HYDRO-ELECTRIC POWER PLANT

MATHEMATICS (ALGEBRA)DAY 1ALCORCON

Engineering Review Center4th floor, Coast Pacific Downtown Center, Sanciangko St., Cebu City Tel. 254-3384Manila: 4th Flr. Anacleta Bldg. 891 Galicia St. cor. Espana Ave. Sampaloc Manila (Tel. 742-56-00)ALCORCON

Engineering Review CenterNUMBER SYSTEM Imaginary Number (i)Rational NumberIrrational Number

Real Number2Complex Number number that is expressible in the form of a + bi.Real numbers is any number that can be represented by a decimal.Rational Numbers -numbers that can be expressed as a fraction of two integers. Terminating decimals. Ex. , 3/4 Non-terminating, repeating decimals. Ex. 1/3, 2/3Irrational Numbers -numbers that cannot be expressed as a fraction of two integers. Non-terminating, non-repeating decimals Example: , , e, etc.Imaginary number are numbers that contains imaginary i.

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Real numbersThe rational and irrational numbersPrime Number integer greater than 1 that is divisible only by 1 and itself.Ex. 2, 3, 5, 7, 11, 13, 17, 19 .Natural numbers{1, 2, 3, }Whole numbers{0, 1, 2, 3, ..}Integers{.., -3, -2, -1, 0, 1, 2, 3,}ALCORCON

Engineering Review CenterSIGNIFICANT FIGURESExample: Find the significant figures of the following:

1. 462 significant figures2. 340005 significant figures3. 3.4 x 1042 significant figures4. 45.604 significant figures5. 68.004 significant figures6. 1.02305 significant figures7. 0.00103005 significant figures ALCORCON

Engineering Review CenterFACTORING

1.

2.

(difference of squares) 3.

4.

5.ALCORCON

Engineering Review CenterFACTORING 6.

7.

(difference of cubes)8.

10.

9.

(sum of cubes)ALCORCON

Engineering Review CenterLAWS OF EXPONENTS

1.

2.

3.

4.

5.

6.

7.

8.

9.1/1 = 1 10.ALCORCON

Engineering Review CenterLAWS OF EXPONENTS11.0/1 = 012.1/0 = infinity13.1/ = 014.0/0 = indeterminate15./ = indeterminate

16.= indeterminateALCORCON

Engineering Review Center1. How many significant digits does 10.097 have? A. 2B. 3C. 4D. 52. Simplify the following expression: i3217 - i427 + i18A. 1 + 2iB. 1 iC. -1 + 2iD. 1 + i3. The sum of all prime numbers between 1 and 15 is _____.A. 39B. 41C. 46D. 1204. Solve 3 . (9)2k = (35)k for k.5. Expand (x - 2)3 - 8y3.6. Find the possible factors of 4x5 4x4 + 25x3 30x2 99x + 54.A. (x 2) B. (2x 1)C. (2x + 3) D. All of the above7. The function f(x) = (x2 4)/(x3 2x2 3x + 10) is discontinuousat x= ?A. 2 B. -2 C. either A or BD. Neither A or BPROBLEMS:ALCORCON

Engineering Review CenterEQUATIONS:1. LINEAR EQUATION (First Degree Equation)

A. Linear equations with one unknownExample: 3x + 2 = x + 8Solution: Simple transposition

B. Linear Equations with two or more unknownsExample: x + y = 4 and x y = 2Solution: 1. Substitution method2. Elimination method3. Determinants ALCORCON

Engineering Review CenterEQUATIONS:2. QUADRATIC EQUATION (Second Degree Equation)A. Quadratic Equations with only one unknownGeneral equation: ax2 + bx + c = 0Solution: Quadratic formulaCompleting the square Factoring if factorable ALCORCON

Engineering Review CenterEQUATIONS:Quadratic FormulaA quadratic equation is an equation of the general form ax2 + bx + c = 0. The roots, x1 and x2, of the equation are the two values of x that satisfy it.From the equation ax2 + bx + c = 0ALCORCON

Engineering Review CenterEQUATIONS:

Where: b2 -4ac is known as discriminantNote:b2 = 4ac - the roots are real and equal. There is only one real solutionb2 4ac - the roots are real and unequal.b2 4ac - the roots are imaginary and conjugate imaginary.ALCORCON

Engineering Review CenterEQUATIONS:Properties of roots:Sum of roots: x1 + x2 =

Product of roots: x1 x2 =

B. Quadratic equations with two unknowns:Example: x2 y2 = 8 and x2 + y2 = 10:

Solution:1. Elimination method2. Substitution methodDeterminantsALCORCON

Engineering Review CenterEQUATIONS:3. CUBIC EQUATION (Third Degree Equation)General Equation: ax3 + bx2 + cx + d = 0

Solution:1. Synthetic division2. Factoring if factorable3. Trial and errorALCORCON

Engineering Review CenterEQUATIONS:4. QUADRIC EQUATION (Fourth Degree Equation)General Equation: ax4 + bx3 + cx2 + dx + c = 0Solution:1. Synthetic division2. Factoring if factorable3. Trial and error5. EQUATIONS SOLVABLE ONLY BY TRIAL AND ERRORExample:Solve for m0.0984 = (1 + 0.095/m)m - 1

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Engineering Review CenterPROBLEMS1. If 4y = 3x, then, what is the value of

A. 4/3B. C. 2/3D. 3/2Solve for x in the equations: x (x + y + z) = 2; y (x + y + z) = 6; and z (x + y + z) = 8.A. B. 1C. 1.5D. 2

3. If what is the value of z?A. 0.453B. 0.618C. 0.816D. 0.681

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Engineering Review CenterPROBLEMSWhat is the value of k to make the expressionkx2 3kx + 9 a perfect square?A. 2B. 4C. 3D. 55. Find the value of x which will satisfy the following expression: A. x = 3/2 B. x = 9/4 C. x = 18/6D. none of theseEvaluate: A x B.

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