SKILL: Fraction arithmetic and reducing fractions back to top

Transcription

1 Table of Contents 050 Skills 1) Fraction Arithmetic 2) Check Solution 3) Graphing and Ordered Pairs 4) Finding Intercepts From a Graph 5) Solve a System of Equations 6) Evaluate an Expression with Exponents 055 Skills 1) Finding Factors of a Number 2) ac-method of Factoring 3) Finding Squares and Cubes 4) Square Roots, Cube Roots, nth Roots 5) Solve a Quadratic Equation by Graphing

2 SKILL: Fraction arithmetic and reducing fractions back to top BUTTONS: MATH > FRAC > ENTER Example: Add/subtract and express result in simplest form. 1) Type the expression you want to simplify. Press MATH > ENTER > ENTER to reduce it to simplest form. 2) This will also work to simplify a single fraction.

3 SKILL: Check a solution for accuracy back to top BUTTON: (value) > STO > X > ENTER Example: You find x = 3 4 is a solution to the equation 5x " $ 1 # 2 + 3x % ' = 8 & 3 x 1. IS THE SOLUTION CORRECT? 1) Type the value you want to check and store it with STO > X > ENTER. TI now treats x as ) Type the left side of the EQN as it appears above. The calculator determines the value of the left side to be one. 3) Now check the right side. Its value is also one. ¾ is a good solution.

4 SKILLS: Graph a linear equation in standard view back to top Find ordered pairs on the line (solutions to y = mx + b) BUTTONS: Y = ZOOM 6 2 nd > TABLE Example: Graph the line given by the equation 2x 3y = 3. Then find ordered pairs on the line (solutions to the equation). 1) You must first isolate y (solve for y) in the original equation. Enter the result into Y 1 in the Y= screen. 2) ZOOM 6 gives a standard view of the graph of. 3) 2 nd > TABLE shows ordered pairs on the line. These are solutions to the EQN

5 SKILLS: Find y-intercept and x-intercept from a graph back to top BUTTONS: TRACE (for y-int); 2 nd > CALC > INTERSECT (for x-int) Example: Use a graph to find both intercepts for the line y = 2 x +1 (from previous example). 3 1) The TRACE button finds a y-value when given an x- value. TRACE > 0 > ENTER finds the y-intercept. 2) To find the x-intercept we type Y 2 = 0 in the Y= screen to serve as the x-axis. 3) Now 2 nd > CALC > 5 finds the intersection of our line with x-axis. This intersection is the x-intercept. Notice you must ENTER 3 times.

6 SKILL: Solve a system of 2 linear equations back to top BUTTONS: 2 nd > CALC > INTERSECT Example: Solve the system x 2y = 6 3x + 4y = 8 using a graphing method on your TI. 1) Solve for y in each equation and put into the Y= screen under Y 1 and Y 2. 2) To solve, find the point where the two lines intersect using 2 nd > CALC > 5. The ordered pair solution to this system of equations. is the

7 SKILL: Evaluate an expression with exponents back to top BUTTONS: ALPHA STO> Example: Evaluate ( 2A 3 B 1 C 2 ) 3 when A = 0.5, B = 3, C = 2. 1) You can store values for green variables A-Z using the green ALPHA key. Remember: (value) > STO > variable > ENTER 2) With values stored for A, B and C, type in the expression just the way it appears above. TI evaluates the expression to be 27.

8 SKILL: Find factors of a number back to top BUTTONS: Y= 2 nd > TABLE Example: Find the factors of 90. 1) Go to the Y= screen and type 90/X. 2) 2 nd > TABLE shows factor pairs of the number 90. For example,.

9 SKILL: Factor a trinomial with the ac-method back to top BUTTONS: Y= 2 nd > TABLE Example: Factor 15x x 40 ( a =15, b = 38, c = 40 ) 1) 2) Type what is shown in the picture at left into the Y= screen. 3) Find 38 (that s b) in column Y 2 of the TABLE. Notice -12 and 50 in the same row as 38. The ac-method requires that we rewrite the polynomial in 4 terms by using -12x + 50x for 38x and then factor by grouping.

10 SKILL: Build a list of perfect squares and cubes back to top BUTTONS: Y= 2 nd > TABLE Example: You are investigating the number 125 to see if it is a perfect square or a perfect cube. 1) Go to the Y= screen and type x 2 in Y 1 and x 3 in Y 2. 2) 2 nd > TABLE gives a list of squares in column Y 1 and cubes in Y 2. The number 125 is found in the cubes column. It is the cube of the number 5 which is found in the X column.

11 SKILL: Square roots, cube roots, nth roots back to top BUTTONS: 2 nd MATH 1) Square root using 2 nd. 2) The MATH button has an option for finding cube roots. 3) To find any root with an index higher than 3, you must type the index first, then use the MATH button. Select number 5 on the list.

12 SKILL: Solve a quadratic equation by graphing on your TI back to top BUTTONS: Y= 2 nd > CALC > 5 Example: Solve x 2 x 12 = 0. 1) Y 1 = Y 2 = 0 (to represent x-axis) 2) 2 nd > CALC > 5 > ENTER > ENTER > ENTER finds the first x-intercept. is a solution. 3) 2 nd > CALC > 5 comes first. Now move the cursor to a position closer to the other x- intercept. ENTER > ENTER > ENTER finds the 2 nd solution.

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