Worksheet 2 7 Logarithms and Exponentials
Section 2 Properties of Logs Logs have some very useful properties which follow from their de nition and the equivalence of the logarithmic form and exponential form. Some useful properties are as follows: logb mn = logb m+logb n logb m n = logb m logb n logb m a = alog b m logb m = logb n if and only if m = n Page 2
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Worksheet 4.8 Composite and Inverse Functions
maths.mq.edu.auNotice 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.
Worksheet 1.4 Fractions and Decimals - Macquarie University
maths.mq.edu.auWorksheet 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 ...
Worksheet 3 6 Arithmetic and Geometric Progressions
maths.mq.edu.au(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 ...
Worksheet 3 5 Simultaneous Equations
maths.mq.edu.aufor 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 …
Worksheet 2 3 Algebraic Fractions - Macquarie University
maths.mq.edu.au2 (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 ...
Worksheet 2 2 Solving Equations in One Variable
maths.mq.edu.au70 = 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 ...
Worksheet 2 6 Factorizing Algebraic Expressions
maths.mq.edu.auWorksheet 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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CAPE Integrated Mathematics
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Become familiar with - Educational Testing Service
www.ets.organd their ability to apply these principles in the solution of problems. Most test questions can be answered on the basis of a mastery of the first three years of undergraduate physics. The test questions are constructed to simplify mathematical manipulations. As a result, neither calculators nor tables of logarithms are needed.
Logarithms and their Properties plus Practice
www.mcckc.eduLOGARITHMS AND THEIR PROPERTIES Definition of a logarithm: If and is a constant , then if and only if . In the equation is referred to as the logarithm, is the base , and is the argument. The notation is read “the logarithm (or log) base of .” The definition of a logarithm indicates that a logarithm is an exponent.