Q1. The perimeter of a rectangle is 560 meters. The length is 20 meters less than twice the width. What are the length and width?

• a) Write an equation using the variable “x”.

• b) Solve the equation.

• c) State the answer.

• d) Check your answer.

Background

Topic: Linear Equations and Geometry

This question tests your ability to translate a word problem into an algebraic equation, solve for unknowns, and interpret the solution in the context of geometry (perimeter of a rectangle).

Key Terms and Formulas

• Perimeter of a rectangle:

• Let represent the width. Then, length (since length is 20 meters less than twice the width).

Step-by-Step Guidance

1. Let be the width of the rectangle. Express the length in terms of $x$ using the information given: .

2. Write the perimeter formula for a rectangle: .

3. Substitute the given perimeter ($560LW.

4. Simplify the equation and combine like terms to form a linear equation in .

5. Set up the equation so you can solve for in the next step.

Try solving on your own before revealing the answer!

Q2. A projectile is launched straight from the ground level with an initial velocity of 96 ft/sec. Its height in feet, , after seconds is given by: .

• a) At what time(s) will it reach a height of 80 ft?

• b) After how many seconds will it return to the ground?

Background

Topic: Quadratic Equations and Applications

This question tests your ability to solve quadratic equations in the context of projectile motion, using algebraic methods to find when the projectile reaches a certain height or returns to the ground.

Key Terms and Formulas

• Quadratic equation:

• Projectile motion formula:

• Quadratic formula:

Step-by-Step Guidance

1. For part (a), set and substitute into the equation: .

2. Rearrange the equation to standard quadratic form: .

3. Multiply both sides by to make the leading coefficient positive: .

4. Identify , , for the quadratic formula.

5. Set up the quadratic formula for but do not compute the discriminant or final values yet.

6. For part (b), set (when the projectile returns to the ground): and factor or use the quadratic formula to set up the solution.

Try solving on your own before revealing the answer!

Q3. Dr. Tydings has found that, over the years, 95% of the babies he has delivered weighed pounds, where . What range of weights corresponds to this inequality?

Background

Topic: Absolute Value Inequalities

This question tests your understanding of how to interpret and solve absolute value inequalities, and how to express the solution as an interval.

Key Terms and Formulas

• Absolute value inequality: means

Step-by-Step Guidance

1. Start with the given inequality: .

2. Recall that is equivalent to .

3. Apply this property to the given values: .

4. Set up the range for but do not compute the final interval yet.

Try solving on your own before revealing the answer!

Q4. Solve this equation using 2 methods: factoring, completing the square, or using the quadratic equation:

Background

Topic: Solving Quadratic Equations

This question tests your ability to solve quadratic equations using multiple methods: factoring, completing the square, and the quadratic formula.

Key Terms and Formulas

• Standard form:

• Factoring: Expressing the quadratic as

• Completing the square: ...

• Quadratic formula:

Step-by-Step Guidance

1. First, rewrite the equation in standard form: .

2. Method 1 (Factoring): Try to factor into two binomials.

3. Set each factor equal to zero to find the possible solutions for .

4. Method 2 (Quadratic Formula): Identify , , and set up the quadratic formula for .

5. Write the formula with the values substituted, but do not compute the discriminant or final values yet.

Try solving on your own before revealing the answer!