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EOC review
eoc review
| Question | Answer |
|---|---|
| What must you do if you multiply or divide both sides of an inequality by a negative number? | Change the inequality sign |
| For linear inequalities, if it is greater than, where do you shade? Less than? | Greater than=shade above, Less than=shade below |
| At most and no more than mean which inequality symbol? | β€ |
| At least or no less than mean which inequality symbol? | β₯ |
| What are the steps to graphing a compound inequality joined by AND? | Use the 3-graph method: Graph each inequality above the number line and draw the INTERSECTION of the two graphs on the final number line. |
| What are the steps to graphing a compound inequality joined by OR? | Use the 3-graph method: Graph each inequality above the number line and draw the UNION of the two graphs on the final number line. |
| Definition of a function. | A relation where each x is paired with exactly one y |
| Whatβs the short cut for recognizing a function in ordered pair form? | If you notice that there is an x value repeated with a different answer for the y value |
| How do you use the vertical line test to tell if a graph is a function? | As the vertical line passes over the graph, the vertical line can only intersect the graph one time |
| If f(x)=3x+4, explain how to find f(4). | Replace the x with 4 and simplify. f(4)=3*4+4 f(4)=16 |
| If g(x)=-2x+5, explain how to solve g(x)=10 | Replace g(x) with 10 and solve for x. 10=-2x+5 x=-5/2 |
| How can you tell if a graph, table, or equation is showing a linear model? | The graph shows a line, the table shows consistent numbering for the x values and repeated addition of the same number for the y values, the equation can be written as slope-intercept form (the exponent of x must be one) or be a special linear equation. |
| If a graph is going uphill from left to right, the graph is said to be. | increasing |
| What is the slope formula? | π¦sub2βπ¦sub1 divided by π₯sub2βπ₯sub1 |
| What is the slope of a vertical line? What is the slope of a horizontal line? | Vertical: Undefined Horizontal: Zero |
| What is the rate of change formula? Rate of change is the same as______ in the context of a word problem. | Difference in the dependent variable Difference in the independent variable Blank: slope |
| hat is the direct variation formula? What letter represents the constant of variation? | π¦ = ππ₯; k is the constant of variation (π ππ π‘βπ π ππππ ππ π ππππππ‘ π£πππππ‘πππ πππ’ππ‘πππ) |
| How do you find βkβ? | y divided by x |
| What is the slope-intercept form of a line? | π¦ = ππ₯ + π |
| What does m and b stand for? | m=slope, b=y-intercept |
| What is the standard form of a line? | π΄π₯ + π΅π¦ = πΆ |
| What are the 3 rules for standard form? | A is non-negative; A, B, & C are integers; A, B, C have a GCF of 1 |
| If you are given a point and a slope, explain how to find the equation. | Substitute the x, y, and m into slope-intercept form and solve for b. Write the equation using m and b. OR plug into point-slope form and isolate y |
| What is the special equation of an undefined line? | π₯ = πππ¦ ππ’ππππ |
| What is the special equation of a zero sloped line? | π¦ = πππ¦ ππ’ππππ |
| How do you find the x and yβintercepts of an equation? | x-int: Substitute 0 for y and solve for x y-int: Substitute 0 for x and solve for y |
| What is true about the slopes of parallel lines? Their y-intercepts? | Parallel lines have the same slopes, but different y-intercepts |
| What is true about the slopes of perpendicular lines? Their y-intercepts? | Perpendicular lines have slopes that are both opposite and reciprocal and can have the same or different y-intercepts |
| In a linear word problem, a one-time fee or starting amount would represent what part of the equation? | The b-value (y-intercept) |
| In a linear word problem, the constant charge per item would represent what part of the equation? | The m-value (the slope) |
| What are the three ways to solve a system? | Graphing, Substitution, and Elimination |
| What should the answer to a system look like? | An ordered pair (intersection point) |
| When will a system have no solution? | Parallel lines |
| When will a system have infinitely many solutions? | Same line (coinciding lines) |
| What keys do you press on your graphing calculator to solve a system? | Y=, enter equations, 2nd TRACE (Calc), 5 (intersection), ENTER, ENTER, ENTER. If graph does not show intersection point, adjust the window. |
| What is the rule of multiplying two powers with the same base? | Keep the base, add the exponents |
| What is the rule of dividing two powers with the same base? | Keep the base, subtract the exponents |
| What is the rule for taking a power to a power? | Keep the base, multiply the exponents |
| Any (nonzero) number to the zero power is equal to what? | 1 |
| List the steps to multiply two numbers in scientific notation. | a) Multiply the numbers. b) Multiply the powers of 10. c) Make adjustments to put in scientific notation |
| List the steps to divide two numbers in scientific notation. | a) Divide the numbers. b) Divide the powers of 10. c) Make adjustments to put in scientific notation |
| What is the rule for changing a negative exponent into a positive? | Move it to the opposite location (numerator/denominator) of the fraction bar and make the exponent positive |
| What would you do to simplify (π₯ + π¦) Β² ? | Write out the binomial multiplied by itself and FOIL |
| To find the degree of a polynomial, find the degree of each term and then take the highest degree of any term. What is the degree of the polynomial 3π₯4 + 2π₯3 β 4π₯2 + 5π₯ β 7 | 4 |
| What should be the first step when you factor? | Look for a GCF |
| List the steps for factoring a trinomial in the form ππ₯2 + ππ₯ + π | Multiply a*c, find the factors that have a sum of b, split the middle term and factor by grouping |
| What is the pattern for difference of perfect squares π₯2 β π¦2? | (π₯ + π¦)(π₯ β π¦) |
| How do you know your final answer of a radical expression is in simplest form? | If there are no perfect square factors under the radical, no fractions under the radical, and no radicals in the denominator |
| What are like terms when adding radicals? | Radicals with the same index and radicand |
| What is the standard form of a quadratic equation? | π¦ = ππ₯2 + ππ₯ + π |
| What does βaβ tell you? | If the parabola opens up or down (if the vertex is a minimum or maximum) and the width of the parabola |
| If the abs value of βaβ was really small, what would be true of the graph? | The parabola would be wide |
| What does the βcβ stand for? | y-intercept |
| How do you find the axis of symmetry? | Use the formula π₯ = βπ divided by 2π |
| How do you find the vertex? | Use the formula π₯ = βπ 2π to find the x-value, substitute the x-value into the original equation, and solve for y. The vertex is an ordered pair. |
| When is the vertex a minimum value? A maximum value? | The vertex is a maximum if the parabola opens down and a minimum if it opens up |
| What are four methods for solving a quadratic equation? | Graphing, square roots, factoring, and the quadratic formula |
| When should you use square roots to solve the quadratic equation? | When the equation is in π¦ = ππ₯2 β π form (NO bx term) |
| What is the quadratic formula? | π₯ = βπΒ±βπ2β4ππ divided by 2π |
| What is the discriminant formula? | π2 β 4ππ |
| How many solutions are there if the discriminant is negative? | no real number solution |
| How many solutions are there if the discriminant is zero? | one real root |
| How many solutions are there if the discriminant is a positive number? | two real roots |
| How many solutions should xΒ²=16 have? What are they? | Two; {-4,4} |
| If the solutions to a quadratic are p and q, the factored form would be? | π¦ = (π₯ β π)(π₯ β π) |
| In a quadratic word problem, when finding when a projectile hits the ground, you are finding what part of the quadratic function? | The positive x-intercept(s). By hand, use factoring or quadratic formula. In the calculator, use 2nd Trace 2:zero |
| In a quadratic word problem, when finding when a projectile reaches its maximum height, you are finding what part of the quadratic function? | The x-value of the vertex. By hand, use π₯ = βπ 2π. In a calculator, use 2nd trace 4:maximum (x-value) |
| In a quadratic word problem, when finding the maximum height of a projectile, you are finding what part of the quadratic function? | The y-value of the vertex. By hand evaluate the function for the x value found using x= βπ 2π. In a calculator, use 2nd trace 4:maximum (y-value) |
| What is the standard form of an exponential equation? | π¦ = π β π to the π₯ power |
| What does βaβ and βbβ stand for? | a is the initial amount, and b the growth or decay factor |
| What are the steps to finding the y-intercept of an exponential function? | Substitute x as 0 and solve for y |
| What is the exponential growth formula? | π¦ = π(1 + π) to the π₯ power |
| What is the exponential decay formula? | π¦ = π(1 β π) to the π₯ power |
| How will you know if the exponential equation is growth or decay? | In equation form: If b is greater than one, it is growth. If b is less than one and greater than zero, it is decay. |
| How will you know if the exponential graph is showing growth or decay? | In graph form: The graph of growth will increase from left to right. For decay, the graph decreases from left to right. |
| What is the formula for half-lives? | π¦ = π(1/2) to the π₯ power x=the number of half lives x can be found by π‘ππ‘ππ π‘πππ divided by π‘πππ πππ 1 βπππ ππππ |
| What is the compound interest formula? | π΄ = π(1 + π/π) to the ππ‘ power |
| What is the difference between an arithmetic and geometric sequence? | Arithmetic sequences add by the same number each time, and geometric sequences multiply by the same number each time |
| What is the EXPLICIT formula for finding the nth term of an arithmetic sequence? | πsubπ = πsub1 + π(π β 1) |
| What is the EXPLICIT formula for finding the nth term of a geometric sequence? | πsubπ = πsub1 β π to the (πβ1) power |
| What is the formal RECURSIVE formula for arithmetic sequences? | π΄πππ‘βπππ‘ππ: πsubπ = πsubπβ1 + π State the first term and π β₯ 2. |
| What is the formal RECURSIVE formula for geometric sequences? | πΊπππππ‘πππ: πsubπ = πsubπβ1 β π State the first term and π β₯ 2. |
| How can you distinguish where data is modeled with linear functions or exponential functions? | Linear functions change at a common difference over equal intervals. An exponential function changes by a common ratio over equal intervals. |
| What is the midpoint formula? | (π₯sub1+π₯sub2)/2 , (π¦sub1+π¦sub2)/2 Average the Xs and the Ys |
| What is the distance formula? | β(π₯sub2 β π₯sub1) to the power of 2 + (π¦sub2 β π¦sub1) to the power of 2 |
| What is the Pythagorean Theorem formula? What kind of triangle do you use it on? | π2 + π2 = π2, πππβπ‘ |
| What math would verify right angles of rectangles and squares? | Use slope to test whether consecutive sides are perpendicular (slopes must be opposite reciprocals). |
| What math would verify opposite sides are parallel in parallelograms. | Use slopes. The slopes of opposite sides must be the same. |
| What math would verify that all sides are congruent in squares or rhombi or that opposite sides are congruent for all parallelograms? | Use the distance formula to make sure the sides are the same length. |
| What is an outlier? | A value in a data set that is much less or much greater than the rest of the data. An outlier is 1.5 times the interquartile range less than the lower quartile or greater than the upper quartile. |
| What is standard deviation? | Variation from the mean |
| What are the calculator keys to find standard deviation? | Stat, Edit (enter data list). Stat, Right Arrow (Calc), Choose 1-Variable Stats. Look for ππ₯ |
| How do you find the line of best fit on a graph and from a table? | Graph-draw a line that goes through as much data as possible and splits any remaining data evenly. Table (using a graphing calculator)-STAT, enter the ordered pairs, STAT, right arrow (CALC), 4 (LinReg), Enter |
| What is a correlation coefficient and what does it tell you about the scatter plot/ line of best fit? | The correlation coefficient is βr,β and it tells you how closely your data fits the line of best fit. The r values range between -1 through +1. |
| What is the difference between correlation and causation? | Correlation is the relationship between two variables. Causation is when one variable directly causes the other variable. |
| How do you clear the memory on the graphing calculator? | 2nd, +, right arrow twice, 7, 1, 2 |
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