📄 SAT Math: Heart of Algebra Worksheet
📌 1. True / False
1. The graph of a linear equation is always a straight line.
2. A system of two linear equations can have exactly two solutions.
3. The slope of the line represented by \(y = 3x - 5\) is -5.
4. If \(x > y\), then \(-x > -y\).
5. The solution to the equation \(2(x+3) = 10\) is \(x = 2\).
✏️ 2. Fill in the Blanks
🔗 3. Matching
✍️ 4. Short Answer Questions
1. In the equation \(C = 50 + 10h\), where \(C\) is the total cost and \(h\) is the number of hours, what does the number 50 represent in the context of the problem?
2. Write a linear equation in slope-intercept form \(y = mx + b\) for a line that passes through the point \((0, 4)\) and has a slope of -2.
🎯 5. Multiple Choice
1. If \(3x - 4 = 11\), what is the value of \(x\)?
2. Which of the following equations represents a line parallel to \(y = 4x - 7\)?
3. If \(2x + y = 7\) and \(x - y = 2\), what is the value of \(x\)?
📝 6. Open-Ended Questions
1. A gym offers two membership options. Option A costs USD 20 per month plus USD 3 per visit. Option B costs USD 50 per month with unlimited visits. For what number of visits per month is Option A cheaper than Option B?
2. Solve the system of equations:
\[
\begin{cases}
3x + 2y = 12 \\
x - y = 1
\end{cases}
\]
3. The function \(f(x) = -2x + 7\) models the temperature in degrees Celsius at a certain altitude, where \(x\) is the altitude in kilometers.
a) What is the temperature at an altitude of 2 kilometers?
b) At what altitude is the temperature 1 degree Celsius?
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Name Surname: .................................. Date: .... / .... / 202...
Heart of Algebra Worksheet
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SCORE
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A. True (T) / False (F)
| ( .... ) | The graph of a linear equation is always a straight line. |
| ( .... ) | A system of two linear equations can have exactly two solutions. |
| ( .... ) | The slope of the line represented by \(y = 3x - 5\) is -5. |
| ( .... ) | If \(x > y\), then \(-x > -y\). |
| ( .... ) | The solution to the equation \(2(x+3) = 10\) is \(x = 2\). |
B. Fill in the Blanks
| 1) | A .................... is an algebraic expression that contains one or more variables and one or more constants, and involves only addition, subtraction, multiplication, and non-negative integer exponents. |
| 2) | The point where a line crosses the y-axis is called the ..................... |
| 3) | When solving an inequality, if you multiply or divide by a negative number, you must .................... the inequality sign. |
| 4) | A .................... of equations is a set of two or more equations containing common variables. |
| 5) | For a linear equation \(y = mx + b\), the variable \(m\) represents the .................... of the line. |
C. Matching Concepts
| ( .... ) | A set of two or more linear equations involving the same variables. | - Solution to a system |
| ( .... ) | The measure of the steepness of a line, calculated as the ratio of the change in y to the change in x. | - Inequality |
| ( .... ) | The point where a graph intersects the y-axis. | - System of linear equations |
| ( .... ) | A set of values for the variables that satisfy all equations in the system simultaneously. | - Y-intercept |
| ( .... ) | A mathematical statement comparing two expressions using symbols such as \(<, >, \le, \ge\). | - Slope |
D. Short Answer Questions
| 1) | In the equation \(C = 50 + 10h\), where \(C\) is the total cost and \(h\) is the number of hours, what does the number 50 represent in the context of the problem? |
| 2) | Write a linear equation in slope-intercept form \(y = mx + b\) for a line that passes through the point \((0, 4)\) and has a slope of -2. |
E. Multiple Choice Questions
| 1) |
If \(3x - 4 = 11\), what is the value of \(x\)?
A) 3
B) 5
C) 15
D) 7/3
|
| 2) |
Which of the following equations represents a line parallel to \(y = 4x - 7\)?
A) \(y = -4x + 2\)
B) \(y = 1/4 x + 3\)
C) \(y = 4x + 5\)
D) \(y = -1/4 x - 1\)
|
| 3) |
If \(2x + y = 7\) and \(x - y = 2\), what is the value of \(x\)?
A) 1
B) 3
C) 5
D) 9
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F. Open-Ended Questions
| 1) | A gym offers two membership options. Option A costs USD 20 per month plus USD 3 per visit. Option B costs USD 50 per month with unlimited visits. For what number of visits per month is Option A cheaper than Option B? |
| 2) |
Solve the system of equations: \[ \begin{cases} 3x + 2y = 12 \\ x - y = 1 \end{cases} \] |
| 3) |
The function \(f(x) = -2x + 7\) models the temperature in degrees Celsius at a certain altitude, where \(x\) is the altitude in kilometers. a) What is the temperature at an altitude of 2 kilometers? b) At what altitude is the temperature 1 degree Celsius? |
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