Worksheet 2 7 Logarithms and Exponentials

Worksheet 2:7 Logarithms and Exponentials Section 1 Logarithms The mathematics of logarithms and exponentials occurs naturally in many branches of science. It is very important in solving problems related to growth and decay. The growth and decay

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Worksheet 4.8 Composite and Inverse Functions

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Notice in each of examples 1 and 2 the operations performed are \opposites" so the functions \undo" each other. Similarly we have example 3. Example 3 : p(x) = x3; q(x) = x1=3 p(x) cubes what we put in and q(x) takes the cube root of what we put in.

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Worksheet 1.4 Fractions and Decimals - Macquarie University

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Worksheet 1.4 Fractions and Decimals Section 1 Fractions to decimals The most common method of converting fractions to decimals is to use a calculator. A fraction represents a division so 1 a is another way of writing 1 a, and with a calculator this operation is easy to perform. The calculator will provide you with the decimal equivalent of the ...

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Worksheet 3 6 Arithmetic and Geometric Progressions

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(b) Find the sum to 5 terms of the geometric progression whose rst term is 54 and fourth term is 2. (c) Find the second term of a geometric progression whose third term is 9 4 and sixth term is 16 81. (d) Find the sum to n terms of an arithmetic progression whose fourth and fth terms are 13 and 15. 4. (a) A university lecturer has an annual ...

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Worksheet 3 5 Simultaneous Equations

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for the equation of a line. This is always the case when solving linear simultaneous equations in two variables. This means that solving simultaneous equations is the same as nding the point of intersection of lines. If certain values of x and y satisfy both …

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Worksheet 2 3 Algebraic Fractions - Macquarie University

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2 (b) m 7 m 5 (c) 4t 5 + t 2 (d) m+1 3 m 2 4 (e) 3m+4 7 + m 1 2 (f) y y+1 y y+3 (g) 5 t+1 + 4 t 3 (h) 3m m+4 + 4m m+5 (i) 4 y+1 5 y+2 (j) 7 4x + 2 5xy Section 2 Multiplication and Division As in numerical fractions, the trick with simplifying the multiplication and division of algebraic fractions is to look for common factors both before and ...

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Worksheet 2 2 Solving Equations in One Variable

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70 = T +2 7 (multiply out the brackets) 70 = T +14 70 14 = T +14 14 56 = T Note: When multiplying through by a number it is important to multiply every term on both sides of the equation. On the whole, it is probably easier to undo addition and subtraction rst. Example 2 : 3x 5 = 16 3x 5+5 = 16+5 (add 5 to both sides) 3x = 21 3x 3 = 21 3 x = 7 ...

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Worksheet 2 6 Factorizing Algebraic Expressions

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Worksheet 2:6 Factorizing Algebraic Expressions Section 1 Finding Factors Factorizing algebraic expressions is a way of turning a sum of terms into a product of smaller ones. The product is a multiplication of the factors. Sometimes it helps to look at a simpler case before venturing into the abstract. The number 48 may be written as a product in a

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