Algebra B Midterm Study Guide PDF

Name: Mrs A Date: 1 21 2025 Algebra B MidTerm Study Guide Module 3: Relations and Functions 1) The number of people, f(x), at a tourist destination is a function of time, in months. Using the graph of f...

Name: Mrs A Date: 1 21 2025 Algebra B MidTerm Study Guide Module 3: Relations and Functions 1) The number of people, f(x), at a tourist destination is a function of time, in months. Using the graph of f(x), find f(4). f4 5 1234 2) Select the transformations of ℎ(𝑥) =− 3|𝑥 − 4| + 5 as it relates to the parent function. Select all that apply. (Note: Parent function - f(x) = |x|) Reflection over x-axis 31 x 41 5 Translated left 4 units Reflectionacross x axis Mm Vertical stretch by a factor of 3 Mm Translated up 5 units Mm Translated right 4 units 2 3) For 𝑓(𝑥) = 3𝑥 + 2 and ℎ(𝑥) = 𝑥 − 1, find the value of 4[f(-2) + h(3)]. (Hint: Recall that the number in parentheses is what you plug in for x.) 2 2 213 32 1 Ⓐ 64 32 3 Ⓑ 52 is Ⓒ 16 Ⓓ0 4 4 8 4,644 4) For 𝑓(𝑥) =− 2𝑥 + 3, find the value of f(3) – f(4). Ⓐ -8 f 3 3 f 4 2 4 3 Ⓑ -3 26431 92 Ⓒ 3 Ⓓ5 3 5 3 5 5) Find the range of the function below if the domain is {-2, 1, 3}. (Note: Domain = x-values) 213 5 3 𝑓(𝑥) = 𝑥 + 𝑥 − 5 f 2 2 Ⓐ {-3, -1, 19} 8 2 5 Ⓑ {-1, 7} Ⓒ {-1, 25} Ⓓ {-15, -3, 25} on an is s 3 3 5 f 3 3 3 5 253 6) The distance, f(x), from a house to a cafe is a function of time. Using the graph of f(x), find f(7.5) f 7.5 7.5 t.aus.is 7) Select the transformations of 𝑘(𝑥) = 2 3| − 4 as it relates to the parent 2| − 𝑥 + 3 function. Select all that apply. 4 Reflectedover Yaxis who Reflected over the y-axis Reflected over the x-axis Translateddown 4units 3units mm Translated left 3 units Translated right 3 units translated Verticalstretch left mm Vertical stretch by a factor of 2 Horizontal stretch by a factor of 2 Translated up 4 units mm Translated down 4 units  8) Write an equation for the nth term of the arithmetic sequence 10, 8, 6, 4, … (Note: 𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑) An 10 n 1 2 a first term 10 10 2n 2 d distance 2 An 2n 12 check 92 12 242 Module 4: Linear and Nonlinear Functions 𝑦2−𝑦1 9) What is the slope of the line that passes through (–3, 5) and (3, 6)? (Note: 𝑥2−𝑥1 ) to 1 Ⓐ− 6 Ⓒ0 1 Ⓑ 6 Ⓓ undefined 10) What is the slope of the line that passes through (-3, 2) and (7, 2)? D O Ⓐ1 Tintyisdways equalto2 2 Ⓑ 5 Ⓒ0 i Slope D Mm Ⓓ undefined if x isalwayssame slope isundefined 11) Which equation models the line on the graph? (Note: Use 2 points to find slope. Use where the line crosses the y-axis to find the y-intercept.) b 3 if m y mx b 1 1 Ⓐ𝑦 = 2 𝑥 + 3 Ⓒ 𝑦 =− 2 𝑥 − 6 Ⓑ 𝑦 = 2𝑥 − 6 Ⓓ 𝑦 =− 2𝑥 + 3 12) Find the value of n so that the line through the points has the given slope. (4, 6) and (m, -2) and slope = ½ n E In it iii 13) Find the value of n so that the line through the points has the given slope. 5 (3, 7) and (p, -4) and slope = − n 4 I EE.EE 14) Which equation models the line on the graph? (Note: These are in point-slope form! Find the slope and use one point to create the equation.) y yil m x x nEreases negative Yadsi Ⓐ 𝑦 + 7 =− Ⓑ 𝑦 + 7 =− 3 4 4 3 (𝑥 + 0) (𝑥 + 0) 3 Ⓒ 𝑦 − 7 =− Mm 4 (𝑥 + 0) 4 Ⓓ 𝑦 + 4 =− 3 (𝑥 − 4) 15) Sopha owns a cafe on the verge of shutting down. She charges $7.50 for 3 pancakes and a cup of coffee. She charges $3.00 for one pancake and a cup of coffee. How much does Sophia charge for a pancake? How much does she charge for a cup of coffee? cost of pancake 3x y 7.50 ycostofcottee y 3x hxt.gg 7.5 g x 3.00 y 0.75 fora coffee Check X 2 25 cupot 3 2.25 75 7.50  16) BrightTalk Mobile charges $0.25 per minute plus a monthly base fee. In August, Sarah used 150 minutes, and her bill was $45. a) Write and solve an equation to find the cost of the monthly base fee. let Lynutes 0.25m b Y 45 0.252150 1 b 3 55 338 7.50 monthlybase fee 7 50 b b) Use your equation to find the cost if Sarah uses 180 minutes in September. 0.25m 7.50 Y 0.25 180 7.50 Y Y 4 5 7.50 y 52 50 52.50 totalbill Module 5: Creating Linear Equations 17) Which equation represents a line passing through the point (4, 2) with a 1 slope of 2 ? 1 Ⓐ y= 2 x –2 1 Ⓑ y= 2 x +4 1 Ⓒ y= 2 1 x a c Ⓓ y= 2 18) Which equation represents a line passing through the point (4, 22) with a slope of -2? Ⓐ y = 2x – 22 Ⓑ Ⓒ Ⓓ I y = -2x + 4 y = 2x + 14 y = -2x + 30 22 2 4 30 22 22 O 19) Write the equation of the line that passes through (-6, -2) and is perpendicular to 3 𝑦 = 𝑥 − 5. 3 2 M m 3 Ⓐ𝑦 = 𝑥 − 5 I 2 2 3 1 6 g x 3 Ⓑ𝑦 = 2 𝑥 − 6 2 Ⓒ 𝑦 =− 𝑥 − 2 2 3 4 4 3 Ⓓ 𝑦 =− 2 x M 3 𝑥 − 6 y 3 6 20) Which equation models the line graphed below in point-slope form? (Hint: 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)) 2 2 Ⓐ 𝑦 + 0 =− (𝑥 − 6) Ⓒ𝑦 + 2 = (𝑥 − 3) 3 3 3 3 2 Ⓑ𝑦 − 3 = 2 (𝑥 + 2) Ⓓ𝑦 − 2 = 3 (𝑥 + 3) 21) Determine the values of A, B, and C when y – 3 = 4(x + 2) is written in standard form. Show your work. Axt By C A: 4 3 42 8 B: Y 11 42 y C: 11 44 4 11 22) Determine the values of A, B, and C when y – 5 = -2(x –1) is written in standard form. Show your work. 5 22 2 A: 2 Y 2x 7 y B: C: 7 23) The scatter plot shows the average price of a National Football League ticket from 2007 to 2016. a) Use the points (2007, 67.11) and (2016, 92.98) to write an equation of the line of fit in slope-intercept 6,80 form. Let x be the number of years since 2006. Show your work. 11 2 87 m 92,908 2.87 2345678910 y80 2.8721 6 2.87 6 b 62.7 12.821 62.75 b) If the trend continues, what will be the price of a ticket in 2030? 30 7 1 24 Y 2 87 24 62.75 68.88 131.63 131.63 Module 6: Linear Inequalities 24) Solve and graph -2y > 10. e Ei 25) Which inequalities have no solution? Select all that apply. 3𝑥 + 5 < 3𝑥 + 7 1 5 7 2(𝑥 − 4) ≤ 2(2𝑥 + 3) IiiiEE 4𝑦 + 3 ≤ 2(2𝑦 − 2) − 5𝑥 + 8 ≥− 5(𝑥 + 2) 7𝑧 + 9 ≥ 3(2𝑧 − 4) 26) Javier is taking part in a charity event at his school. Candy is being sold for $3 per bag and cookies are being sold for $6 per bag. What inequality represents the number of bags of candies (x) and the number of bags of cookies (y) that need to be sold to raise at least $600? so Ⓐ 3𝑥 + 6𝑦 ≥ 600 Ⓒ 6𝑥 + 3𝑦 ≥ 600 3211 by 2600 Ⓑ 3𝑥 + 6𝑦 ≤ 600 Ⓓ 6𝑥 + 3𝑦 ≤ 600 27) Solve -8y < –3y + 5 for y. 34 3g E 1 y 7 28) Select the possible solutions of 15𝑥 ≥ 10 + 12𝑥. Select ALL that apply. 124 10 38𝑥 ≥ 3 124 10 𝑥 ≤ 3 𝑥 ≥ 2 32 10 5 𝑥 ≥ 3 3 5 1 we𝑥 ≥ 3 3 10 a 3 ≤𝑥 29) Which graph shows 5𝑥 ≥ 20 or − 𝑥 − 14 13? 14 14 or 3 3 6 62 0 33) Solve and graph 8(− 𝑥 + 1) ≥− 65 and 9 − 8𝑥 ≥− 79 on a number line. 8 82 65 and 9 8 2 79 8 2 73 and 822 88 228 and X 11 X 11 12 98 it 34) A thermometer is accurate within 0.3 degrees Fahrenheit. a) Write an absolute value inequality that represents the possible actual temperature t if the thermometer reads 68.5℉. X 68.51 0.3 b) Solve the inequality and graph it on a number line. 2 68.5 0.3 and 4 68.52 0.3 LEFT x 68.8 and 2268.2 68.2 X 68.8 35) Solve the inequality |2𝑦 + 5| < 15. Then, graph your solution. 5215 and 57 15 24 24 5 and 10 4 y 5 1024 95mmI  x y I 2 icy 36) Graph the inequality 3 𝑥 + 5 − 𝑦 < 6. Give one point that is a solution. AMII 37) Match each of the 3 graphs to its inequality. see video on googleclassroom i) 3x + 6y > -18 ii) 6x + 6y < -18 iii) 6x - 6y > -18 A. B. C. For which graph is (7, 0) a solution? A C 38) Solve and graph the inequality |4x – 7| > 11. 421 7711 or 42 7 11 42 718 44 C 4 1 27 19 x 271 time Module 7: Systems of Equations and Inequalities 39) Which of the following represents a line parallel to the x-axis? Ⓐy=9 So horizontalline b Ⓑy=x y yisalways Ⓒx=1 slope o Ⓓ y=3–x 40) Select all the ways the system of equations could be solved. 8x - 9y = 13 16x + 3y = 22 Ⓐ Multiply the first equation by 2, then subtract the equations. me Ⓑ Multiply the second equation by 3, then subtract the equations. Ⓒ Multiply the first equation by 2, then add the equations. Ⓓ Multiply the second equation by 3, then add the equations. Wh Ⓔ Multiply the second equation by 2, then add the equations. 41) Solve the system of equations using substitution. 1 3 𝑐− 𝑑= 6 2 4 _8 Ed 6 2 48 8 𝑐 = 4𝑑 − 8 2d 4 Ed 6 24 E ge F9 t 42) Solve the system of equations using elimination. ce.d 24,8 1 1 𝑓− 𝑒 = 7 Efi.it niiiii i 4 3 1 1 − 3 𝑒 + 2 𝑓= 9 ÉÉ.FI Trce f 15,8 43) What is the value of x if Lines 1 and 2 are parallel? Line 1: (1, 3) and (4, 7) Line 2: (x, 10) and (2, 6) si sieequae It r Iiii 44) Graph the system of inequalities. 𝑦 ≥ 3𝑥 + 2 E E ositiveid 𝑦