Vijaya Nallari -Math 8 SOL TEST STUDY GUIDE

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$1- Simplifying Expressins and Fractins, Decimals, Percents, and Scientific Ntatin ORDER OF OPERATIONS -- GROUPING SYMBOLS Parentheses ( ), brackets [ ], braces { }, the abslute value, divisin/fractin$

1 Name Perid SOL Test Date Vijaya Nallari -Math 8 SOL TEST STUDY GUIDE Highlighted with RED is Semester 1 and BLUE is Semester Simplifying Expressins and Fractins, Decimals, Percents, and Scientific Ntatin ORDER OF OPERATIONS -- GROUPING SYMBOLS Parentheses ( ), brackets [ ], braces { }, the abslute value, divisin/fractin bar, and the square rt symbl shuld be treated as gruping symbls EXPONENTS!! MULTIPLY/DIVIDE -LEFT TO RIGHT r ADD/SUBTRACT - LEFT TO RIGHT + r # Fractin t decimal - numeratr divided by denminatr. The tp number ges int the calculatr first. If yu can't use a calculatr, then the NUMERATOR ges INside the huse. (anther way is t say Tp dg ges in the huse ) Decimal t percent - mve the decimal right 2 times. If yu d nt see a decimal it is at the end f the number..16 = 16% OR multiply yur decimal by 100 (.16 x 100 = 16%) Percent t decimal mve the decimal left 2 times. IF THE PERCENT HAS A DECIMAL IN IT, YOU STILL MUST MOVE IT 2 TIMES...EXAMPLE.16% =.0016 OR divide percent by 100! Scientific Ntatin t Standard Frm Mve the decimal the number f places the expnent says and the directin f the value f the expnent (psitive expnent mve decimal right/ negative expnent mve decimal left). EXAMPLE: x 10-5 means the decimal will mve 5 places t the left since the expnent is a negative 5. S the answer is *When cmparing/rdering decimals, fractins, percents and scientific ntatin - change ALL f them t decimals. Line up yur decimals (mney) and cmpare!! 8.2 Real Number System The set f real numbers includes natural numbers, cunting numbers, whle numbers, integers, ratinal and irratinal numbers. The set f natural numbers is the set f cunting numbers {1, 2, 3, 4,...}. The set f whle numbers includes the set f all the natural numbers r cunting numbers and zer {0, 1, 2, 3 }. The set f integers includes the set f whle numbers and their ppsites { -2, -1, 0, 1, 2 }. The set f ratinal numbers includes the set f all numbers that can be expressed as fractins in the frm a b where a and b are integers and b des nt equal zer (e.g., 25, 1, -2.3, 75%, 4.59 ). 4

2 The set f irratinal numbers is the set f all nnrepeating, nnterminating decimals. An irratinal number cannt be written in fractin frm {e.g., π, 2, } Taxes, Tips, Discunts, Prprtins, Simple Interest, and Percent Increase/Decrease Taxes, Tips and Discunts Step 1: Change yur percent t a decimal Step 2: Multiply yur decimal by the amunt f the prduct! This will represent the TAX, TIP, r the AMOUNT TO TAKE OFF f the prduct.! Check t see if yu need Step 3 step 3 is asking fr the FINAL TOTAL Step 3! Fr TAX and TIP ADD yur answer frm step 2 t the cst f the riginal prduct.! Fr DISCOUNT SUBTRACT yur answer frm step 2 frm the riginal prduct. Prprtins Step 1: Set up yur KEY in rder t have infrmatin matching in the rati. Step 2: Set up yur prblem using yur key. Step 3: Crss multiply. Step 4: Slve yur ne step equatins.! Example: A plant grws 2 millimeters every 6 hurs. If it cntinues t grw at the same rate, hw many millimeters will it have grwn in 15 hurs? Step 1: Step 2: Step 3: Step 4: Simple Interest Frmula: I = prt I- interest, p- principal (amunt f $ yu start with), r- rate (given in % change t decimal), t- time in years (if given in mnths use that as the numeratr and 12 as the denminatr)

3 ! Read carefully t determine whether the questin is asking fr interest nly r the ttal amunt f mney. Ttal value f the investment--- add the Interest yu calculated t the Principal Percent Increase/Decrease Percent Increase: determines the rate f grwth: results in a psitive number Percent Decrease: determines the rate f decline: results in a negative number! Frmula Change (new riginal) riginal 8.4 Algebraic Expressin Plug the numbers in fr the letters Slve the prblem fllwing the rder f peratins (lk back at 8.1). TAKE YOUR TIME AND SHOW ALL WORK! Remember the SOL test is ging t try t trick yu, s if yu shw yur wrk they cannt trick yu up! 8.5 Perfect Squares and Estimating Square Rts Perfect Squares: A whle number whse square rt is an integer Example: 25 is 5 and -5 s 25 is a perfect square Square Rt f a number: any number which when multiplies by itself equals the number Example: 25 is 5 and -5 s 5 and -5 are the square rts f 25 Example: is nt a perfect square but it lies between the perfect squares 9 and 16 s the tw cnsecutive whle numbers between which 15 lies are 3 and 4 because 9 = 3 and 16 = Vertical Angles, Adjacent Angles, Supplementary Angles, and Cmplementary Angles Vertical angles are (all nnadjacent angles) frmed by tw intersecting lines. Vertical angles are cngruent and share a cmmn vertex. Cmplementary angles are any tw angles such that the sum f their measures is 90. Supplementary angles are any tw angles such that the sum f their measures is 180. Reflex angles measure mre than 180.

4 Adjacent angles are any tw nn-verlapping angles that share a cmmn side and a cmmn vertex Surface Area and Vlume Surface Area: wrapping a present, aluminum the makes a sda can, cardbard that makes a bx (there is n pattern if yu change an attribute) Vlume: sand inside a bx, sda inside a can, water inside a pl, cereal inside a bx (whatever change yu make t the attribute is made t the new vlume (example: duble length the vlume dubles) Step 1: Determine if the questin is asking fr Surface Area r Vlume Step 2: Write the frmula Step 3: Make yur key fr yur variables! Be careful smetimes they give yu a diameter instead f a radius fr cylinders! Step 4: Plug in yur numbers t the frmula Step 5: Slve using the Order f Operatins REMEMBER: surface area is units 2 and fr vlume is units Transfrmatins Translatins: when an bject SLIDES t anther lcatin Rtatin: when an bject TURNS Remember each quadrant is equivalent t 90 degrees. Dilatin: when an bject gets bigger OR smaller Remember t multiply each number in the rdered pair by the scale factr. Reflectin: when an bject FLIPS ver a line f reflectin

5 8.9 - Three Dimensinal Views Cnstruct a 3-D mdel, given the tp r bttm, side, and frnt views. Identify a 3-D mdel given a 2-D perspective Example: Given the 2-D perspectives belw, cnstruct the 3-D mdel 8.10 Pythagrean Therem In a right triangle, the square f the length f the hyptenuse (c) equals the sum f the squares f the legs (a and b). This relatinship is knwn as the Pythagrean Therem: a 2 + b 2 = c Cmpsite Plane Figures Subdivide a figure int triangles, rectangles, squares, trapezids and semicircles. Estimate the area f subdivisins and cmbine t determine the area f the cmpsite figure. Use the attributes f the subdivisins t determine the perimeter and circumference f a figure. Apply perimeter (distance arund a plygn), circumference (distance arund a circle) and area (inside prtin f a plygn r circle) frmulas t slve practical prblems Prbability Prbability is the chance that a particular utcme will ccur, measured as the rati f the ttal f pssible utcmes. Independent event: the utcme f ne event DOES NOT affect the utcme f the ther event. Dependent event: the secnd event depends n the utcme f the first event. When yu have tw events: multiply yur fractins tgether. When finding the number f pssible cmbinatins yu can Make a tree diagram (LONG WAY) Multiply the ptins tgether 8.13 Scatterplts A scatterplt illustrates the relatinship between tw sets f data. A scatterplt cnsists f pints. The crdinates f the pint represent the measures f the tw attributes f the pint. Scatterplts can be used t predict trends and estimate a line f best fit.

In a scatterplt, each pint is represented by an independent and dependent variable.

14 Tables, Graphs, Rules, and Wrds Tables, graphs and equatins represent the SAME infrmatin.

Find the matching graphs and equatins by CREATING a table t make rdered pairs.

6 In a scatterplt, each pint is represented by an independent and dependent variable. The independent variable is graphed n the hrizntal axis (x-axis) and the dependent is graphed n the vertical axis (yaxis) Tables, Graphs, Rules, and Wrds Tables, graphs and equatins represent the SAME infrmatin. Find matching graphs and tables by pltting pints frm the tables nt the graph t see which table cntains pints fr the graphed line. Find the matching graphs and equatins by CREATING a table t make rdered pairs.! Mst f the time, yu can create yur x/y table by using the x values f -2, -1, 0, 1, 2 Find the matching equatins and tables by plugging in ALL f the values frm the tables t see which table cntains rdered pairs that make the equatin true Slving Equatins & Inequalities, and Prperties 8.15 a Equatins Yur gal = GET THE VARIABLE ALONE! Fllw these steps: Step 1: Draw a line thrugh yur equal sign, this reminds yu what yu d t ne side f the equatins needs t be dne t the ther. Step 2: Identify yur variable: this is what yu are trying t get alne Step 3: Use the inverse peratins the get the numbers away frm the variable. Yu can use a DO/UNDO chart t help yu identify what the rder f peratins are being dne t the variable then Example 1: Steps 1 & 2: Step 3: Step 3 cnt: Answer: Example 2:

SOL8.15 b Inequalities Always start by asking yurself these tw questins t determine if the inequality sign flips!! Questin 1: Is the prblem multiplying r dividing?

7 SOL8.15 b Inequalities Always start by asking yurself these tw questins t determine if the inequality sign flips!! Questin 1: Is the prblem multiplying r dividing? If the answer is n then the inequality sign stays the same If the answer is yes ask questin number 2! Questin 2: Is the number ATTACHED t the variable negative? If the answer is n then the inequality sign stays the same If the answer is yes THEN FLIP THE INEQUALITY SIGN IN THE ANSWER! Slve the prblem by islating the variable. When graphing inequalities, there are tw steps:! Step 1: Put the crrect circle ver the number! Step 2: Draw an arrw twards all the numbers that are true fr the inequality SOL 8.15 c Prperties Cmmutative: Changes Order! Ex: = Assciative: Always Stays Same Order (parenthesis mve)! Ex: 7+ (9 + 1) = (7+ 9) + 1 Distributive: Teacher Prperty the number utside gives itself away t the numbers inside parenthesis! Ex: 5(6+8) = 5(6) + 5(8) Identity: Stays the same! Ex: a + 0 = a OR a x 1 = a Inverse: The ppsite! Ex: a!! = 1 Multiplicative Prperty f Zer: Multiply by zer... t get zer 8.16 Graph Linear Equatins Make a table f values with at least 3 pints Graph the pints frm the table f values yu created Example:

8 8.17 Dmain, Range, Independent Variable, and Dependent Variable Dmain all x values Range all y values Independent Variable (x) graphed n the hrizntal/x-axis INPUT Dependent Variable (y) graphed n the vertical/y-axis OUTPUT

Geometry Strand Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.

Geometry Strand Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes. 2005 Gemetry Standards Algebra Strand Nte: The algebraic skills and cncepts within the Algebra prcess and cntent perfrmance indicatrs must me maintained and applied as students are asked t investigate,