7th Grade Math Mid-Term Study Guide 2024-2025 PDF

Br. Zeyad Mohamed Al-Ghazaly Jr./Sr. High School Mid-Term Study Guide – 7th Grade (Math) 2024-2025 Please be advised that your Math Mid-Term Exam is based on the following topics. You must study all the top...

Br. Zeyad Mohamed Al-Ghazaly Jr./Sr. High School Mid-Term Study Guide – 7th Grade (Math) 2024-2025 Please be advised that your Math Mid-Term Exam is based on the following topics. You must study all the topics that are mentioned in this study guide. The best way to study and prepare is to go through the study guide topics and practice problems based on it. The practice problems are posted on the Google Classroom. You must understand and solve all the practice problems in order to be prepared for the Mid-Term Exam. JAK! Br. Zeyad 01/10/2025 Chapter.1. Rational Number Operations ►​ 1.1. Relate Integers and Their Operations ​ Absolute value of an integer ​ Combining opposite quantities makes to 0. Example: 6 + (−6) = 0 ​ Absolute value is the distance of a number from 0 ​ Represent change using a + or a − integer ►​ 1.2. Understand Rational Numbers ​ Recognize rational numbers in a fraction form or as a terminating or repeating decimals ​ Concert rational numbers from fraction form to decimal form and vise- a-versa ►​ 1.3 to 1.9. Adding, Subtracting, Multiplying, and Dividing Integers, Decimals, and Fractions ​ Practice Addition, Subtraction, Multiplication, and Division of Integers ​ Subtraction is same as adding the opposite number (remember the Keep-Change-Change Rule) Example: 14 − (−6) = 14 + 6 − 22 – 18 = − 22 + (−18) ​ When you multiply or divide two negative integers, it results into a positive integer ​ Practice Addition, Subtraction, Multiplication, and Division of Decimals and Fractions. ​ While adding or subtracting fractions, make denominator equal. ​ While dividing fractions remember Keep-Change-Flip Rule  ►​ 1.10. Solve Problems with Rational Numbers ​ Practice Word Problems from lesson 1.10 like finding Change in temperature, Finding average of a set of + and − integers Chapter.2. Analyze and Use Proportional Relationships ►​ 2.1. Connect Ratios, Rates, and Unit Rates ​ Find unit rates (rate for one) ​ Compare unit rates to decide which is a better deal or cheaper ►​ 2.2. Identify Unit Rates from Ratios of Fractions ​ Find Unit Rate involving Unit Fractions and any other fraction. (see examples on pages 96, 97 from Volume 1 book) ►​ 2.3. Understand Proportional Relationships: Equivalent Ratios ​ Use equivalent ratio test to decide if quantities are proportional ►​ 2.4. Describe Proportional Relationships: Constant of Proportionality ​ Constant of Proportionality is the same as unit rate and can be calculated by finding y (y divided by x) x ​ Equation of a Proportional Relationship is of the form 𝑦 = 𝑘𝑥 where k is the Constant of Proportionality. ►​ 2.5. Graph Proportional Relationships ​ Graph of Proportional Relationships always pass through the origin (0, 0). Unit rate from the graph is the y value when x=1. ►​ 2.6. Apply Proportional Reasoning to Solve Problems ​ Word problems involving ratios (see examples on page 126 from Volume 1 book) Chapter.3. Analyze and Solve Percent Problems ►​ 3.1. Analyze Percents of Numbers ​ Percent means out of 100. Convert % into a decimal number before using it in a calculation to calculate a part or a whole ►​ 3.2. Connect Percent and Proportion ​ part =100 percent w whole ►​ 3.3. Represent and Use the Percent Equation ​ part = percent × whole part ​ whole =​ percent ►​ 3.4. Solve Percent Change and Percent Error Problems ​ % change = change × 100 original  ​ Change can be increase or decrease ►​ 3.5. Solve Markup and Markdown Problems ​ Markup = % markup × original value ​ Final amount = Original + markup ​ Markdown = % markdown × original value ​ Final amount = Original – markdown ►​ 3.6. Solve Simple Interest Problems ​ Interest = Principal × interest rate × time ​ interest rate (convert in decimal) , time (convert in years) ​ I = P r t Chapter.4. Generate Equivalent Expressions ►​ 4.1. Write and Evaluate Algebraic Expressions ​ Use a variable to write an algebraic expression ​ Substitute the values of the given variables to evaluate the algebraic expression ►​ 4.2. Generate Equivalent Expressions ​ Combine like terms to write or identify equivalent expressions. Like terms are either numbers (constants) or terms with same variable. ​ Use Distributive Property when needed.  Br. Zeyad: 7th Grade Math: Mid-Term Practice Problems: 1.​ What is the absolute value of − 5 ? 2.​ Add: You may use a number line or any method.​ 5 + (− 3) = ​ 3.​ Add:​ − 32 + 32 = ​ 4.​ Add:​ − 6​ +​ 12​ =​ 5.​ Which of these situations can be represented by the opposite of -25? A.​ A scuba diver is 25 feet below sea level. B.​ Ahmed gets paid $25. C.​ An airplane descends 25 feet. D.​ Sara has a $25 debt. 6.​ Choose whether each decimal terminates or repeats. Terminates Repeats 3.232323… 1.789 0.9 9 6.25 7.​ What is the difference between a repeating decimal and a terminating decimal? Explain. 8.​ What is the decimal equivalent of this mixed number 2 1 ? 4 9.​ Order the numbers from least to greatest: 10, 7,​ 5, −3, −5,​ 0,​ 4,​ −8 10.​ The temperature in Anchorage, Alaska, was -3ºC in the afternoon. After the sun went down, the temperature dropped 6 degrees. Write an equation to represent the situation. What was the temperature after the sun went down? 11.​ Maryam and Yara simplified the expression –8 – (–6). Whose answer is correct? Explain where the error was made. Maryam’s Work Yara’s Work –8 – (–6) = –14 –8 – (–6) = –2 1 + 11. Show your work. 12.​ Simplify the expression 20.25 – 9 13.​ Select all the expressions that are equivalent to 1 + 16.15 – 4. – 24 1 – 16.15 + 4 24 2 ​ 16.15 – 28.5 ​ –28.5 + 16.15 1 + 16.5 ​ −20 2 1 ​ 12.15 − 24 2 14.​ Find the quotient. 7 5 1 a.​ ​ ÷​ 1 b.​ 4.2​ ÷​ 5 8 16 7 15.​ In 6 rounds of a game, Kassam scored​ 5, 9, 22, 8, 15, and 9. What integer represents his average score for the 6 rounds? Chapter 2 1.​ The equation y = 5.5x represents a proportional relationship. What is the constant of proportionality? A.​ x B.​ y C.​ 5.5 1 D.​ 5.5 2.​ The tables show the numbers of white and yellow flowers Cara and Hector used in 5 different arrangements. Cara’s Flower Arrangements White 3 6 9 12 15 Yellow 5 10 15 20 25 Part A Are the numbers of white and yellow flowers in Cara’s arrangements proportional? Write an equation that relates the number of yellow flowers, y, to the number of white flowers, w. _ _________________________ Part B Hector’s Flower Arrangements White 4 8 12 16 20 Yellow 6 10 14 18 22 Are the numbers of white and yellow flowers in Hector’s arrangements proportional? Write an equation that relates the number of yellow flowers, y, to the number of white flowers, w. ​  3.​ The graph shows how many bottles a machine fills in a certain number of seconds. a.​ What is the constant of proportionality? ​ b.​ What does the constant of proportionality mean in this situation? c.​ Choose one ordered pair on the graph. What does it represent in this situation?  1 hour. How fast did she walk, in 4.​ Natalie walked 3 mile in miles per hour? 3 m A.​ 10 i 5 B.​ 6 l e p e r h o u r m i l e p e r u h r o C.​ 1 miles per hour 5 D.​ 2 miles per hour 5.​ Sarah used 2.5 cups of cheese in a dish that serves 10 people. Arun used 1.2 cups of cheese in a dish that serves 6 people. How much more cheese is in one serving of Sarah’s dish? Show your work. A.​ 0.5 cup B.​ 0.25 cup C.​ 0.2 cup D.​ 0.05 cup 6.​ A garden hose fills a 2-gallon bucket in 5 seconds. The number of gallons, g, is proportional to the number of seconds, t, that the water is running. Select all the equations that represent the relationship between g and t. g= 5 t 2 t = 0.4g g = 2.5t t = 2.5g 7.​ At the local bakery, Ariel bought 2 oatmeal cookies for $1.50. Mei bought 6 oatmeal cookies for $4.50. Becky bought 8 oatmeal cookies for $6.00. Part A Use a graph to represent the situation.  Part B Do the number of cookies and the cost have a proportional relationship? Explain. Part C What does the point (1, 0.75) represent in this situation? What does the point (0, 0) represent? 3 mile in 10 minutes along the bike trail. 8.​ Luis rides his bicycle 4 Assuming he rides at a constant rate, what is his speed, in miles per hour? 9.​ Henry is making a corn grits-recipe that calls for 1 cup of corn grits for every 1 cups of corn grits? cup of water. How much water will he need if he uses 1 1 10.​Write an equation that relates two proportional quantities x and y if the constant of proportionality is 45? ​ 11.​A graph is a straight line through the point (0, 15). Can the graph represent a proportional relationship? Explain. 3 crate of oranges 12.​A grocery store crate of apples for every manager uses 1 1 in a fruit display. How many crates of oranges will she need if she uses 2 crates of apples?  Chapter 3: 1.​ ​In Game 1, Emerson struck out 30 times in 90 times at bat. In Game 2, he struck out 40 times in 120 times at bat. InGame 3, Emerson struck out 42 times in 140 times at bat. Part A Complete the proportion to represent the percent of strike outs per at-bats. Part B What percentage of times at bat did Emerson actually hit the ball? 2.​ A department store sells a pair of shoes with an 85% markup. If the original price of the shoes was $110, then what is the selling price of the shoes (price after markup)? A.​ $185​ C. $203.50 B.​ $195​ D. $103.50 3.​ Andrew took out a $600 loan from the bank. At the end of 5 years, he pays back the principal, plus $60 of interest. What was the annual interest rate? 4.​ Emily bought a pair of headphones on sale. If they usually cost $39.99, and Emily purchased them at 20% off, how much did she pay? A. $7.99 B. $14.99 C. $31.99 D. $39.74 5.​ During bowling practice, Maryam rolled 42 strikes out of 70 attempts. What percent of Maryam’s attempts were strikes? 6.​ What is 45% of 220? 7.​ Tyson multiplies 75 by 1.25. Which number is Tyson trying to find? A.​ 125% of 75​ C. 12.5% of 75 B.​ 15% of 75​ D. 1.25% of 75 8.​ Show your work to find the price of a $400 telescope after a 65% markup. 9.​ Liu deposited $2,500 into a savings account. The simple interest rate is 4%. How much interest will the account earn in 3 years? Interest = interest rate principal time Interest =​ $​ Interest = $ Chapter 4: 1.​ The price of nails is $1.29/lb, the price of washers is $0.79/lb, and the price of bolts is $2.39/lb. Part A Write an expression to represent the total price of n pounds of nails, w pounds of washers, and b pounds of bolts. Part B What is the total cost of buying 2 pounds of nails, 4 pounds of washers, and 3 pounds of bolts? 2.​ Simplify the expression 2(x − 6) + 2(8). a.​ 2x + 4 b.​ 2x + 2 c.​ x+4 d.​ x+2