Algebra I EOC Review (Part 2)

Size: px
Start display at page:

Download "Algebra I EOC Review (Part 2)"

Transcription

1 1. Let x = total miles the car can travel Answer: x 22 = 18 or x 18 = A = 1 2 ah 1 2 bh A = 1 h(a b) 2 2A = h(a b) 2A = h a b Note that when solving for a variable that appears more than once, consider factoring. The variable being solved for should NEVER be on both sides of the equation. Answer: B. If the gas mileage can vary by 2 miles per gallon from 24 miles per gallon, keep in mind that it can to 22 at the lowest and 26 at the highest. Remember that the absolute-value equation is x m = a. x m = a x 24 = 2 x 24 = 2 or x 24 = 2 x = 26 x = 22 If you forget or think that it could be written as x 2 = 24, just solve to check, like shown above. Answer: x 24 = 22 and x = 22,26 4. y + 2 > 5 y > 7 this means y is STRICTLY GREATER than 7 Testing y = 6 Testing y = 6 Testing y = 8 Testing y = 0 6 > > 7 Note that a good majority of students will think 7 is the answer because they are thinking of the inequality as an equation, y + 2 = 5, and solving for y would make it y = 7. Keep in mind how inequalities behave differently. [ x ] 6 [ ] 7 [ ] 8 [ x ] 0

2 5. Jasmine total savings > Jasmine s sister s total savings w > w 50 + w > 80 w > 0 w > 10 Note that it would take more than 10 weeks for Jasmine to have more money than her sister. Answer: D 6. Remember that rate of change = slope = y Answer: B = distance x time, and in this case, speed = miles hour 7. Remember that the slope-intercept form is y = mx + b [m = slope and b = y-intercept] Answer: y-intercept 8. When finding a relationship from a table, look for PATTERNS. Since the answers are LINEAR functions, find the changes in y and the changes in x. Substituting x-values into the answers is an option, BUT it should not be relied on because the question may NOT be multiple choice. m = y x = 4 2 = 2 Using (6,9): y y 1 = m(x x 1 ) y 9 = 2(x 6) y 9 = 2x 12 y = 2x f(x) = 2x 9. Remember to use y y 1 = m(x x 1 ) and y = mx + b when dealing with linear relationships. m = y = 7 11 = 4 = 2 x Using (0,11): y y 1 = m(x x 1 ) y 11 = 2(x 0) y 11 = 2x y = 2x + 11 To find the x-coordinate of the point that intersects the x-axis is the same as finding the x-intercept (so let y = 0). 0 = 2x x = 11 x = 11 2 Answer: 11 2

3 10. 2x 6y = 15 6y = 2x + 15 y = 2 15 x y = 1 x 5 2 So, m = 1 For parallel lines, use the SAME SLOPE. Using (8,1): y y 1 = m(x x 1 ) y 1 = 1 (x 8) y 1 = 1 x 8 y = 1 x 5 To find the x-intercept, let y = 0 0 = 1 x 5 5 = 1 x 5 = x Answer: 5 or (5,0) 11. Slope of AB = y x = ( 4) = 2 4 = 1 2 For perpendicular lines, use the NEGATIVE RECIPROCAL or 2 Answer: Remember that the slope-intercept form is y = mx + b [m = slope (or rate of change) and b = y-intercept (or CONSTANT)] The constant (or y-intercept), 90, is the initial average temperature at the equator. The slope (or rate of change), 1, is the drop in temperature degree per latitude degree. Answer: A 1. Use x- and y-intercepts to help. x-intercept (let y = 0): y-intercept (let x = 0): 5x + 2y 50 5x + 2y 50 5x + 2(0) 50 5(0) + 2y 50 5x 50 2y 50 x 10 y 25 Note that answer choice D would indicate that the inequality must be GREATER THAN or equal to $50.

4 14. B 15. D 16. C 17. Remember that in order for a relation to be a function, NO x-values can repeat. Answer: D 18. Remember that in order for a relation to be a function, NO x-values can repeat. [ x ] 5 [ ] 1 [ ] 0 [ x ] 2 [ ] 11 [ ] This is a DISCRETE graph, so each x- and y-value has to be listed for the domain and range. Answer: B 20. Note that OPENED CIRCLES in a graph CANNOT have: - equal signs in the inequality - brackets in the interval notation Answer: Domain: { 4 < x } or ( 4,] Range: { 5 < y 2} or ( 5,2] 21. Note that arrows continue to infinity. Since the arrow points at the x = 5 or y =, it does not mean it stops there. Note that < x < 2 is REDUNDANT to write and would be INCORRECT because x < 2 already means all real numbers STRICTLY LESS than 2. and can ONLY be used in INTERVAL NOTATION. Answer: Domain: {x < 2} or (, 2) Range: {y < 0} or (, 0)

5 22. The domain (x-values) for f(x) can only include values greater than or equal to 5. [ x ] f (2 1 ) this one DOES NOT represent the range 2 [ ] f(6) [ ] f( ) [ ] f(100,000) 2. The domain (x-values) for f(x) can only include values STRICTLY greater than 5. [ x ] f(4.8) [ x ] f( 2) [ ] f( 5) [ x ] f(8) [ x ] f ( 1 2 ) [ x ] f(0) [ x ] f(14) [ ] f( 18) 24. Remember that the RANGE is the set of y-values. To find the domain (or x-values) be sure to substitute the range into f(x). f(x) = 6x + 11 f(x) = 6x + 11 f(x) = 6x + 11 f(x) = 6x = 6x = 6x = 6x = 6x = 6x 6 = 6x 24 = 6x 12 = 6x 8 = x 6 = x 4 = x 2 = x [ ] 1 [ x ] 2 [ ] [ x ] 4 [ ] 5 [ x ] 6 [ ] 7 [ x ] Consider that the expression for 5 cents per pencil can be written as 5x, where x represents the number of pencils. Also, the equation can be written as y = 5x, where x represents the domain. For 0 pencils: For 1 pencil: For 2 pencils: For 20 pencils: f(0) = 5(0) f(1) = 5(1) f(2) = 5(2) f(20) = 5(20) f(0) = 0 cents f(1) = 5 cents f(2) = 10 cents f(20) = 100 cents Since only 0,1, 2,, or 20 pencils can be purchased, the domain is the integers from 0 to 20. Answer: A 26. Note that x represents the pairs of sunglasses, and C(x) represents the total cost.

6 27. Note that n is the domain and represents the number of customers, and it goes up to 100 people. Note that M(n) is the range and represents the amount of money the theater takes in on Thursday nights. Answer: D 28. Note that t is the domain and represents the time in weeks. Note that P(t) is the range and represents the population growth. 29. Note that n is the domain and represents the number of tickets. Note that h(n) is the range and represents the amount of money a movie theater receives. 0. Note that the function is supposed to model the population from 1900 (x = 0) to 2000 (x = 10). Answer: D 1. Since the domain of the function in the graph is all real numbers, the functions listed must also have all real numbers. - The domains of f(x) and g(x) cannot have all real numbers because you cannot get a real number if you take the square root of a negative number. - h(x) allows any x-value to be substituted. - The domain of k(x) is restricted only real numbers greater than or equal to In order to find the fastest speed, find the greatest slope between each interval or look for the STEEPEST slope. 0 x 0.5 m = y x = = x 2 m = y x = = x 2.5 m = y x = 0 (H.O.Y.) 2.5 x 4 m = y x = = 1 1 Answer: 0.5 x 2

7 . There are two criteria: i. Obtaining a greater y-intercept from the table. ii. Obtaining a perpendicular slope from the equation. i. m = y x = 8 4 = 2 1 = 2 Using ( 1, 6): y y 1 = m(x x 1 ) y ( 6) = 2(x ( 1)) y + 6 = 2(x + 1) y + 6 = 2x + 2 y = 2x 4 Use a number greater than the y-intercept of 4. ii. y x = 2 y = 1 4 x + 2 So, m = 1 4 For perpendicular lines, use the NEGATIVE RECIPROCAL. Since the slope of the equation is 1, then the slope to use is 4. 4 Therefore, you can make up a linear function, such as y = 4x. Answer: 4. Note that average rate of growth refers to average rate of change (or slope). Average rate of growth = slope = y = meters = 1 meter = 0.5 meter/year x 6 years 2 years Answer: B

8 5. Remember that average rate of change refers to slope. To find the average rate of change (or slope), first identify the (x, y) coordinates. For x = 9 For x = 21 f(x) = 2 x 5 + f(x) = 2 x 5 + f(9) = 2 (9) 5 + f(21) = 2 (21) 5 + f(9) = f(21) = f(9) = 2(2) + f(21) = 2(4) + f(9) = 4 + f(21) = 8 + f(9) = 7 f(21) = 11 (9, 7) is one point (21, 11) is another point So, the average rate of change = slope = y x = = 4 12 = 1 6. Remember that (average) rate of change refers to slope. To find the (average) rate of change (or slope), first identify the (x, y) coordinates. For a radius of 4 inches For a radius of 12 inches A(r) = πr 2 A(r) = πr 2 A(4) = π(4) 2 A(12) = π(12) 2 A(4) = π(16) A(12) = π(144) A(4) = 16π A(12) = 144π (4, 16π) is one point (12, 144π) is another point So, the rate of change = slope = y = 144π 16π = 128π = 16π = 16π 50. x Answer: 16π or Remember that average rate of change refers to slope. To find the average rate of change (or slope), first identify the (x, y) coordinates. For t = 1.5 seconds For t = 1.75 seconds (1.5, 12) is one point (1.75, 7) is another point So, the average rate of change = slope = y = 7 12 = 5 = 20 x Answer: A

9

10 9. Remember that slope-intercept is y = mx + b m = slope (or SPEED) and b = y-intercept (or starting point) For d = 1 15 t + 1, Monika s speed is 1 mile 15 minutes Note that if Mark s speed is as fast as Monika s speed, then he is slower than Monika. 4 So, 1 = 1 Mark s speed a. d = 1 20 t b. Note that running one time around the park would indicate a 7-mile run, so the range would be from 0 to 7 miles. c. Domain: {0 x 140} or [0,140] 40. Remember that the x-intercepts are when y = 0, so this refers to ( 1,0) and (,0) from the table. x y Find the x-intercepts of each answer choice to find which has the same as f(x). g(x) = 2x + 2 h(x) = 1 x + 2 j(x) = x2 + 2x k(x) = x = 2x = 1 x = x2 + 2x 0 = x 1 2 2x = 2 1 x = 2 0 = (x + )(x 1) 2 = x 1 x = 1 x = 6 x =, 1 x = 1, Answer: D

11 41. A way to determine which function matches the graph, select one point on the graph to substitute into each function. I suggest using ( 2, 4): g(x) = x g(x) = x g(x) = x g(x) = x = ( 2) = ( 2) = ( 2) = ( 2) = = = 4 ALTERNATIVE: Sketch what f(x) = x looks like and see which transformations match. For g(x) = x 2 + 4, this is the same as g(x) = f(x 2) + 4, which shifts right 2 units and up 4 units. For g(x) = x + 2 4, this is the same as g(x) = f(x + 2) 4, which shifts left 2 units and down 4 units. For g(x) = x + 4 2, this is the same as g(x) = f(x + 4) 2, which shifts left 4 units and down 2 units. For g(x) = x 4 + 2, this is the same as g(x) = f(x 4) + 2, which shifts right 4 units and up 2 units. Answer: B 42. Note that f(x) = x is the parent function. Consider that: - f(x + 2) means the graph shifts left 2 units. - f(x) + 2 means the graph shifts up 2 units. - 2f(x) means the graph vertically stretches by a factor of f(x) means the graph vertically shrinks by a factor of Substitute f(x) = 5x + 2 y = f(x) 4 y = (5x + 2) 4 y = 5x y = 5x 2 Answer: y = 5x 2

12 44. Remember that translating ANY function 8 units to the right can be written as f(x 8). f(x) = 1 2 x f(x 8) = 1 (x 8) 2 f(x 8) = 1 x f(x 8) = 1 2 x + 1 Answer: y = 1 2 x Remember that translating ANY function 2 units to the left can be written as f(x + 2). f(x) = x 2 4x f(x + 2) = (x + 2) 2 4(x + 2) f(x + 2) = (x + 2)(x + 2) 4x 8 f(x + 2) = x 2 + 4x + 4 4x 8 f(x + 2) = x 2 4 Answer: y = x Remember that the area of a rectangle is A = bh. A = bh A = (x + 4)(2x + 1) A = 2x 2 + x + 8x + 4 A = 2x 2 + 9x Since x + 8 is the height and the height is 20 cm, set x + 8 = 20, which x = 12. Use x = 12 to substitute to the other dimensions. a. For (x + 1) dimension For (x ) dimension (12) + 1 = 1 (12) = 9 Answer: 1 cm and 9 cm b. Since the volume of the rectangular pyramid is represented by 1 (x + 1)(x )(x + 8), then 1 (1)(9)(20) = 780 Answer: 780 cm

13 48. f(x) + g(x) f(x) g(x) (x 2 x 2) + (x 2 + x 6) (x 2 x 2) (x 2 + x 6) be sure to use PARENTHESIS!!! x 2 x 2 + x 2 + x 6 x 2 x 2 x 2 x + 6 2x 2 8 2x + 4 Answer: Quadratic Answer: Linear f(x) = x2 x 2 = (x 2)(x+1) = x+1 f(x) g(x) g(x) x 2 +x 6 (x 2)(x+) x+ (x 2 x 2)(x 2 + x 6) Answer: Neither x 4 + x 6x 2 x x 2 + 6x 2x 2 2x + 12 x 4 9x 2 + 4x + 12 Answer: Neither 49. To find the base of the shaded region, take (x + 10) (x + 4), which is 2x + 6. So, the base of the shaded region = 2x + 6 and the height of the shaded region = x + 5 a. Perimeter = (2x + 6) + (2x + 6) + (x + 5) + (x + 5) = 2(2x + 6) + 2(x + 5) = 4x x + 10 = 6x + 22 Answer: (6x + 22) units b. Area = (2x + 6)(x + 5) = 2x x + 6x + 0 = 2x x + 0 Answer: (2x x + 0) units Area of shaded region = area of bigger rectangle area of smaller rectangle 24 = (x 2)(x + ) (6)(x) 24 = (x 2 + 9x 2x 6) 6x 24 = x 2 + x 6 0 = x 2 + x 0 0 = (x + 10)(x ) x = 10, Remember that there cannot be negative dimensions, so ignore 10. Answer: B 51. Remember to SUBTRACT exponents when dividing the same bases. x 18 y 12 +x 9 y 8 x y 4 = x18 y 12 x y 4 + x9 y 8 x y 4 = x15 y 8 + x 6 y 4

14 52. Completely factor the numerator. x 2 27 x Answer: A = (x2 9) x = (x+)(x ) x = (x+) = (x + ) 1 5. Remember that y = f(x). The answer choices are comparing the RANGE (or y-values), since they are given as f( 2), f( 1), g( 2), g(0), It is highly recommended to sketch the graphs of g(x) and f(x) by using the given vertex and zeros (or x-intercepts). To write f(x) as a function: - Write the zeros x = 2 and x = 4 as factors (x + 2) and (x 4). - y = (x + 2)(x 4) could give the equation y = x 2 2x But the vertex of this equation would be (1, 9) - Multiplying the equation by 1 (or reflecting over x-axis) would give y = 1(x 2 2x + 8), which then has the same given vertex, (1,9), from the question So, f(x) = x 2 + 2x 8 and g(x) = x + 2 Then the x-values can be substituted to check which has the greater y-value. [ ] f( 2) is greater than g( 2) [ ] f( 1) is greater than g(0) [ x ] f(0) is greater than g(0) [ ] f(1) is less than g(1) [ x ] f(2) is greater than g(2)

15 54. C 55. Since g(x) = k f(x), then finding the value of k can be written as k = g(x) f(x). Write the linear functions for g(x) and f(x): - g(x) = 6x - f(x) = 2x + 1 So, k = g(x) f(x) = 6x 2x+1 = (2x 1) ( 1)(2x 1) = Answer: k = 56. Remember that finding the y-intercept is setting x = 0 (or t = 0 in this case). y = 16t t + y = 16(0) (0) + y = this is the initial height Note that y represents the height in feet, and t represents the seconds after the ball is thrown. 57. Note h(t) represents the height and t represents the time. 58. B

16 59. It is required to solve this quadratic equation by completing the square. Moving to the LEFT side of the equal sign: Moving 7 to the RIGHT side of the equal sign: 4x 2 24x + 7 = 4x 2 24x + 7 = 4x 2 24x + 4 = 0 4x 2 24x = 4 4(x 2 6x) + 4 = 0 4(x 2 6x) = 4 4(x 2 6x + 9) = 0 4(x 2 6x + 9) = (x )(x ) 2 = 0 4(x )(x ) = 2 4(x ) 2 2 = 0 4(x ) 2 = 2 4(x ) 2 = 2 4(x ) 2 = 2 (x ) 2 = 8 (x ) 2 = ± 8 x = ± 8 x = ± 8 also note that it can be written as x = ± 2 2 Step: 4(x [ ]) 2 = [ 2 ] Solution: x = [ ] ± [ 8 ] 60. It is required to solve this quadratic equation by completing the square. Moving 4 to the LEFT side of the equal sign: Moving 7 to the RIGHT side of the equal sign: x 2 12x + 7 = 4 x 2 12x + 7 = 4 x 2 12x + = 0 x 2 12x = (x 2 4x) + = 0 should not factor by GCF (x 2 4x) = should not divide by on both sides (x 2 4x + 4) 12 + = 0 (x 2 4x + 4) = + 12 (x 2)(x 2) 9 = 0 (x 2)(x 2) = 9 (x 2) 2 9 = 0 (x 2) 2 = 9 (x 2) 2 = 9 (x 2) 2 = 9 (x 2) 2 = (x 2) 2 = ± x 2 = ± x = 2 ± Step: (x [ 2 ]) 2 = [ 9 ] Solution: x = [ 2 ] ± [ ] 61. Note that C represents the production cost, and since the cost needs to be at or below $115,000, the constraint of range (or y-values) must be less than or equal to $115,000. Note that x represents the number of balls produced in one day, and it cannot be negative. Answer: D

17 62. Recall that finding the zeros is finding the x-intercepts (or setting y = 0 or f(x) = 0) f(x) = (x 2 + 2x 8)(x 6) 0 = (x 2 + 2x 8)(x 6) 0 = (x + 4)(x 2)(x 6) x + 4 = 0 x 2 = 0 x 6 = 0 x = 4 x = 2 x = 6 ( 4,0) (2,0) (6,0) [ x ] (2,0) [ x ] (6,0) [ ] (0, 8) [ x ] ( 4,0) [ ] ( 6,0) [ ] (0,2) [ ] (0,8) 6. Recall that the formula to find the axis of symmetry is x = b So, x = b 2a = 6 2() = 1 Answer: B 2a 64. Note that t represents the time in minutes, and to find the time for the water to DRAIN refers to finding the xintercepts. Answer: D Note that the PROPERTY the question is referring to is the ZERO PRODUCT PROPERTY, which is setting the factors equal to zero. Also, note that although answer choice C does find the zeros of the function, it is NOT using the Zero Product Property to find the x-intercepts. When solving the function by completing the square, it is finished by using square roots. 0 = 4t 2 2t = 4t 2 2t = (2t 7)(2t 9) 0 = 4(t 2 8t) = 4(t 2 8t + 16) The Zero Product Property allows: 0 = 4(t 4)(t 4) 1 2t 7 = 0 2t 9 = 0 0 = 4(t 4) 2 1 would then be solved by using square roots Answer: B

18 65. Remember that exponential growth function is y = a(1 + r) t, and when 1 + r is greater than 1, it is a growth. [ x ] f(t) = 1.25 t [ ] f(t) = 2(0.9) 0.5t [ x ] f(t) = (1.07) t [ ] f(t) = 18(0.85) t [ x ] f(t) = 0.5(1.05) t [ x ] f(t) = (1.71) 5t [ ] f(t) = t [ x ] f(t) = 8(1.56) 1.4t 66. Remember that the exponential function is y = a b x [a = y-intercept (or initial value) and b = common ratio] 67. Remember that the exponential function is y = a b x, [a = y-intercept (or initial value) and b = common ratio] Note that t represents the time in years, and y represents the estimated number of elephants. If the base years is worked back to t = 0, that would be the y-intercept (or initial value). Year Base Year Estimated Number of Elephants , , , , ,571 Answer: B 68. Remember that the exponential growth function is y = a(1 + r) t, and when 1 + r is greater than 1, it is a growth. Note that 44,000 is the initial value. Note that = 1 + r, so r = Then changing this decimal to a percent is 4.5%. [ x ] Johanna initially earns $44,000 per year. [ ] Johanna initially earns $45,980 per year. [ ] Johanna s salary increases by 1.045% per year. [ x ] Johanna s salary increases by 4.5% per year. [ ] Johanna s salary increases by 104.5% per year

19 69. Remember that the exponential growth function is y = a(1 + r) t, and when 1 + r is greater than 1, it is a growth. a. Note that r = 0.025, so changing this decimal to a percent is 2.5%. Answer: 2.5% b. Increasing by 0.4% would be 2.5% + 0.4% = 2.9%, and changing this percent to a decimal is f(x) = 2,400( ) x Answer: f(x) = 2,400(1.029) x 70. Recall that the compound interest function is A = P (1 + r n )nt, but compounding ANNUALLY is the SAME as the formula used for exponential growth. A = P (1 + r 1 )1t annually means that n = 1 A = P(1 + r) t y = a(1 + r) t y = a(1 + r) t y = 1000( ) t V(t) = 1000(1.08) t Answer: D simplified same as the exponential growth function 71. Remember that the exponential decay function is y = a(1 r) t. Since the value of the car DEPRECIATES, it is referring to a DECREASE, so use the exponential growth function. y = a(1 r) t y = 60,000(1 0.15) t y = 60,000(0.85) t f(x) = 60,000(0.85) x Answer: D 72. Note that if Bill plans to charge DOUBLE the amount every week, the ratio is 2 (r = 2). Note that this should NOT be confused with exponential growth or decay. Also, note that this should NOT be confused with the exponential function, y = a b x. To test that this DOES NOT work, use x = 1 for one week versus x = 2 for two weeks. Instead, this requires the geometric sequence formula, a n = a 1 r n 1.

20 7. Note that the salesperson starts with a monthly salary of $500, which acts as the initial value (or y-intercept) on the graph. Note that since the salesperson also gets an additional percentage based on what he sells, it refers to the average rate of change (or slope). Answer: A 74. Note that in order to have a linear relationship (or straight line) on the graph between two points, the slope must have a CONSTANT rate of change. When there is a horizontal slope, the rate of change is zero. H 0 zero slope Y Answer: 75. Since both functions f(x) and g(x) are equal to each other ONLY WHEN x = 1 and x =, they also both share the SAME y-values at x = 1 and at x =. If there at least two ordered pairs, g(x) can be written as a linear function. In order to get the ordered pairs, using x = 1 and x = in f(x) will obtain the y-values. For x = 1 For x = f(x) = 2 x f(x) = 2 x f(1) = 2 1 f() = 2 f(1) = 2 f() = 8 (1,2) is one point (,8) is another point To create a linear function for g(x): m = y = 8 2 = 6 = x 1 2 Using (1,2): y y 1 = m(x x 1 ) y 2 = (x 1) y 2 = x y = x 1 Answer: g(x) = x 1

21 76. Since both functions f(x) and g(x) are equal to each other ONLY WHEN x = 0 and x = 2, they also both share the SAME y-values at x = 0 and at x = 2. If there at least two ordered pairs, g(x) can be written as an exponential function. In order to get the ordered pairs, using x = 0 and x = 2 in f(x) will obtain the y-values. For x = 0 For x = 2 f(x) = 2 x + 4 f(x) = 2 x + 4 f(0) = 2 (0) + 4 f(2) = 2 (2) + 4 f(0) = 4 f(2) = + 4 f(2) = 1 (0,4) is one point (2,1) is another point To create an exponential function for g(x): x f(x) Note that the pattern is 1 4, and since there are 2 jumps, take the square root, so 1 4 = 1 2 = r. Remember that the exponential function is y = a b x. y = a b x y = 4 ( 1 2 )x Answer: g(x) = 4 ( 1 2 )x

22 77. To know what numbers to use, create 20 empty spaces. i. Before attempting to create a list of numbers from the box plot, FIRST identify the FIVE-NUMBER SUMMARY. Minimum: 58 First quartile (Q1): 62 Median: 65 Third quartile (Q): 70 Maximum: 76 ii. Then place the five-number summary around the list of 20 spaces. iii. Then consider how the 10 other points already listed can be placed in the spaces. iv. Lastly, select remaining numbers that will properly fit in the list. Sample Answer: 78. C 79. Remember than if the correlation coefficient is: - close to 1 or 1, then it is a STRONG correlation - close to 0, then it is a WEAK correlation. Negative correlation: 1 r < 0 Positive correlation: 0 < r 1 Since 0.4 is closer to 0 than 1, then it is a weak correlation. Note that a WEAK correlation means that the scattered points are NOT close to the LINE OF BEST FIT. Answer: B

23 80. Note that a residual plot is created from a line of fit through a scattered plot, and the points should be evenly distributed above and below the horizontal line of the residual plot. Note that this residual plot starts with points above the line, and for the other half, it ends with points below the line. Thus, this would NOT be a good model. [ ] It would be a good model because residual plot indicates a strong linear trend. [ ] It would be a good model because the residual values are allowed to form a linear pattern. [ ] It would be a good model because there seems to be an equal number of points above and below the x-axis. [ x ] It would not be a good model because the points on the residual plot have a linear pattern. [ x ] It would not be a good model because the points on the residual plot are not randomly distributed. [ ] It would not be a good model because the points are too far from 0. [ x ] It would not be a good model because the residual values should be randomly distributed and have values close to 0. Px + Qy = R 81. Note that since (, 1) is a solution to {, any manipulation can be done to either equation, AS LONG AS Fx + Gy = H is it done evenly to the equations (PROPERTIES OF EQUALITY). (P + F)x + (Q + G)y = R + H [ x ] { Fx + Gy = H (P + F)x + Qy = R + H [ ] { Fx + (G + Q)y = H Px + Qy = R [ ] { (P + F)x + (Q + G)y = H + R Px + Qy = R [ x ] { (F 2P)x + (G 2Q)y = H 2R Px + Qy = R [ x ] { 5Fx + 5Gy = 5H the 2 nd equation is added to the 1 st equation cannot add a PART of one equation to another equation (must use entire equation) the 1 st equation that is added to the 2 nd equation is not FULLY multiplied by the 2 nd equation is subtracted by the 1 st equation that is multiplied by 2 the 2 nd equation is multiplied by 5 ax + by = c 82. Note that since (10, ) works for {, any manipulation can be done to either equation, AS LONG AS is it fx + gy = h done evenly to the equations (PROPERTIES OF EQUALITY). (a + f)x + (b + g)y = c + h [ x ] { fx + gy = h (a + f)x + (b + g)y = c + h [ ] { (b + f)x + (a + g)y = c + h ax + by = c [ x ] { (a + f)x + (b + g)y = c + h fx + gy = h [ x ] { (f a)x + (g b)y = h c (a f)x + (b g)y = c h [ x ] { ax + by = c [ x ] { ax2 + bxy = xc 5fx 5gy = 5h the 2 nd equation is added to the 1 st equation cannot mix coefficients of different terms the 1 st equation is added to the 2 nd equation the 2 nd equation is subtracted by the 1 st equation the 1 st equation is multiplied by and then subtracted by the 2 nd equation the 1 st equation is multiplied by x, and the 2 nd equation is multiplied by 5 (5a f)x + (b 5g)y = c 5h [ ] { the 1 st equation is NOT multiplied by the same number (same with the 2 nd equation) 2fx + 2gy = 2h ax + by = c [ ] { ax + by = c the 2 nd equation is missing

Algebra I EOC Review (Part 2) NO CALCULATORS

Algebra I EOC Review (Part 2) NO CALCULATORS 1. A Nissan 370Z holds up to 18 gallons of gasoline. If it can travel on 22 miles per gallon in the city, write an equation to model this. 2. Carol wants to make a sculpture using brass and aluminum, with

More information

In #1 and 2, use inverse operations to solve each equation. 2.

In #1 and 2, use inverse operations to solve each equation. 2. In #1 and 2, use inverse operations to solve each equation. 1. 3x + 12 + 5x = 7 2. 1 (4x + 10) = x 5 2 3. Alex and Alyssa both have savings accounts. Alex has $515 and saves $23 per month. Alyssa has $725

More information

4x 2-5x+3. 7x-1 HOMEWORK 1-1

4x 2-5x+3. 7x-1 HOMEWORK 1-1 HOMEWORK 1-1 As it is always the case that correct answers without sufficient mathematical justification may not receive full credit, make sure that you show all your work. Please circle, draw a box around,

More information

SY14-15 Algebra Exit Exam - PRACTICE Version

SY14-15 Algebra Exit Exam - PRACTICE Version Student Name: Directions: Solve each problem. You have a total of 90 minutes. Choose the best answer and fill in your answer document accordingly. For questions requiring a written response, write your

More information

Using the Laws of Exponents to Simplify Rational Exponents

Using the Laws of Exponents to Simplify Rational Exponents 6. Explain Radicals and Rational Exponents - Notes Main Ideas/ Questions Essential Question: How do you simplify expressions with rational exponents? Notes/Examples What You Will Learn Evaluate and simplify

More information

UNIT 3: MODELING AND ANALYZING QUADRATIC FUNCTIONS

UNIT 3: MODELING AND ANALYZING QUADRATIC FUNCTIONS UNIT 3: MODELING AND ANALYZING QUADRATIC FUNCTIONS This unit investigates quadratic functions. Students study the structure of quadratic expressions and write quadratic expressions in equivalent forms.

More information

Algebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals

Algebra 1. Math Review Packet. Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals Algebra 1 Math Review Packet Equations, Inequalities, Linear Functions, Linear Systems, Exponents, Polynomials, Factoring, Quadratics, Radicals 2017 Math in the Middle 1. Clear parentheses using the distributive

More information

EOC FSA Practice Test. Algebra 1. Calculator Portion

EOC FSA Practice Test. Algebra 1. Calculator Portion EOC FSA Practice Test Algebra 1 Calculator Portion FSA Mathematics Reference Sheets Packet Algebra 1 EOC FSA Mathematics Reference Sheet Customary Conversions 1 foot = 12 inches 1 yard = 3 feet 1 mile

More information

Solving Multi-Step Equations

Solving Multi-Step Equations 1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving Multi-Step Equations 3. Add/subtract terms to both sides of the equation to get the

More information

(MATH 1203, 1204, 1204R)

(MATH 1203, 1204, 1204R) College Algebra (MATH 1203, 1204, 1204R) Departmental Review Problems For all questions that ask for an approximate answer, round to two decimal places (unless otherwise specified). The most closely related

More information

Checkpoint 1 Simplifying Like Terms and Distributive Property

Checkpoint 1 Simplifying Like Terms and Distributive Property Checkpoint 1 Simplifying Like Terms and Distributive Property Simplify the following expressions completely. 1. 3 2 2. 3 ( 2) 3. 2 5 4. 7 3 2 3 2 5. 1 6 6. (8x 5) + (4x 6) 7. (6t + 1)(t 2) 8. (2k + 11)

More information

Math 3 Variable Manipulation Part 7 Absolute Value & Inequalities

Math 3 Variable Manipulation Part 7 Absolute Value & Inequalities Math 3 Variable Manipulation Part 7 Absolute Value & Inequalities 1 MATH 1 REVIEW SOLVING AN ABSOLUTE VALUE EQUATION Absolute value is a measure of distance; how far a number is from zero. In practice,

More information

Algebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher

Algebra 1 S1 Lesson Summaries. Lesson Goal: Mastery 70% or higher Algebra 1 S1 Lesson Summaries For every lesson, you need to: Read through the LESSON REVIEW which is located below or on the last page of the lesson and 3-hole punch into your MATH BINDER. Read and work

More information

(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks)

(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks) 1. Let f(x) = p(x q)(x r). Part of the graph of f is shown below. The graph passes through the points ( 2, 0), (0, 4) and (4, 0). (a) Write down the value of q and of r. (b) Write down the equation of

More information

My Math Plan Assessment #3 Study Guide

My Math Plan Assessment #3 Study Guide My Math Plan Assessment # Study Guide 1. Identify the vertex of the parabola with the given equation. f(x) = (x 5) 2 7 2. Find the value of the function. Find f( 6) for f(x) = 2x + 11. Graph the linear

More information

Algebra I Vocabulary Cards

Algebra I Vocabulary Cards Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Absolute Value Order of Operations Expression

More information

College Algebra Joysheet 1 MAT 140, Fall 2015 D. Ivanšić. Name: Simplify and write the answer so all exponents are positive:

College Algebra Joysheet 1 MAT 140, Fall 2015 D. Ivanšić. Name: Simplify and write the answer so all exponents are positive: College Algebra Joysheet 1 MAT 140, Fall 2015 D. Ivanšić Name: Covers: R.1 R.4 Show all your work! Simplify and write the answer so all exponents are positive: 1. (5pts) (3x 4 y 2 ) 2 (5x 2 y 6 ) 3 = 2.

More information

Math 2 Variable Manipulation Part 7 Absolute Value & Inequalities

Math 2 Variable Manipulation Part 7 Absolute Value & Inequalities Math 2 Variable Manipulation Part 7 Absolute Value & Inequalities 1 MATH 1 REVIEW SOLVING AN ABSOLUTE VALUE EQUATION Absolute value is a measure of distance; how far a number is from zero. In practice,

More information

Intermediate Algebra Final Exam Review

Intermediate Algebra Final Exam Review Intermediate Algebra Final Exam Review Note to students: The final exam for MAT10, MAT 11 and MAT1 will consist of 30 multiple-choice questions and a few open-ended questions. The exam itself will cover

More information

Midterm Review Packet

Midterm Review Packet Algebra 1 CHAPTER 1 Midterm Review Packet Name Date Match the following with the appropriate property. 1. x y y x A. Distributive Property. 6 u v 6u 1v B. Commutative Property of Multiplication. m n 5

More information

June If you want, you may scan your assignment and convert it to a.pdf file and it to me.

June If you want, you may scan your assignment and convert it to a.pdf file and  it to me. Summer Assignment Pre-Calculus Honors June 2016 Dear Student: This assignment is a mandatory part of the Pre-Calculus Honors course. Students who do not complete the assignment will be placed in the regular

More information

Subtract 6 to both sides Divide by 2 on both sides. Cross Multiply. Answer: x = -9

Subtract 6 to both sides Divide by 2 on both sides. Cross Multiply. Answer: x = -9 Subtract 6 to both sides Divide by 2 on both sides Answer: x = -9 Cross Multiply. = 3 Distribute 2 to parenthesis Combine like terms Subtract 4x to both sides Subtract 10 from both sides x = -20 Subtract

More information

SOLUTIONS FOR PROBLEMS 1-30

SOLUTIONS FOR PROBLEMS 1-30 . Answer: 5 Evaluate x x + 9 for x SOLUTIONS FOR PROBLEMS - 0 When substituting x in x be sure to do the exponent before the multiplication by to get (). + 9 5 + When multiplying ( ) so that ( 7) ( ).

More information

Mock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28}

Mock Final Exam Name. Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) A) {- 30} B) {- 6} C) {30} D) {- 28} Mock Final Exam Name Solve and check the linear equation. 1) (-8x + 8) + 1 = -7(x + 3) 1) A) {- 30} B) {- 6} C) {30} D) {- 28} First, write the value(s) that make the denominator(s) zero. Then solve the

More information

Pre-AP Algebra II Summer Packet

Pre-AP Algebra II Summer Packet Summer Packet Pre-AP Algebra II Name Period Pre-AP Algebra II 2018-2019 Summer Packet The purpose of this packet is to make sure that you have the mathematical skills you will need to succeed in Pre-AP

More information

Algebra I Vocabulary Cards

Algebra I Vocabulary Cards Algebra I Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Order of Operations Expression Variable Coefficient

More information

Reading Mathematical Expressions & Arithmetic Operations Expression Reads Note

Reading Mathematical Expressions & Arithmetic Operations Expression Reads Note Math 001 - Term 171 Reading Mathematical Expressions & Arithmetic Operations Expression Reads Note x A x belongs to A,x is in A Between an element and a set. A B A is a subset of B Between two sets. φ

More information

The Ultimate Algebra I Regents Review Guide

The Ultimate Algebra I Regents Review Guide Name Algebra I The Ultimate Algebra I Regents Review Guide Mr. Peralta Individual Score Log: Regents June 2014 August 2014 January 2015 June 2015 August 2015 January 2016 June 2016 August 2016 January

More information

The P/Q Mathematics Study Guide

The P/Q Mathematics Study Guide The P/Q Mathematics Study Guide Copyright 007 by Lawrence Perez and Patrick Quigley All Rights Reserved Table of Contents Ch. Numerical Operations - Integers... - Fractions... - Proportion and Percent...

More information

Unit 3: Linear and Exponential Functions

Unit 3: Linear and Exponential Functions Unit 3: Linear and Exponential Functions In Unit 3, students will learn function notation and develop the concepts of domain and range. They will discover that functions can be combined in ways similar

More information

Math 1 Unit 1 EOC Review

Math 1 Unit 1 EOC Review Math 1 Unit 1 EOC Review Name: Solving Equations (including Literal Equations) - Get the variable to show what it equals to satisfy the equation or inequality - Steps (each step only where necessary):

More information

1. Find all relations which are functions. 2. Find all one to one functions.

1. Find all relations which are functions. 2. Find all one to one functions. 1 PRACTICE PROBLEMS FOR FINAL (1) Function or not (vertical line test or y = x expression) 1. Find all relations which are functions. (A) x + y = (C) y = x (B) y = x 1 x+ (D) y = x 5 x () One to one function

More information

Algebra I EOC Review (Part 3)

Algebra I EOC Review (Part 3) 1. Statement Reason 1. 2.5(6.25x + 0.5) = 11 1. Given 2. 15.625x + 1.25 = 11 2. Distribution Property 3. 15.625x = 9.75 3. Subtraction Property of Equality 4. x = 0.624 4. Division Property of Equality

More information

Unit 1 Study Guide Answers. 1a. Domain: 2, -3 Range: -3, 4, -4, 0 Inverse: {(-3,2), (4, -3), (-4, 2), (0, -3)}

Unit 1 Study Guide Answers. 1a. Domain: 2, -3 Range: -3, 4, -4, 0 Inverse: {(-3,2), (4, -3), (-4, 2), (0, -3)} Unit 1 Study Guide Answers 1a. Domain: 2, -3 Range: -3, 4, -4, 0 Inverse: {(-3,2), (4, -3), (-4, 2), (0, -3)} 1b. x 2-3 2-3 y -3 4-4 0 1c. no 2a. y = x 2b. y = mx+ b 2c. 2e. 2d. all real numbers 2f. yes

More information

Algebra II Vocabulary Word Wall Cards

Algebra II Vocabulary Word Wall Cards Algebra II Vocabulary Word Wall Cards Mathematics vocabulary word wall cards provide a display of mathematics content words and associated visual cues to assist in vocabulary development. The cards should

More information

4. Solve for x: 5. Use the FOIL pattern to multiply (4x 2)(x + 3). 6. Simplify using exponent rules: (6x 3 )(2x) 3

4. Solve for x: 5. Use the FOIL pattern to multiply (4x 2)(x + 3). 6. Simplify using exponent rules: (6x 3 )(2x) 3 SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I WEEK 1 1. Write the slope-intercept form of an equation of a. Write a definition of slope. 7 line with a slope of, and a y-intercept of 3. 11 3. You want

More information

Unit 4. Exponential Function

Unit 4. Exponential Function Unit 4. Exponential Function In mathematics, an exponential function is a function of the form, f(x) = a(b) x + c + d, where b is a base, c and d are the constants, x is the independent variable, and f(x)

More information

Area Formulas. Linear

Area Formulas. Linear Math Vocabulary and Formulas Approximate Area Arithmetic Sequences Average Rate of Change Axis of Symmetry Base Behavior of the Graph Bell Curve Bi-annually(with Compound Interest) Binomials Boundary Lines

More information

Answer Explanations for: ACT June 2012, Form 70C

Answer Explanations for: ACT June 2012, Form 70C Answer Explanations for: ACT June 2012, Form 70C Mathematics 1) C) A mean is a regular average and can be found using the following formula: (average of set) = (sum of items in set)/(number of items in

More information

ALGEBRA 1 FINAL EXAM TOPICS

ALGEBRA 1 FINAL EXAM TOPICS ALGEBRA 1 FINAL EXAM TOPICS Chapter 2 2-1 Writing Equations 2-2 Solving One Step Equations 2-3 Solving Multi-Step Equations 2-4 Solving Equations with the Variable on Each Side 2-5 Solving Equations Involving

More information

Algebra 32 Midterm Review Packet

Algebra 32 Midterm Review Packet Algebra 2 Midterm Review Packet Formulas you will receive on the Midterm: y = a b x A = Pe rt A = P (1 + r n ) nt A = P(1 + r) t A = P(1 r) t x = b ± b2 4ac 2a Name: Teacher: Day/Period: Date of Midterm:

More information

Subtract 16 from both sides. Divide both sides by 9. b. Will the swing touch the ground? Explain how you know.

Subtract 16 from both sides. Divide both sides by 9. b. Will the swing touch the ground? Explain how you know. REVIEW EXAMPLES 1) Solve 9x + 16 = 0 for x. 9x + 16 = 0 9x = 16 Original equation. Subtract 16 from both sides. 16 x 9 Divide both sides by 9. 16 x Take the square root of both sides. 9 4 x i 3 Evaluate.

More information

MAT 1033 Final Review for Intermediate Algebra (Revised April 2013)

MAT 1033 Final Review for Intermediate Algebra (Revised April 2013) 1 This review corresponds to the Charles McKeague textbook. Answers will be posted separately. Section 2.1: Solve a Linear Equation in One Variable 1. Solve: " = " 2. Solve: "# = " 3. Solve: " " = " Section

More information

Keystone Exam Concept Review. Properties and Order of Operations. Linear Equations and Inequalities Solve the equations. 1)

Keystone Exam Concept Review. Properties and Order of Operations. Linear Equations and Inequalities Solve the equations. 1) Keystone Exam Concept Review Name: Properties and Order of Operations COMMUTATIVE Property of: Addition ASSOCIATIVE Property of: Addition ( ) ( ) IDENTITY Property of Addition ZERO PRODUCT PROPERTY Let

More information

MA.8.1 Students will apply properties of the real number system to simplify algebraic expressions and solve linear equations.

MA.8.1 Students will apply properties of the real number system to simplify algebraic expressions and solve linear equations. Focus Statement: Students will solve multi-step linear, quadratic, and compound equations and inequalities using the algebraic properties of the real number system. They will also graph linear and quadratic

More information

Name: Class: Date: ID: A. c. the quotient of z and 28 z divided by 28 b. z subtracted from 28 z less than 28

Name: Class: Date: ID: A. c. the quotient of z and 28 z divided by 28 b. z subtracted from 28 z less than 28 Name: Class: Date: ID: A Review for Final Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Give two ways to write the algebraic expression z 28 in words.

More information

Notes for exponential functions The week of March 6. Math 140

Notes for exponential functions The week of March 6. Math 140 Notes for exponential functions The week of March 6 Math 140 Exponential functions: formulas An exponential function has the formula f (t) = ab t, where b is a positive constant; a is the initial value

More information

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14

Final Exam A Name. 20 i C) Solve the equation by factoring. 4) x2 = x + 30 A) {-5, 6} B) {5, 6} C) {1, 30} D) {-5, -6} -9 ± i 3 14 Final Exam A Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 1 1) x + 3 + 5 x - 3 = 30 (x + 3)(x - 3) 1) A) x -3, 3; B) x -3, 3; {4} C) No restrictions; {3} D)

More information

Lecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions. Recall that a power function has the form f(x) = x r where r is a real number.

Lecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions. Recall that a power function has the form f(x) = x r where r is a real number. L7-1 Lecture 7: Sections 2.3 and 2.4 Rational and Exponential Functions Recall that a power function has the form f(x) = x r where r is a real number. f(x) = x 1/2 f(x) = x 1/3 ex. Sketch the graph of

More information

CCGPS UNIT 1 Semester 1 COORDINATE ALGEBRA Page 1 of 33. Relationships Between Quantities Name:

CCGPS UNIT 1 Semester 1 COORDINATE ALGEBRA Page 1 of 33. Relationships Between Quantities Name: CCGPS UNIT 1 Semester 1 COORDINATE ALGEBRA Page 1 of 33 Relationships Between Quantities Name: Date: Reason quantitatively and use units to solve problems. MCC9-12.N.Q.1 Use units as a way to understand

More information

Solving Equations Quick Reference

Solving Equations Quick Reference Solving Equations Quick Reference Integer Rules Addition: If the signs are the same, add the numbers and keep the sign. If the signs are different, subtract the numbers and keep the sign of the number

More information

CP Algebra 2 Midterm Review Multiple Choice (40 questions)

CP Algebra 2 Midterm Review Multiple Choice (40 questions) CP Algebra 2 Midterm Review Multiple Choice (40 questions) Evaluate each expression if r = -1, n = 3, t = 12, and w = 1 2. 1. w[t + (t r)] 2. 9r 2 + (n 2 1)t Solve each equation. Check your solution. 3.

More information

Algebra II Vocabulary Cards

Algebra II Vocabulary Cards Algebra II Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Complex Numbers Complex Number (examples)

More information

Solutions Manual for Precalculus An Investigation of Functions

Solutions Manual for Precalculus An Investigation of Functions Solutions Manual for Precalculus An Investigation of Functions David Lippman, Melonie Rasmussen nd Edition Solutions created at The Evergreen State College and Shoreline Community College Last edited 9/6/17

More information

Archdiocese of Washington Catholic Schools Academic Standards Mathematics

Archdiocese of Washington Catholic Schools Academic Standards Mathematics 8 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students know the properties of rational* and irrational* numbers expressed in a variety of forms. They understand and use

More information

1. Consider the following graphs and choose the correct name of each function.

1. Consider the following graphs and choose the correct name of each function. Name Date Summary of Functions Comparing Linear, Quadratic, and Exponential Functions - Part 1 Independent Practice 1. Consider the following graphs and choose the correct name of each function. Part A:

More information

Math 1 Unit 1 EOC Review

Math 1 Unit 1 EOC Review Math 1 Unit 1 EOC Review Solving Equations (including Literal Equations) - Get the variable to show what it equals to satisfy the equation or inequality - Steps (each step only where necessary): 1. Distribute

More information

Answer Explanations SAT Practice Test #1

Answer Explanations SAT Practice Test #1 Answer Explanations SAT Practice Test #1 2015 The College Board. College Board, SAT, and the acorn logo are registered trademarks of the College Board. 5KSA09 Section 4: Math Test Calculator QUESTION 1.

More information

Algebra 2. Curriculum (524 topics additional topics)

Algebra 2. Curriculum (524 topics additional topics) Algebra 2 This course covers the topics shown below. Students navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs.

More information

Algebra One Dictionary

Algebra One Dictionary Algebra One Dictionary Page 1 of 17 A Absolute Value - the distance between the number and 0 on a number line Algebraic Expression - An expression that contains numbers, operations and at least one variable.

More information

1. The graph of a quadratic function is shown. Each square is one unit.

1. The graph of a quadratic function is shown. Each square is one unit. 1. The graph of a quadratic function is shown. Each square is one unit. a. What is the vertex of the function? b. If the lead coefficient (the value of a) is 1, write the formula for the function in vertex

More information

PETERS TOWNSHIP HIGH SCHOOL

PETERS TOWNSHIP HIGH SCHOOL PETERS TOWNSHIP HIGH SCHOOL COURSE SYLLABUS: ALGEBRA 1 ACADEMIC Course Overview and Essential Skills This course is a study of the language, concepts, and techniques of Algebra that will prepare students

More information

LT1: Adding and Subtracting Polynomials. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms.

LT1: Adding and Subtracting Polynomials. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms. LT1: Adding and Subtracting Polynomials *When adding polynomials, simply combine like terms. *When subtracting polynomials, distribute the negative to the second parentheses. Then combine like terms. 1.

More information

Algebra, Functions, and Data Analysis Vocabulary Cards

Algebra, Functions, and Data Analysis Vocabulary Cards Algebra, Functions, and Data Analysis Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Complex Numbers

More information

Algebra II Vocabulary Cards

Algebra II Vocabulary Cards Algebra II Vocabulary Cards Table of Contents Expressions and Operations Natural Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers Complex Numbers Complex Number (examples)

More information

Fall 09/MAT 140/Worksheet 1 Name: Show all your work. 1. (6pts) Simplify and write the answer so all exponents are positive:

Fall 09/MAT 140/Worksheet 1 Name: Show all your work. 1. (6pts) Simplify and write the answer so all exponents are positive: Fall 09/MAT 140/Worksheet 1 Name: Show all your work. 1. (6pts) Simplify and write the answer so all exponents are positive: a) (x 3 y 6 ) 3 x 4 y 5 = b) 4x 2 (3y) 2 (6x 3 y 4 ) 2 = 2. (2pts) Convert to

More information

1010 REAL Review for Final Exam

1010 REAL Review for Final Exam 1010 REAL Review for Final Exam Chapter 1: Function Sense 1) The notation T(c) represents the amount of tuition paid depending on the number of credit hours for which a student is registered. Interpret

More information

MAT 135. In Class Assignments

MAT 135. In Class Assignments MAT 15 In Class Assignments 1 Chapter 1 1. Simplify each expression: a) 5 b) (5 ) c) 4 d )0 6 4. a)factor 4,56 into the product of prime factors b) Reduce 4,56 5,148 to lowest terms.. Translate each statement

More information

= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives:

= 9 = x + 8 = = -5x 19. For today: 2.5 (Review) and. 4.4a (also review) Objectives: Math 65 / Notes & Practice #1 / 20 points / Due. / Name: Home Work Practice: Simplify the following expressions by reducing the fractions: 16 = 4 = 8xy =? = 9 40 32 38x 64 16 Solve the following equations

More information

Which boxplot represents the same information as the histogram? Test Scores Test Scores

Which boxplot represents the same information as the histogram? Test Scores Test Scores 01 013 SEMESTER EXAMS SEMESTER 1. Mrs. Johnson created this histogram of her 3 rd period students test scores. 8 Frequency of Test Scores 6 4 50 60 70 80 90 100 Test Scores Which boxplot represents the

More information

Math 46 Final Exam Review Packet

Math 46 Final Exam Review Packet Math 46 Final Exam Review Packet Question 1. Perform the indicated operation. Simplify if possible. 7 x x 2 2x + 3 2 x Question 2. The sum of a number and its square is 72. Find the number. Question 3.

More information

Equations and Inequalities in One Variable

Equations and Inequalities in One Variable Name Date lass Equations and Inequalities in One Variable. Which of the following is ( r ) 5 + + s evaluated for r = 8 and s =? A 3 B 50 58. Solve 3x 9= for x. A B 7 3. What is the best first step for

More information

Algebra I+ Pacing Guide. Days Units Notes Chapter 1 ( , )

Algebra I+ Pacing Guide. Days Units Notes Chapter 1 ( , ) Algebra I+ Pacing Guide Days Units Notes Chapter 1 (1.1-1.4, 1.6-1.7) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order

More information

Rising 8th Grade Math. Algebra 1 Summer Review Packet

Rising 8th Grade Math. Algebra 1 Summer Review Packet Rising 8th Grade Math Algebra 1 Summer Review Packet 1. Clear parentheses using the distributive property. 2. Combine like terms within each side of the equal sign. Solving Multi-Step Equations 3. Add/subtract

More information

Math 75 Mini-Mod Due Dates Spring 2016

Math 75 Mini-Mod Due Dates Spring 2016 Mini-Mod 1 Whole Numbers Due: 4/3 1.1 Whole Numbers 1.2 Rounding 1.3 Adding Whole Numbers; Estimation 1.4 Subtracting Whole Numbers 1.5 Basic Problem Solving 1.6 Multiplying Whole Numbers 1.7 Dividing

More information

King Fahd University of Petroleum and Minerals Prep-Year Math Program Math Term 161 Recitation (R1, R2)

King Fahd University of Petroleum and Minerals Prep-Year Math Program Math Term 161 Recitation (R1, R2) Math 001 - Term 161 Recitation (R1, R) Question 1: How many rational and irrational numbers are possible between 0 and 1? (a) 1 (b) Finite (c) 0 (d) Infinite (e) Question : A will contain how many elements

More information

Spring 06/MAT 140/Worksheet 1 Name: Show all your work.

Spring 06/MAT 140/Worksheet 1 Name: Show all your work. Spring 06/MAT 140/Worksheet 1 Name: Show all your work. 1. (4pts) Write two examples of each kind of number: natural integer rational irrational 2. (12pts) Simplify: ( a) 3 4 2 + 4 2 ) = 3 b) 3 20 7 15

More information

Please print the following information in case your scan sheet is misplaced:

Please print the following information in case your scan sheet is misplaced: MATH 1100 Common Final Exam FALL 010 December 10, 010 Please print the following information in case your scan sheet is misplaced: Name: Instructor: Student ID: Section/Time: The exam consists of 40 multiple

More information

Booker T. Washington Summer Math Packet 2015 Completed by Thursday, August 20, 2015 Each student will need to print the packet from our website.

Booker T. Washington Summer Math Packet 2015 Completed by Thursday, August 20, 2015 Each student will need to print the packet from our website. BTW Math Packet Advanced Math Name Booker T. Washington Summer Math Packet 2015 Completed by Thursday, August 20, 2015 Each student will need to print the packet from our website. Go to the BTW website

More information

Final Exam Study Aid

Final Exam Study Aid Math 112 Final Exam Study Aid 1 of 33 Final Exam Study Aid Note: This study aid is intended to help you review for the final exam. It covers the primary concepts in the course, with a large emphasis on

More information

Solve the following equations. Show all work to receive credit. No decimal answers. 8) 4x 2 = 100

Solve the following equations. Show all work to receive credit. No decimal answers. 8) 4x 2 = 100 Algebra 2 1.1 Worksheet Name Solve the following equations. Show all work to receive credit. No decimal answers. 1) 3x 5(2 4x) = 18 2) 17 + 11x = -19x 25 3) 2 6x+9 b 4 = 7 4) = 2x 3 4 5) 3 = 5 7 x x+1

More information

College Algebra Through Problem Solving (2018 Edition)

College Algebra Through Problem Solving (2018 Edition) City University of New York (CUNY) CUNY Academic Works Open Educational Resources Queensborough Community College Winter 1-25-2018 College Algebra Through Problem Solving (2018 Edition) Danielle Cifone

More information

Name: Geometry & Intermediate Algebra Summer Assignment

Name: Geometry & Intermediate Algebra Summer Assignment Name: Geometry & Intermediate Algebra Summer Assignment Instructions: This packet contains material that you have seen in your previous math courses (Pre- Algebra and/or Algebra 1). We understand that

More information

Final Jeopardy! Appendix Ch. 1 Ch. 2 Ch. 3 Ch. 4 Ch. 5

Final Jeopardy! Appendix Ch. 1 Ch. 2 Ch. 3 Ch. 4 Ch. 5 Final Jeopardy! Appendix Ch. 1 Ch. Ch. 3 Ch. 4 Ch. 5 00 00 00 00 00 00 400 400 400 400 400 400 600 600 600 600 600 600 800 800 800 800 800 800 1000 1000 1000 1000 1000 1000 APPENDIX 00 Is the triangle

More information

ACCELERATED ALGEBRA ONE SEMESTER ONE REVIEW. Systems. Families of Statistics Equations. Models 16% 24% 26% 12% 21% 3. Solve for y.

ACCELERATED ALGEBRA ONE SEMESTER ONE REVIEW. Systems. Families of Statistics Equations. Models 16% 24% 26% 12% 21% 3. Solve for y. ACCELERATED ALGEBRA ONE SEMESTER ONE REVIEW NAME: The midterm assessment assesses the following topics. Solving Linear Systems Families of Statistics Equations Models and Matrices Functions 16% 24% 26%

More information

Ch2 practice test. for the following functions. f (x) = 6x 2 + 2, Find the domain of the function using interval notation:

Ch2 practice test. for the following functions. f (x) = 6x 2 + 2, Find the domain of the function using interval notation: Ch2 practice test Find for the following functions. f (x) = 6x 2 + 2, Find the domain of the function using interval notation: A hotel chain charges $75 each night for the first two nights and $55 for

More information

Georgia Department of Education Common Core Georgia Performance Standards Framework CCGPS Advanced Algebra Unit 2

Georgia Department of Education Common Core Georgia Performance Standards Framework CCGPS Advanced Algebra Unit 2 Polynomials Patterns Task 1. To get an idea of what polynomial functions look like, we can graph the first through fifth degree polynomials with leading coefficients of 1. For each polynomial function,

More information

4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account?

4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account? Name: Period: Date: Algebra 1 Common Semester 1 Final Review Like PS4 1. How many surveyed do not like PS4 and do not like X-Box? 2. What percent of people surveyed like the X-Box, but not the PS4? 3.

More information

Final Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i

Final Exam C Name i D) 2. Solve the equation by factoring. 4) x2 = x + 72 A) {1, 72} B) {-8, 9} C) {-8, -9} D) {8, 9} 9 ± i Final Exam C Name First, write the value(s) that make the denominator(s) zero. Then solve the equation. 7 ) x + + 3 x - = 6 (x + )(x - ) ) A) No restrictions; {} B) x -, ; C) x -; {} D) x -, ; {2} Add

More information

4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account?

4. Based on the table below, what is the joint relative frequency of the people surveyed who do not have a job and have a savings account? Name: Period: Date: Algebra 1 Common Semester 1 Final Review 1. How many surveyed do not like PS4 and do not like X-Box? 2. What percent of people surveyed like the X-Box, but not the PS4? 3. What is the

More information

Variables and Expressions

Variables and Expressions Variables and Expressions A variable is a letter that represents a value that can change. A constant is a value that does not change. A numerical expression contains only constants and operations. An algebraic

More information

MATH 1710 College Algebra Final Exam Review

MATH 1710 College Algebra Final Exam Review MATH 1710 College Algebra Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) There were 480 people at a play.

More information

R1: Sets A set is a collection of objects sets are written using set brackets each object in onset is called an element or member

R1: Sets A set is a collection of objects sets are written using set brackets each object in onset is called an element or member Chapter R Review of basic concepts * R1: Sets A set is a collection of objects sets are written using set brackets each object in onset is called an element or member Ex: Write the set of counting numbers

More information

Chapter 1 Review Applied Calculus 31

Chapter 1 Review Applied Calculus 31 Chapter Review Applied Calculus Section : Linear Functions As you hop into a taxicab in Allentown, the meter will immediately read $.0; this is the drop charge made when the taximeter is activated. After

More information

CHAPTER FIVE. g(t) = t, h(n) = n, v(z) = z, w(c) = c, u(k) = ( 0.003)k,

CHAPTER FIVE. g(t) = t, h(n) = n, v(z) = z, w(c) = c, u(k) = ( 0.003)k, CHAPTER FIVE 5.1 SOLUTIONS 121 Solutions for Section 5.1 EXERCISES 1. Since the distance is decreasing, the rate of change is negative. The initial value of D is 1000 and it decreases by 50 each day, so

More information

0115AI Common Core State Standards

0115AI Common Core State Standards 0115AI Common Core State Standards 1 The owner of a small computer repair business has one employee, who is paid an hourly rate of $22. The owner estimates his weekly profit using the function P(x) = 8600

More information

Chapter 14: Basics of Functions

Chapter 14: Basics of Functions Math 91 Final Exam Study Guide Name Chapter 14: Basics of Functions Find the domain and range. 1) {(5,1), (5,-4), (6,7), (3,4), (-9,-6)} Find the indicated function value. 2) Find f(3) when f(x) = x2 +

More information

Algebra 1 Honors EOC Review #3 Non-Calculator Portion

Algebra 1 Honors EOC Review #3 Non-Calculator Portion Algebra 1 Honors EOC Review #3 Non-Calculator Portion 1. Select any the expressions that are equivalent to 15 3 6 3 3 [A] 15 [B] 1 5 6 1 [C] 3 [D] 5 1 15. Which expression is equivalent to : 3 3 4 8 x

More information

Willmar Public Schools Curriculum Map

Willmar Public Schools Curriculum Map Note: Problem Solving Algebra Prep is an elective credit. It is not a math credit at the high school as its intent is to help students prepare for Algebra by providing students with the opportunity to

More information

Algebra II. Slide 1 / 261. Slide 2 / 261. Slide 3 / 261. Linear, Exponential and Logarithmic Functions. Table of Contents

Algebra II. Slide 1 / 261. Slide 2 / 261. Slide 3 / 261. Linear, Exponential and Logarithmic Functions. Table of Contents Slide 1 / 261 Algebra II Slide 2 / 261 Linear, Exponential and 2015-04-21 www.njctl.org Table of Contents click on the topic to go to that section Slide 3 / 261 Linear Functions Exponential Functions Properties

More information