higher ook P199 x 11 Q 1 to 4, 8 I can use the double angle formulae, including expanding sin4x, cos6x, etc. Higher ook P201 x 11G Q 1 to 14 I can solve trigonometric equations which require the substitution of a trigonometric identity. Higher ook P203 x 11H Q 1 to 6 G Revision xercise Higher ook P206 x11j

10 Wave unction I can recall deriving equations, max and min values from graphs Higher ook P310 Introduction to Wave unction through adding 2 waves Higher ook P311 x 16 Q1 C I can convert acosx + bsinx to kcos(x - α), with angle α in the first quadrant and k > 0. Higher ook P313 x 16C Q1-9 I can convert acosx + bsinx to kcos(x ± α) or ksin(x ± α), with angle α as a value in 1 of 4 quadrants and k > 0. Higher ook P313 x 16 Q 1 a,c,e,f, Q 2 Higher ook P314 x 16 Q 1 a,c,d,f Q2 a,d,c,e Q3 a,b,c,e Q4 a,c,d,e Q5 a,b,c,e I can apply the wave function formula to multiple angles. Higher ook P315 x 16 Q 1 to 3 I can find maximum and minimum values of a function by expressing the function acosx + bsinx as a single trigonometric function. Higher ook P316 x 16G Q 1, 2, 4, 6, 7, 8, 9, 10, 11 G I can solve equations involving acosx + bsinx using the wave function. Higher ook P318 x 16H Q 1 to 4

11 H I can solve mathematical applications in the form acosx + bsinx and sketch associated graph. Higher ook P320 x 16I Q 1 to 4 I Revision xercise Higher ook P321 x 16J

12 Vectors A I have revised 3 vectors from National 5. Higher ook P256 X 13N Q 1 c,d, Q 2 a,b,e,f Q4 a,b, Q 6,- 12 I can find position vectors. Higher ook P248 x 13 G Q1 and 2 Higher ook P256 X 13N Q 13 and 14 C I can find 2 unit vectors. Higher ook P247 x 13 Q 1 and 2 I can express and use properties of 3 vectors in the form ai+bj+ck. Higher ook P256 x 13N Q1 a,b, Q2 c,d,g Q3, Q4 c,d I can determine whether or not coordinates are collinear, using the appropriate language. Higher ook P249 x 13I Q 1 to 5 Higher ook P256 x 13N Q15-18 I can apply the section formula. Higher ook P250 x 13J Q 1 to 3 Higher ook P251 x 13K Q 1 to 7 Higher ook P256 x 13N Q19 to 24 G I can calculate the scalar product. Higher ook P259 x 13O Q 1 to 3 Higher ook P261 x 13P Q 1 to 4

13 H I know the properties of the scalar product and their uses: Namely: Angles between vectors Higher ook P262 x 13Q Q 1 to 6 Perpendicular vectors Higher ook P263 x 13R Q 1 to 8 Applications Higher ook P264 x 13S Q1-7 Commutative and istributive Laws for Vectors Higher ook P265 x 13T Q 1 and 2 Higher ook P266 x 13U Q 1 to 9 I Revision xercise Higher ook P267 x 13V