Algebra 1 SOL Questions. Reporting Category: Expressions and Operations. Twelve less than the square of a number times three is thirty-six

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1 1. Translate between verbal and algebraic expressions Algebra 1 SOL Questions Reporting Category: Expressions and Operations Twelve less than the square of a number times three is thirty-six x + 7 = 13 Hint: Identify operations that are being used by key words. Pay attention to the order!. Use the laws of exponents to simplify an expression 3x x (4 y ) xy 5 4xy 3 Hints: Multiply coefficients, Distribute exponent on outside Divide coefficients, subtract add exponents multiply by any exponent already there exponents, move negatives 3. Use the laws of exponents to simplify an expression 3 (5 x y ) ( xy) xy 7 3 Hint: Combine the top of the expression first, then combine the top and bottom, then get rid of negatives 4. Evaluate an expression given replacement values 6x 5y ; when x=4 and y=- xy Hint: substitute the values in and follow order of operations, make sure to combine the numerator before dividing by the denominator.

2 5. Simplify the cube root of a whole number Hint: Make a factor tree for 108, all branches need to end in prime numbers. Any group of three primes brings one of them outside. 6. Multiply polynomial Expressions (x 5)( 3x+ 6) Hint: Make a x box to help organize your work or FOIL. 7. Completely Factor a polynomial x 4x 30 Hints: Look for GCF first, then numbers and add to b 3x x 4 Multiply to ac and add to b, then that multiply to c create a box to help. 8. Simplify the square root of a whole number Hint: Factor tree, pairs of factors go outside, leftovers go back inside. Multiply what comes outside by anything already there. 9. Divide polynomial Expressions (4x 18x + 1 x ) 7x 5 3 Hint: Put 7x under each term, divide coefficients and subtract the exponents.

3 10. Completely factor a polynomial 3 56x + 8x 1x 3 Hint: Group the first two terms together and the third and fourth terms together (negative goes with the 1) 11. Simplify the square root of a monomial expression: Simplify. 1. Evaluate an expression given replacement values: What is the value of the expression when x=4 and y=6? Reporting Category: Equations and Inequalities 13. Graph a line given the equation in standard form: Graph the line x y = 6

4 14. Justify a property of inequality: Match the steps with the property which justifies it: 3(-x + 7) -15 Step 1: 3(-x) + 3(7) -15 Justification: -6x Step : -6x Justification: -6x -4 Step 3: 1 1 ( 6 x) ( 4) 6 6 Justification: x 7 Distributive Property Commutative Property of Multiplication Inverse Property of Multiplication Identity Property of Multiplication Multiplication Property of Inequality Addition Property of Inequality 15. Identify a field property: Choose the property which justifies the following: (4 + 7) -5 = 4+ (7 5) A. Associative Property B. Commutative Property C. Identity Property D. Distributive Property 16. Find solutions to a system of Inequalities: Given the system: 4x 3y > 6 x+ 3y 9 Circle the points which are solutions and cross out the points which are not (0,) (3,) (3,-4) (-1,-4) (-3,-) (-, 4)

5 17. Generate the slope-intercept form of a line given two points: Write the linear equation in slope-intercept form of the line through the points (-3,1) and (0,-4). 18. Solve a literal equation for a variable: Solve for a. 4ab+1b = 8bc 19. Find the solutions to a quadratic equation given its graph: What are the solutions to this quadratic equation? 0. Find the solution to a multistep linear equation: Solve for x x= 6 + 4(9x+ 10) 1. Find an algebraic solution to a system of equations. Hint: Since both equations a set equal to y they can be set equal to each other and solved. Hint: You need to eliminate one of the variables

6 . Generate the slope-intercept form of a line when given two points. Hint: 1. Use the slope formula first, then use one of the points and write the point-slope equation, now solve for y.. Enter the two points into the STAT, Edit, L1 (x-coordinates) and L (ycoordinates) now use the linear regression #4 and find the equation of the line. 3. The school band needs a banner to carry in a parade. The length of the banner should be 18 feet. What are the possible lengths of the banner if they can use no more than 48 feet of trim? Reporting Category: Functions and Statistics Hint: Use the formula: l+ w = P and substitute for =. Determine whether a relation is a function 4. Put an X over the ordered pairs that would make it so this relation is not a function (-3, 4) (-, 5) (0, 5) (3, -1) (4, -3) (-, 6) (5, 0) (3, 0) Hint: The x values can t repeat Determine the x and y intercepts of a function represented algebraically 5. 3x 4y = 4 x-intercept: y-intercept: Hint: Plug in a 0 for x and solve for y, then plug in a 0 for y and solve for x.

7 Determine a data point given a z-score 6. What number would have a z-score of -.5 if the mean was 70 and the standard deviation was 8? Hint: z = x µ σ Find the curve of best fit for a set of data. 7.Using the following set of data, solve for the curve of best fit. (1, 1), (3, 3), (4, 5), (5, 6), (6, 9) (Hint: Use the STAT button on your calculator.) What would the y-value be if x were -6? (round answer to the nearest tenth) Determine the zeros of a function given the equation. Look at the graph. Use a large dot to mark the zeros for the function. Place your answers on the graph. (Hint: Look at the x-axis.) 9.

8 Determine the quadratic equation from its x-intercepts. 30. Determine the quadratic equation represented on this graph. (Hint: Look at where the graph hits the x-axis, set that answer equal to zero, and solve for your variable.) 3. Determine whether a relation is a function. 31. Circle all of the following that are functions: (Hint: Vertical line test.) Represent a direct or inverse variation relationship algebraically. 3. The formula Rate X Time = Distance uses direct variation. If you travel 400 miles at a rate of 50 mph, which equation below represents this relationship? (Hint: Substitute the given numbers in, see which equation works.) a. y = 8k b. y = c. y = 0000k d. y = x x 33. Write an equation to represent this variation: Hint: Remember : Direct variation is y = kx Inverse variation is y = k x x y

9 Model and make predictions for a set of data using the curve of best fit. 34. Based upon the given information, make a prediction what the height will be after 8 seconds. seconds height 1 5 Hint: Find the equation for Answer Choices: 15 curve of best fit, then substitute 8 in for the x value 3 30 a and solve b c d Analyze the changes to a box-and-whisker plot when a data point is added or removed. 35. The median for this box and whisker is 15, the upper extreme is 4. If 7 is added, as a new piece of data, and a new box and whisker is drawn. Which of the following will remain unchanged? (Hint: Create a set of data with and without the 7, see how the graphs differ.) a. Upper extreme c. Median b. Lower quartile d. Upper quartile Determine a z-score for a data point given statistical information. 36. The scores on a math test have a mean of 75 with a standard deviation of 6. What is the z-score for a student who earned an 8 on the test? Hint: Use z score = x µ σ 9.

10 Analyze and compare box and whisker plots. 37. Boys Girls Using the box and whisker graphs above: Which group has a greater median? Boys Girls Neither Hint: The line in the middle is called the median. The highest and lowest points are called extremes. Which group has a greater upper extreme? Boys Girls Neither Which group has a greater lower quartile? Boys Girls Neither

11 Algebra Reporting Category: Expressions and Operations Multiply and/or Divide Rational Expressions: Hint: When dividing rational expressions, flip (take the reciprocal) the divisor (second term) and then multiply. FACTOR all terms as much as possible. Be sure to look for GCF first! Add radical expressions: Hint: First reduce each radical to the simplest form. The expression under the radical has to be exactly the same, same number, same variable and exponent. Then add or subtract the coefficient of each like term. Factor a Polynomial: x 3 x + 56x 4x 4x x 0 Hint: Look for the GCF first. Then factor by grouping if a>1 or factor regularly if a=1. Factors of ac that sum to b. Multiply Complex Numbers: Hint: These problems can be done very easily with the calculator. Just type in exactly what you see, I can be typed in by hitting nd then period. DON T FORGET THE ()!!!

12 Add or Subtract Rational Expressions: x + x 4 3x 6 x x 8 x x + 6x 16 x x + 5 x + 10x + 5 x 5 Hint: the denominator must be the same to add or subtract. First factor each dominator. Then figure out what the LCM (least common multiple) is. After multiplying by each term to get the LCM, add or subtract the numerators. When subtracting, remember to distribute the negative to all terms. Factor the sum of two cubes 3 7x x 8y 3 6 Hint: Look for the GCF first. Remember SOPS (Square, Opposite, product, square) to factor correctly. Multiply Radical Expressions ( ) Find the difference between two complex numbers (5+6i) (7 3i) (8 i) (6 11i) (3+5i) (4+5i) Hint: Add real numbers together and add complex numbers together. When subtracting, don t forget to distribute the negative. You can also use the calculator. Convert between radical notation and exponential notation x x a Hint: b m n n m = b or b m n = n b m

13 Identify field properties over the complex number system. Give the property. ( + 6i) - (8 + 3i) + 6i - 8-3i i - 3i ( - 8) + (6i - 3i) i Commutative Property -order changes Associative Property-grouping changes- look for ( ) s ( + 6i) + (3-5i) becomes i + 5i (-7-8i) + (-3-4i) becomes ( ) + (-8i + -4i) Distributive Property -( 6 + 4i) = -1-8i Substitution-Replaces equivalent terms 15 can be put in place of Simplify two rational expressions Hint: Remember to write the problem sideways like a division problem. Flip the second expression, factor each part, and then cancel. Subtract two rational expressions Hint: Factor the denominator and find a common denominator. Multiply each numerator by the "missing part" of the denominator. Distribute/FOIL, combine like terms, and then determine if the numerator will factor again. If it does, see if you can cancel terms with the denominator.

14 Algebra Reporting Category: Equations and Inequalities Find the solution to an absolute value inequality graphically. Hint: Test a point in each section to see if it makes the equation true. < or > are open circles and or are closed circles. Remember if you divide by a negative the inequality sign has to change. Find the algebraic solution to a nonlinear system of equations. What is the solution set for this system of equations? y = x -6x y = x - 9 a. (, -8) (6,0) b. (, -8) (7,7) c. (0, -9) (6, 0) d. (-8, ) (0, 6) Hint 1: Plug and chug the answers if given Hint : Option : Make sure both equations are solved for y. Put these in the calculator under y 1 = and y =. Graph, then use nd Trace(Calc) Intersect The calculator will have First Curve in the upper left corner. Put your cursor on the point of intersection. Now the calculator will have Second Curve in the upper left corner. Put cursor on the point of intersection. Hit enter. Don't guess, just hit enter again. The intersection will appear at the bottom of the screen as x = y= Solve a quadratic equation with complex roots. Solve: x - 8x = -9 Hint: 1. Set equal to zero. If an equation will not factor use quadratic formula. 3. If the number under the radical is negative, the answer has an "i" in it. Remember you can also use APP: plysmlt

15 Find the solution to an equation containing a radical expression. Hint: Isolate the radical first. Raise both side to power of the root. Example square root then square both sides, cube root then cube both sides. Graph the solution to an absolute value inequality. Hint: 1. Isolate the absolute value first.. Then, determine less than or greater than. 3. If the absolute value expression is or >, rewrite the inequality as "problem" < -a or "problem" > a. Greater than problems should have arrows pointing out. 4. If the absolute value expression is < or, rewrite the inequality as "problem" < a and "problem" >- a or -a < Problem < a. Determine the number of solutions for a system of quadratic equations. What is the solution set for this system of equations? y + 16 = x y 14 = x 4x Option 1: Make sure both equations are solved for y. Put these in the calculator under y 1 = and y =. Graph, then use nd Trace(Calc) Intersect The calculator will have First Curve in the upper left corner. Put your cursor on the point of intersection. Now the calculator will have Second Curve in the upper left corner. Put cursor on the point of intersection. Hit enter. Don't guess, just hit enter again. The intersection will appear at the bottom of the screen as x = y= Option : Solve each equation for y. Set the x expressions equal to each other and solve for x. Plug x back in and solve for y. Find the solution to an equation with rational expressions. Hint: Factor the denominator and find a common denominator. Multiply through by common denominator. Distribute/FOIL if need be and then solve like normal. BE CAREFUL-Check for extraneous solutions!

16 Solve a quadratic equation with complex roots x 3x+ 7= 0 Hint: Use the quadratic formula ± x = b b 4ac a Find the solutions to an equation with rational expressions = x 1 x+ x 1 Hint: Multiply everything by the least common denominator; factor each denominator first to see what factors each denominator is missing. Given a graph, determine the solution set for a system of equations 9 y f(x)=-x^+4x+3 f(x)=x x Hint: Find where the two graphs intersect and list the coordinates Find the solution to an equation containing a radical expression x = x Hint: Isolate the radical first, then square both sides to eliminate the radical (don t forget to FOIL) Find the algebraic solution to an absolute value equation 3 4w 1 5 = 10 Hint: Isolate the absolute value expression first, then make sure to solve for both the positive and negative number/expression.

17 Find the algebraic solution to a quadratic equation 9x + 48x+ 64 = 0 Hint: Use factoring, the quadratic formula, or your calculator (table or plysmlt app) Find the nth term of an arithmetic or geometric sequence Algebra Reporting Category: Functions and Statistics Find the 43 rd term 19.5, 19.9, 0.3, 0.7, Find the 10 th term 1 1,, 1,... 4 Hint: Use a = a1 + ( n 1) d Hint: use n an = ar n 1 1 Determine the x-intercepts of a polynomial function represented algebraically 5 3 3x 39x + 108x= 0 Hint: Look for a common factor first, then use factoring a quadratic trinomial concepts to factor completely. Or, use your calculator (graph and table or plysmlt app). Interpret, model, and/or solve a variation problem Find z when x=6 and y=4 if z varies directly with x and inversely with the cube of y. When x = 8 and y =, z = 3 Hint: write the variation model first, then find k. Then use k, x, and y to find z. Determine the intervals in which a function represented algebraically is increasing or decreasing 3 f( x) = x x 4x+ 5 Hint: Use calculator to graph and look at the table Determine the zero of a polynomial function represented algebraically. Example: Find all the zeros of x 4 5x 3 + 0x 16 = 0 Hint: Go to Y= and enter the polynomial expression x 4 5x 3 + 0x 16 then press GRAPH. The x-intercepts are the zeros. If you have a TI-84: APPS PlySmlt 1:Poly Root Finder Order refers to the degree of the polynomial. Enter the coefficients and constant.

18 Identify the equation that best represents a graph. Example: Match each graph with its equation. I. II. III. IV V. VI. VII f(x) = x 5x + 6 f(x) = x 4 + x f(x) = log x f(x) = x f( x) = x f( x) = x Solve a permutation or combination problem (). Example: The names of 11 students are placed in a hat. A teacher will reach into the hat and select 3 names at one time. Each of those students wins the same prize. How many different groups of 3 winners could be chosen? Example: A web site requires the user to choose a password with 5 letters and digits, in that order. Each letter or digit can be used only once. How many different passwords are possible? Hint: Does the order matter? If yes permutation, if no combination. Use the formulas on the SOL formula sheet or using a TI calculator, go to MATH PRB :npr or 3:nCr Given the equation of a function, determine an intercept. Example: Find the x-intercept and y-intercept of the function 1 f( x) = 4 x Hint: Go to Y= and type the function. Algebraically, let x = 0 to find the y-int and let y = 0 to find the x-int.

19 Determine which numbers are not in the domain of a function. Example: Select all the numbers that do not belong to the domain of f( x) = x ½ 1 Hint: The domain is the set of x-values. Identify the equation that models a practical problem involving inverse variation. The volume, V, of a gas is inversely proportional to the pressure on it, p. If the volume of a gas at a constant temperature is 13 liters at a pressure of 45 millimeters, what is the formula used to represent this relationship? Hint: Translate the sentence using the symbols. Place an = symbol followed by k where you read inversely and remember that inverse variation involves division. Find the area under a normal curve using the empirical rule. Example: The number of crackers in a box of Crackerbox Crackers is normally distributed with a mean of 75 and a standard deviation of. Shade the region under the curve that represents the probability that a box has between 73 and 77 crackers. What is that probability? Hint: Areas can be found under a normal curve by using the Empirical Rule ( Rule) if the areas are bounded at places where an exact standard deviation occurs. Example: In a herd of 97 adult unicorns, the lengths of the horns are normally distributed with a mean of 10.1 cm and a standard deviation of 1.04 cm. a. On the graph at right, label the mean and three standard deviations above and below the mean.

20 b. On the graph at right, shade the region that represents the probability of a unicorn s horn being longer than 9 cm. Calculate the area of that region by finding the appropriate z-score and using the Standard Normal Probabilities Table. Hint: Areas that are not bounded at specific standard deviation units can be found by using a z-table or calculator. x µ When using a z-table, first find the z-score using the formula z = σ Using a TI-83/84: nd VARS :normalcdf(lower, upper, µ, σ ) automatically calculates the probability under the curve from the lower bound to the upper bound without needing to find the associated z-score. Find the composition of multiple functions. Example: Given f(x) = x + 3 and g(x) = x + 5, find ( f o g)(x). Hint: Input g(x) into f(x) at x. Example: Given f(x) = x + 3 and g(x) = x + 5, find (g o f )(x). Hint: input f(x) into g(x) at x. Evaluate a series represented in Sigma notation. Example: What is the indicated sum for the arithmetic series: 10 k = 1 (10 k) Hint: k is the index of summation and tells you what numbers to input into the formula (1,, 3,, 10). Sum the values you just found. You can also use the formulas on the SOL formula sheet if you do not want to build each term of the sum. Using a TI-83/84: nd STAT MATH 5:sum( nd STAT OPS 5:seq( Expression, Variable, Start, End, Step) Determine the asymptote of an exponential function represented algebraically. Example: Which is an asymptote of the graph f(x) = x 4 x = -3 x = -4 y = -3 y = -4 Hint: Graph the function. An asymptote is a line that the function approaches.

21 Determine the domain and/or range of a function represented algebraically. Example: Find the domain and range of f( x) = x 5+ 3 Hint: Look at the Graph of the equation!!! Remember domain is x-values (where the graph is left to right), range is y- values (where the graph is down to up) Given a normally distributed data set with a specified mean and standard deviation, find the probability for a given situation. Example: The school paper surveyed students about the time it takes them to drive to school and found a mean of 14 minutes and a standard deviation of minutes. What is the probability that a student has a commute longer than 17 minutes? Hint: nd VARS :normalcdf(lower, upper, µ, σ ) Given a scatterplot, determine the equation for the curve of best fit. Example: What type of equation would best fit the data to the right. Hint: Know the parent graph shapes for linear, quadratic, cubic, radical, exponential and logarithmic Determine the inverse of a function. Example: Find the inverse of f(x) = 5x 3 1 Hint: First switch x and y then solve for y Identify the equation that best represents a graph. Example: Find an equation for the graph below: Hint: Use transformations- look at how the graph moved (up/down, left/right, flip, stretch/shrink) then graph the equation in your calculator to check if it matches the given graph.

22 Describe the end behavior of a quadratic function represented algebraically. Example: What is the end behavior of f(x) = x 5 5x + 1 Hint: Look at the graph!!! As x means what is happening as x gets very small (left side of the graph). As x is when x is getting very large (right side of the graph). Determine a curve of best fit for data. Example: A cup of soup is left on the countertop to cool. The table below gives the temperature, in degrees Fahrenheit, of the soup recorded over a 10-minute period. Time in minutes (x) Temperature in F (y) Write an exponential equation that fits the data, rounding all values to the nearest thousandth. Hint: Put data into STAT. Use STAT CALC to find the best regression model (0:ExpReg) Identify the graph of a function given a zero. Example: Sketch a graph of a quadratic equation with a zero at -4. Hint: Zeros are the same thing as roots or x-intercepts. Given a function, determine the number of horizontal and vertical asymptotes. Example: Determine the horizontal and vertical asymptotes of the following: a) y = x + 1 b) y = x + x+ x Hint: Graph the function (remember to use parenthesis around numerator and denominator). An asymptote is a line that the function approaches. Use your table of values.

23 Reasoning and Logic SOL Define or Describe: NAME 3. Conditional statement: Converse: Inverse: Contrapositive: 4. Biconditional statement: 1. If 4x = 8, then x =

24 7. 8. Let m represent: Angle A is obtuse. Let n represent: Angle B is obtuse. Which is a symbolic representation of the following argument? Angle A is obtuse if and only if Angle B is obtuse. Angle A is obtuse or Angle B is obtuse. Therefore, Angle A is obtuse and Angle B is obtuse.

25 Triangle Inequalities SOL If we are given 3 lengths, how do we determine if they form a triangle? 4. How do we determine the ordering of sides or angles in a triangle?

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27 Triangle Congruency SOL What are 5 ways to prove that triangles are congruent?

28 6. CHOICES: Place the letter of the choice into the Reason column above A. Base Angles of an Isosceles Triangle are Congruent B. Corresponding Parts of Congruent Triangles are Congruent (CPCTC) C. Reflexive Property D. Angle-Side-Angle (A.S.A.) Postulate E. Side-Angle-Side (S.A.S.) Postulate

29 Triangle Similarity SOL What is the definition of similarity? 3. What are 3 ways to prove that triangles are similar? Similarity means that figures are proportional. How are proportions solved?

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31 Quadrilateral SOL Write the definition and characteristics of each quadrilateral: Parallelogram: Rhombus: Rectangle: Square:

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33 Polygons SOL Define Regular polygon : 3. What is the Sum of the Interior angles formula? What is the Sum of the Exterior angles? What operation is useful when finding individual angles of regular polygons?

34 Pythagorean Theorem SOL. What are the parts of a right triangle? What is the Pythagorean Theorem?

35 Sine/Cosine/Tangent SOL S-O-H C-A-H T-O-A In right triangle ABC: AB=10 BC=8 and AC=6. What is the measure of ABC, to the nearest degree?

36 First Semester Review: Show all Work! (Reduce all Fractions) NAME 1. Write the Distance formula. 1.. Write the Midpoint formula.. 3. Write the Slope formula Define and Draw an example : Linear Pair 5. What is the Vertical Angles Congruence Theorem? Then draw a diagram that explains the theorem: 6. Define and Draw an example : Corresponding Angles with Parallel Lines 7. Define and Draw an example : Alternate Interior Angles with Parallel Lines 8. Define and Draw an example : Consecutive Interior Angles with Parallel Lines

37 9. What is the Triangle Sum Theorem? Then draw a diagram that explains the theorem: 10. What is the Exterior Angle Theorem? Then draw a diagram that explains the theorem: 11. What is the Triangle Inequality Theorem? Then draw a diagram that explains the theorem: 1. What is the slope of a line that passes through the points (-, -3) and (-, 7)? What is the slope of a line perpendicular to a line with a slope of 3/5? What is the equation of a line that is parallel to a line with the equation y = -8x 4, and passes through the point (7, -)? What is the slope of a line perpendicular to a line that passes through (3, 0) and (7, 6)? Find the length of the segment with endpoints (6, -3) and (3, 5). Round to the nearest tenth: 16.

38 17. Find the midpoint of the segment with endpoints (9, 8) and (3, 5): 18. Is it possible to construct a triangle with the given side lengths: 4, 1, 6? Is it possible to construct a triangle with the given side lengths: 5, 5, 10? 0. Is it possible to construct a triangle with the given side lengths: 1, 13, 4? Describe, (using inequality symbols), the possible lengths of a third side of a triangle with the given lengths: 1 ft and 18 ft 1.. Describe, (using inequality symbols), the possible lengths of a third side of a triangle with the given lengths: 7 ft and 4 in. 3. The complement of an angle is 39. What is the measure of the angle? The supplement of an angle is 118. What is the measure of the angle? 5. List the sides of RPQ from shortest to longest: 4. 5.

39 Study Guide: First Semester Topics: All page numbers are from McDougal/Littell 007 Geometry text 1. Distance Formula (Page 17). Midpoint Formula (Page 16) 3. Slope Formula (Page 171) 4. Linear Pair (Page 16) 5. Vertical Angles Congruence Theorem (Page 16) 6. Corresponding Angles (Page 154) 7. Alternate Interior Angles (Page 155) 8. Consecutive Interior Angles (Page 155) 9. Triangle Sum Theorem (Page 18) 10. Exterior Angle Theorem (Page 19) 11. Triangle Inequality Theorem (Page 330) 1. Determine slope of a line given two points on the line (Page 171) 13. Determine slope of a line perpendicular to a line, given the slope of that line (Page 17 and Page 173) 14. Determine equation of a line parallel to a line, given the equation of the original line and a point on the new line. (Use rule on Page 17 and y = mx + b) 15. Determine the slope of a line perpendicular to a line that passes through two given points (Example 3, Page 173) 16. Determine length of a segment given two endpoints (Example 4, Page 18) 17. Determine the midpoint of a segment given two endpoints (Example 3a, Page 17) 18. Determine if a triangle can be constructed given three lengths (Exercise 17, Page 331) 19. Determine if a triangle can be constructed given three lengths (Exercise 17, Page 331) 0. Determine if a triangle can be constructed given three lengths (Exercise 17, Page 331) 1. Describe (using inequality symbols), the possible lengths of a third side of a triangle given the lengths of the other two sides (Page 330). Describe, (using inequality symbols), the possible lengths of a third side of a triangle given the lengths of the other two sides (Page 330 and pay attention to units) 3. Complementary Angles (Page 35) 4. Supplementary Angles (Page 35) 5. List the sides of a triangle in order from shortest to longest given two of the angles of the triangle (Page 38)

40 Algebra 1 SOL Questions Reporting Category: Expressions and Operations 1. Translate between verbal and algebraic expressions Twelve less than the square of a number times three is thirty-six 3x 1 = 36 x The sum of 7 and x divided by is = 13 The quotient of x and increased by 7 is 13. Hint: Identify operations that are being used by key words. Pay attention to the order!. Use the laws of exponents to simplify an expression xy 3x x (4 y ) 5 4xy 9 6x 6 16y x 3 y Hints: Multiply coefficients, Distribute exponent on outside Divide coefficients, subtract add exponents multiply by any exponent already there exponents, move negatives 3. Use the laws of exponents to simplify an expression 3 (5 x y ) ( xy) xy 7 3 5y x 4 Hint: Combine the top of the expression first, then combine the top and bottom, then get rid of negatives 4. Evaluate an expression given replacement values 6x 5y ; when x=4 and y=- xy = 8 4 Hint: substitute the values in and follow order of operations, make sure to combine the numerator before dividing by the denominator.

41 5. Simplify the cube root of a whole number Hint: Make a factor tree for 108, all branches need to end in prime numbers. Any group of three primes brings one of them outside. 6. Multiply polynomial Expressions (x 5)( 3x+ 6) x 1x 15x 30 Hint: Make a x box to help organize your work or FOIL. 7. Completely Factor a polynomial x 4x 30 Hints: Look for GCF first, then numbers and add to b 3x x 4 Multiply to ac and add to b, then that multiply to c create a box to help. ( x+ )( x ) ( 3x 4)( x+ 1) Simplify the square root of a whole number Hint: Factor tree, pairs of factors go outside, leftovers go back inside. Multiply what comes outside by anything already there. 9. Divide polynomial Expressions (4x 18x + 1 x ) 7x 4x 18x Hint: Put 7x under each term, divide coefficients and subtract the exponents.

42 10. Completely factor a polynomial 3 56x + 8x 1x 3 Hint: Group the first two terms together and the third and fourth terms together (negative goes with the 1) x ( x+ ) ( x+ ) ( x )( x+ ) GCF first and last : Take out common GCF: Simplify the square root of a monomial expression: Simplify. 3 30x z xy 1. Evaluate an expression given replacement values: What is the value of the expression when x=4 and y=6? 1 ( ) + 8 = 1 7 Reporting Category: Equations and Inequalities 13. Graph a line given the equation in standard form: Graph the line x y = 6 y = x 6

43 14. Justify a property of inequality: Match the steps with the property which justifies it: 3(-x + 7) -15 Step 1: 3(-x) + 3(7) -15 Justification: -6x Step : -6x Justification: -6x -4 Step 3: 1 1 ( 6 x) ( 4) 6 6 Justification: x 7 Distributive Property Commutative Property of Multiplication Inverse Property of Multiplication Identity Property of Multiplication Multiplication Property of Inequality Addition Property of Inequality 15. Identify a field property: Choose the property which justifies the following: (4 + 7) -5 = 4+ (7 5) A. Associative Property B. Commutative Property C. Identity Property D. Distributive Property 16. Find solutions to a system of Inequalities: Given the system: 4x 3y > 6 x+ 3y 9 4 y< x+ 3 1x y 3 3 Circle the points which are solutions and cross out the points which are not (0,) (3,) (3,-4) (-1,-4) (-3,-) (-, 4)

44 17. Generate the slope-intercept form of a line given two points: Write the linear equation in slope-intercept form of the line through the points (-3,1) and (0,-4). 5 y = x Solve a literal equation for a variable: Solve for a. 4ab+1b = 8bc 8bc 1b a = 4b REDUCE a = c Find the solutions to a quadratic equation given its graph: solutions What are the solutions to this quadratic equation? solutions as points ( 3,0 ) and ( 1,0 ) solutions as x intercepts x= 3 and x= 1 0. Find the solution to a multistep linear equation: Solve for x x= 6 + 4(9x+ 10) x = 3 1. Find an algebraic solution to a system of equations , 7. or, 5 5 ( ) Hint: Since both equations a set equal to y they can be set equal to each other and solved. ( 1, 5) Hint: You need to eliminate one of the variables

45 . Generate the slope-intercept form of a line when given two points. y = 1x+ Hint: 1. Use the slope formula first, then use one of the points and write the point-slope equation, now solve for y.. Enter the two points into the STAT, Edit, L1 (x-coordinates) and L (ycoordinates) now use the linear regression #4 and find the equation of the line. 3. The school band needs a banner to carry in a parade. The length of the banner should be 18 feet. What are the possible lengths of the banner if they can use no more than 48 feet of trim? length = 18 ( ) 18 + w = 48 width = 6 Reporting Category: Functions and Statistics Hint: Use the formula: l+ w = P and substitute for =. Determine whether a relation is a function 4. Put an X over the ordered pairs that would make it so this relation is not a function (-3, 4) (-, 5) (0, 5) (3, -1) (4, -3) (-, 6) (5, 0) (3, 0) Hint: The x values can t repeat Determine the x and y intercepts of a function represented algebraically 5. 3x 4y = 4 x-intercept: x = 8 y-intercept: y = 4 Hint: Plug in a 0 for x and solve for y, then plug in a 0 for y and solve for x.

46 Determine a data point given a z-score 6. What number would have a z-score of -.5 if the mean was 70 and the standard deviation was 8? Hint: z = x µ σ.5 = x = 50 x 70 8 Find the curve of best fit for a set of data. 7.Using the following set of data, solve for the curve of best fit. (1, 1), (3, 3), (4, 5), (5, 6), (6, 9) (Hint: Use the STAT button on your calculator.) Linear Reg: y = 1.54x 1.05 Quadratic Reg: y = 0.18x + 0.8x What would the y-value be if x were -6? (round answer to the nearest tenth) ( ) ( ) y = y = 5.4 Determine the zeros of a function given the equation. 9. Look at the graph. Use a large dot to mark the zeros for the function. Place your answers on the graph. (Hint: Look at the x-axis.) Determine the quadratic equation from its x-intercepts. 30. Determine the quadratic equation represented on the graph above. (Hint: Look at where the graph hits the x-axis, set that answer equal to zero, and solve for your variable.) x= 3 x= x+ 3= 0 x = 0 3. ( )( ) y = x + 3 x or y = x + x 6

47 Determine whether a relation is a function. 31. Circle all of the following that are functions: (Hint: Vertical line test.) Represent a direct or inverse variation relationship algebraically. 3. The formula Rate Time = Distance uses direct variation. If you travel 400 miles at a rate of 50 mph, which equation below represents this relationship? (Hint: Substitute the given numbers in, see which equation works.) a. y = 8x b. y = c. y = 0000x d. y = x x 33. Write an equation to represent this variation: Hint: Remember : Direct variation is y = kx Inverse variation is y = k x x y y = 3x 6.

48 Model and make predictions for a set of data using the curve of best fit. 34. Based upon the given information, make a prediction what the height will be after 8 seconds. seconds height 1 5 Hint: Find the equation for Answer Choices: 15 curve of best fit, then substitute 8 in for the x value 3 30 a and solve b c d Analyze the changes to a box-and-whisker plot when a data point is added or removed. 35. The median for this box and whisker is 15, the upper extreme is 4. If 7 is added, as a new piece of data, and a new box and whisker is drawn. Which of the following will remain unchanged? (Hint: Create a set of data with and without the 7, see how the graphs differ.) a. Upper extreme d. Median b. Lower quartile e. Upper quartile c. Lower extreme f. Range Determine a z-score for a data point given statistical information. 36. The scores on a math test have a mean of 75 with a standard deviation of 6. What is the z-score for a student who earned an 8 on the test? Hint: Use z score = x µ σ 8 75 z = 6 z =

49 Analyze and compare box and whisker plots. 37. Boys Girls Using the box and whisker graphs above: Which group has a greater median? Boys Girls Neither Hint: The line in the middle is called the median. The highest and lowest points are called extremes. Which group has a greater upper extreme? Boys Girls Neither Which group has a greater lower quartile? Boys Girls Neither