Algebra 1 If you are okay with that placement then you have no further action to take Algebra 1 Portion of the Math Placement Test


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1 Dear Parents, Based on the results of the High School Placement Test (HSPT), your child should forecast to take Algebra 1 this fall. If you are okay with that placement then you have no further action to take. If you would like your child to be in Geometry this fall, then he/she must take and pass the Algebra 1 portion of the Math Placement Test. In order to pass the test the student must earn an overall score of at least 70% and no individual section can be below 60%. Algebra 1 Portion of the Math Placement Test: Below you will find a brief description of each section found in the Algebra 1 Portion of the test and a list of example problems. Students are encouraged to work through the following problems like they would when taking a test (i.e. without a calculator and without help.) An answer key is provided at the end. If you notice an area of weakness the student is encouraged to do extra studying in that area before they sit for the test. I. Algebra 1 skills and Concepts A. The Real Number System: students can simplify numeric expressions using order of operations and can evaluate expressions. Examples follow. 1. Simplify Simplify Evaluate 3ab 4 2 if a = 2/3 and b = 7 4. Evaluate (a + b)/c if a = ¾, b = 7/12, and c = ½ B. Solving Linear Equations: students can solve linear equations including equations with variables on both sides of the equal sign, equations which require distribution, and equations with rational coefficients. Students can solve literal equations (i.e. solving for one variable in terms of another variable.) Examples follow. 1. Solve 3 2(n 5) (n 9) = Solve 4n + 6 = 3(n 5) Solve 5n/4 3 = 7 4. Solve 7n 4(n + 2) = 5n 8 5. Solve (2x 7)/3 = (x + 1)/2 6. Solve for b 1 A = h(b 1 + b 2 )/2 C. Lines: Slope and Intercepts: students can calculate the slope of a line given a graph, given two points, or given its equation. Students can calculate the x and y intercepts of a line given its graph or its equation. Students can apply slope and intercept concepts to real life situations. Examples follow. 1. Find the slope of the line shown in the graph.
2 graph for #1 2. Find the slope of the line containing the points P( 6,3) and Q(5,9) 3. Find the slope of the line containing the points R(5,7) and S(5,3) 4. Find the x and y intercepts of the line shown in the graph. graph for #4 5. Find the x and y intercepts of the line 6x 5y = A candle is left to burn. After 2 hours it is inches tall and after 5 hours it is 5.25 inches tall. Find the slope and in a sentence explain what the slope means (i.e. how does slope relate to the burning candle?) D. Lines and their Graphs: students can graph a line from its equation which may be written in either standard form (Ax + By = C) or slope intercept form (y = mx + b). Examples follow. You should graph these on your own graph paper. Be accurate. 1. Graph the line y = ¼ x 6 2. Graph the line y = x 3 3. Graph the line 2x + 3y = 0 4. Graph the line y = 4 5. Graph the line x = 1 E. Lines and their Equations: students can write the equation of a line given a graph, given a point and a slope, given two points, or given a verbal description. Students can write the equation of a line that fits a real life situation. Examples follow. 1. Write the equation of the line shown in the graph.
3 graph for #1 2. Write the equation of the line that contains the point (4, 3) and has a slope of 1/2. 3. Write the equation of the line that contains the points (3,9) and (4,11) 4. Write the equation of the line that is perfectly horizontal and contains the point (4,7) 5. Write the equation of the line that contains the points (7,3) and (7,1) 6. A taxicab company charges $5.00 to send a cab to your location plus $2.25 for every mile the cab takes you. a) Write the equation of the line that fits this situation using m for the number of miles you are driven and C for the cost of your trip. b) If your trip cost $11.75 then how many miles did the cab take you? F. Polynomials: Operations on Polynomials: students can add, subtract, and multiply polynomials. The word simplify will mean to add, subtract, or multiply as indicated in the problem. Examples follow. 1. Simplify 3a 2 5b + 6a 9a 2 + 5b 2. Simplify (7x 2 3x + 4) + (x 2 5x) + (4x 1) 3. Simplify (5x 7)(2x + 3) 4. Simplify (2x 3)(x 2 + x 5) 5. Simplify (7x + 3) 2 6. Simplify (8x 2 + 4x 1) (x 2)(x 9) G. Polynomials: Factoring and Solving Quadratic Equations by Factoring. Students can factor polynomials by factoring out the greatest common term, factoring special cases (difference of two squares and perfect square trinomials), and general factoring. (There are no sum/difference of cubes problems nor factoring by grouping problems.) Students can solve quadratic equations by factoring. (While students are allowed to use the quadratic formula, no problem requires the use of the quadratic formula.) 1. Factor 4x 2 20x 2. Factor 4x Factor x 2 8x Factor 5x 2 5
4 5. Factor 2x 2 x 3 6. Solve x 2 5x 6 = 0 7. Solve 3x 2 + 7x 6 = 0 8. Solve x 2 + 7x 14 = 3x 2 H. Systems of Equations: students can determine if an ordered pair is a solution to a given system of equations. Students can solve a system of equations by graphing. Students can solve a system of equations by the algebraic method of their choice [i.e. The substitution method or the addition method (sometimes called the elimination method.)] Students can determine when a system has no solution. 1. Solve the system of equations by graphing. y = 2x 4 and y = x + 2 graph for #1 2. Solve the system of equations by the algebraic method of your choice 2x 5y = 34 and 4x + 3y = Solve the system of equations by the algebraic method of your choice y = 3x 1 and 5x 2y = 2 4. Solve the system of equations by the algebraic method of your choice 2x y = 4 and 6x + 3y = 5 5. Determine if the ordered pair (1/2, 10) is a solution to the system of equations 2x y = 9 and 4x + y = 11 I. Radicals: students can differentiate between a radical that has been simplified and its decimal approximation. Students can simplify square roots by factoring out the greatest perfect square factor. Students can add, subtract, and multiply radicals. Students will not be required to rationalize denominators. 1. A student was asked to give the exact, simplified value for 12. Which is the correct answer? , , Simplify Simplify Simplify Simplify
5 6. Simplify (2 3)(4 2) 7. Simplify (5 3)(7 6) 8. Simplify (2 3) 2 Extra Credit: Not all 8 th grade Algebra 1 classes teach the same topics. If you have learned how to do the following types of problems then we will give you extra credit. You score will not be hurt by skipping or missing these problems. On the extra credit it is possible you may need to use the quadratic formula. 1. Solve 2x + 3 = Solve (2x + 7) = 5 3. Solve 4/x + (x + 2)/(x + 3) = 4 4. Solve and graph (on a number line) 6 < 5 2x < x Simplify (x + 1)/x + (x + 2)/(x + 3) 6. Simplify (x 2 3x 10)/(x 2 4)
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