Algebra 1 Launch Pad

QUESTION 10 2 Points

Find \(12.5\%\) of \(160\).

Write percent as decimal or fraction first: Ans: ______

Algebra 1 Launch Pad Packet Page 2 of 4

RATIONAL ORBIT • STAGE 3

Real World Operations

STAGE 3

Multi-Step Real World Problems (Questions 11–15)

QUESTION 11 2 Points

Evaluate: \(\frac{2}{3} \times (1.5 - \frac{3}{4})\)

Workspace

Ans: ________________

QUESTION 12 2 Points

Evaluate: \(-0.8 \div \frac{4}{5} - \frac{1}{2}\)

Workspace

Ans: ________________

QUESTION 13 2 Points

A jacket is originally priced at \$84.00. It is on sale for \(25\%\) off. If the NYS sales tax rate is \(8\%\), what is the final price of the jacket including tax?

Workspace

Final Price: \$________________

QUESTION 14 2 Points

A recipe for pancake batter requires \(2\frac{1}{2}\) cups of flour. If Sarah wants to make only \(\frac{3}{4}\) of the recipe size, how many cups of flour should she use?

Workspace

Flour: ________________ cups

QUESTION 15 2 Points

Max's bank balance was \$45.50. He deposited \(3\) checks of \$18.75 each, and then withdrew \$60.00. What is his new bank balance?

Workspace

Balance: \$________________

Algebra 1 Launch Pad Packet Page 3 of 4

RATIONAL ORBIT • CHALLENGE ZONE

Boss Level

BOSS FIGHT

Elite Challenge Problems (Questions 16–18)

CHALLENGE 16 3 Points

Perform the multi-step operation and write the final result as a fraction in simplest form:
\(\left( \frac{5}{6} - 1.25 \right) \div \left( -2\frac{1}{3} \right) + \frac{3}{8}\)

Use a common form (fractions are recommended): Simplest Fraction Ans: ______________

CHALLENGE 17 3 Points

The high temperatures for a 5-day school week in Rochester, NY were: -4.5°C, 2.3°C, -1.8°C, 0.6°C, and -3.1°C. What was the mean daily high temperature, to the nearest hundredth?

Sum the values and divide by 5: Mean: ______________ °C

CHALLENGE 18 3 Points

An investment account of \$1,200 grew by \(15\%\) in year 1. In year 2, the new balance decreased by \(10\%\). Is the final balance higher or lower than the original \$1,200, and by what exact dollar amount?

Calculate year 1, then use that result for year 2: Result: Higher/Lower by $______________

Section 2 Complete!

Page 4 of 4

STAGE 3

Writing & Translating Expressions (Questions 11–15)

QUESTION 11 2 Points

Translate the verbal phrase into an algebraic expression:
"Four less than three times a number, x"

Watch for "less than" order flip!

Expression: ________________

QUESTION 12 2 Points

Translate the verbal phrase into an algebraic expression:
"The product of negative five and the sum of a number, y, and eight"

Parentheses are required for sums.

Expression: ________________

QUESTION 13 2 Points

Write an algebraic expression representing the perimeter of a rectangle with a width of x and a length of \(2x - 3\). Simplify the expression completely.

Formula: \(P = 2L + 2W\)

Simplified: ________________

QUESTION 14 2 Points

Write an expression to represent the total cost of buying s shirts for \$15 each and p pairs of pants for \$32 each, plus a shipping fee of \$6.50.

Workspace

Expression: ________________

QUESTION 15 2 Points

Simplify the following expression completely:
\(4(x + 2) - 3(2x - 1) + 2x\)

Watch out for signs!

Simplest Form: ________________

Algebra 1 Launch Pad Packet Page 3 of 4

EXPRESSION FORCE • CHALLENGE ZONE

Boss Level

BOSS FIGHT

Elite Challenge Problems (Questions 16–18)

CHALLENGE 16 3 Points

Simplify the following expression completely by distributing and combining like terms:
\(-\frac{1}{2}(12x - 8) - \frac{2}{3}(9x - 15) + \frac{1}{4}(16x + 24)\)

Distribute fraction elements carefully: Simplified Expression: ______________

CHALLENGE 17 3 Points

Write an algebraic expression that represents the area of a trapezoid with height h = 4x, and bases b_1 = 3x - 2 and b_2 = x + 6. Simplify the final expression completely.

Formula: \(A = \frac{1}{2}h(b_1 + b_2)\) Area Expression: ______________

CHALLENGE 18 3 Points

If \(x = -2\) and \(y = -3\), evaluate the complex expression:
\(\frac{-3x^3 + 2y^2}{4xy + 14}\)

Substitute, solve numerator and denominator separately: Value: ______________

Section 3 Complete!

Page 4 of 4

Solve: \(5x + 9 = 2x - 12\)

Workspace

x = ________________

QUESTION 12 2 Points

Solve: \(-3(2y - 4) = 18\)

Workspace

y = ________________

QUESTION 13 2 Points

Solve: \(4(w - 2) = 2(w + 5)\)

Workspace

w = ________________

QUESTION 14 2 Points

Solve: \(15 - 2p = 5p + 39\)

Workspace

p = ________________

QUESTION 15 2 Points

Solve: \(3(x - 5) - x = -23\)

Workspace

x = ________________

Algebra 1 Launch Pad Packet Page 3 of 4

EQUATION SENTINEL • STAGE 4

Literal & Advanced Solving

STAGE 4

Advanced Equations & Literal Forms (Questions 16–20)

QUESTION 16 2 Points

Solve: \(\frac{2}{3}(6x - 9) = 3(x + 4) - 20\)

Workspace x = ______________

QUESTION 17 2 Points

Solve: \(12.5 - 2.5y = -3.5y - 7.5\)

Workspace y = ______________

QUESTION 18 2 Points

Solve: \(\frac{3}{4}(12a - 8) = -2(2a - 5) - 3\)

Workspace a = ______________

QUESTION 19 (Literal Equation) 2 Points

Solve the literal equation for the variable w:
\(P = 2l + 2w\)

Isolate the variable w w = ______________

QUESTION 20 (Real World Application) 2 Points

The total cost of printing summer shirts is represented by the formula \(C = 5.50n + 45\), where \(n\) is the number of shirts. If a school spends \$320, how many shirts did they print?

Set C = 320 and solve for n n = ______________ shirts

Section 4 Complete!

Page 4 of 4

Calculate \(k = \frac{y}{x}\): k = ______

QUESTION 7 2 Points

Write an equation for the proportional relationship in Q6.

Format equation as \(y = kx\): Equation: ______

QUESTION 8 2 Points

State the constant of proportionality for the equation:
\(3y = 15x\)

Isolate y to find k: k = ______

QUESTION 9 2 Points

An elevator climbs 45 floors in 15 seconds. If it climbs at a constant rate, write an equation representing the height in floors (\(y\)) after \(x\) seconds.

Find unit rate \(k\), then construct \(y=kx\): Equation: ______________

QUESTION 10 2 Points

A straight line passes through \((0,0)\) and the point \((4, 28)\). What is the equation of this line?

Calculate the unit rate using \((x, y) \rightarrow \frac{y}{x}\): Equation: ______

Algebra 1 Launch Pad Packet Page 2 of 3

PROPORTIONAL PATROL • STAGE 3

Graphs & Applications

STAGE 3

Graphical Analysis & Multi-Step Rates (Questions 11–15)

QUESTION 11 2 Points

The point (1, 3.5) lies on a graph representing a proportional relationship. Describe what this point represents in the context of unit rate.

Explain clearly: Ans: _______________________________

QUESTION 12 2 Points

A map has a scale of 2 inches = 75 miles. If two towns are 6.4 inches apart on the map, what is the actual distance between them in miles?

Set up a proportion: ______ miles

QUESTION 13 2 Points

Store A sells a 5-pound bag of flour for \$4.25. Store B sells an 8-pound bag of the same flour for \$6.40. Which store has the better buy, and what is its unit price?

Calculate unit cost for both stores: Better Buy: _________ at \$______/lb

QUESTION 14 2 Points

A pool fills at a constant rate of 12 gallons per minute. How many hours will it take to fill a 1,800-gallon pool?

Find total minutes, then convert to hours: ______ hours

QUESTION 15 3 Points

If \(y\) is directly proportional to \(x\), and \(y = 15\) when \(x = 6\), find the value of \(y\) when \(x = 10\).

Find constant k first: y = ______

Section 5 Complete!

Page 3 of 3

Q4: -\(\frac{10}{3}\) or -3\(\frac{1}{3}\)

Multiply by Reciprocal: \(-\frac{5}{2} \times \frac{4}{3} = -\frac{20}{6} = -\frac{10}{3}\)

Q5: -18.16

Same signs, add with negative: \(-4.26 + (-13.90) = -18.16\)

Q6: 0.054

Negative times negative is positive: \(0.045 \times 1.2 = 0.054\)

Q7: -5.2

Divide decimals: \(15.6 \div (-3) = -5.2\)

Q8: 0.4375, 43.75%

Divide 7 by 16 = 0.4375, then multiply by 100.

Q9: 42%, \(\frac{4}{9}\), \(0.45\), \(\frac{9}{20}\)

Decimals: \(0.42 < 0.444... < 0.450 < 0.452\)

Q10: 20

Convert: \(12.5\% = \frac{1}{8}\). Then \(\frac{1}{8} \times 160 = 20\)

Q11: \(\frac{1}{2}\) or 0.5

Parentheses first: \(\frac{2}{3} \times (1.5 - 0.75) = \frac{2}{3} \times \frac{3}{4} = \frac{1}{2}\)

Q12: -1.5 or -\(\frac{3}{2}\)

Divide first: \(-0.8 \div 0.8 = -1\). Then \(-1 - 0.5 = -1.5\)

Q13: \$68.04

Sale Price: \(84 \times 0.75 = 63\). Taxed Price: \(63 \times 1.08 = \$68.04\)

Q14: 1\(\frac{7}{8}\) cups

Multiply fractions: \(\frac{5}{2} \times \frac{3}{4} = \frac{15}{8} = 1\frac{7}{8}\) cups

Q15: \$41.75

Balance: \(45.50 + 3(18.75) - 60 = 45.50 + 56.25 - 60 = 41.75\)

CHALLENGE 16: \(\frac{13}{24}\)

\(\left(\frac{5}{6} - \frac{5}{4}\right) \div \left(-\frac{7}{3}\right) + \frac{3}{8} = -\frac{5}{12} \times \left(-\frac{3}{7}\right) + \frac{3}{8} = \frac{5}{28} + \frac{3}{8} = \frac{13}{24}\)

CHALLENGE 17: -1.32°C

Sum: \(-6.60\). Divide by 5: \(-6.60 \div 5 = -1.32°C\)

CHALLENGE 18: Higher by \$42

Year 1: \(1200 \times 1.15 = 1380\). Year 2: \(1380 \times 0.90 = \$1242\). \(1242 - 1200 = +42\)

Algebra 1 Launch Pad Keys Page 2 of 4

EXPRESSION & EQUATION KEY

Section 3 & 4 Answers

SECTION 3

Expression Force Keys (1–18)

Q1: -19

Q2: -18

Q3: \(15w - 20\)

Q4: \(-12a - 21b\)

Q5: \(15x + 7\)

Q6: \(-3a - 4b\)

Q7: \(-2k + 10\)

Q8: \(6p + 7\)

Q9: \(6(3x - 4)\)

Q10: \(9x - 8\)

Q11: \(3x - 4\)

Q12: \(-5(y + 8)\)

Q13: \(6x - 6\)

Q14: \(15s + 32p + 6.50\)

Q15: \(11\)

CHALLENGE 16: \(-8x + 20\)

Steps: \(-6x + 4 - 6x + 10 + 4x + 6 = -8x + 20\)

CHALLENGE 17: \(8x^2 + 8x\)

Steps: \(A = \frac{1}{2}(4x)((3x-2) + (x+6)) = 2x(4x + 4) = 8x^2 + 8x\)

CHALLENGE 18: \(\frac{21}{19}\) or 1\(\frac{2}{19}\)

Steps: Substitute \(x = -2, y = -3\). Numerator: \(-3(-2)^3 + 2(-3)^2 = 24 + 18 = 42\). Denominator: \(4(-2)(-3) + 14 = 24 + 14 = 38\). \(\frac{42}{38} = \frac{21}{19}\).

SECTION 4

Equation Sentinel Keys (1–10)

Q1: x = -15

Add 14 to both sides: \(-29 + 14 = -15\)

Q2: y = -12

Divide both sides by -8: \(96 \div -8 = -12\)

Q3: w = 60

Multiply by -5: \(-12 \times -5 = 60\)

Q4: m = -7

Subtract 15: \(3m = -21 \rightarrow m = -7\)

Q5: a = -7

Add 11: \(-4a = 28 \rightarrow a = -7\)

Q6: x = -20

Add 7: \(\frac{x}{4} = -5 \rightarrow x = -20\)

y = -18

Subtract 8: \(\frac{2}{3}y = -12 \rightarrow y = -12 \times \frac{3}{2} = -18\)

Q8: k = -22

Multiply by 3: \(k - 5 = -27 \rightarrow k = -22\)

Q9: a = 4

Add 3.4: \(1.2a = 4.8 \rightarrow a = 4\)

Q10: w = 7

Subtract 8: \(-3w = -21 \rightarrow w = 7\)

Algebra 1 Launch Pad Keys Page 3 of 4

EQUATION & PROPORTION KEY

Section 4 & 5 Answers

SECTION 4

Equation Sentinel Keys (11–20)

Q11: x = -7

Subtract 2x, subtract 9: \(3x = -21 \rightarrow x = -7\)

Q12: y = -1

Distribute: \(-6y + 12 = 18 \rightarrow -6y = 6 \rightarrow y = -1\)

Q13: w = 9

Expand: \(4w - 8 = 2w + 10 \rightarrow 2w = 18 \rightarrow w = 9\)

Q14: p = -24/7 or -3.43

Add 2p, subtract 39: \(-24 = 7p \rightarrow p = -24/7\)

Q15: x = -4

Expand: \(3x - 15 - x = -23 \rightarrow 2x = -8 \rightarrow x = -4\)

Q16: x = 2

Expand: \(4x - 6 = 3x + 12 - 20 \rightarrow 4x - 6 = 3x - 8 \rightarrow x = 2\)

Q17: y = -20

Add 3.5y, subtract 12.5: \(y = -20\)

Q18: a = 1

Expand: \(9a - 6 = -4a + 10 - 3 \rightarrow 13a = 13 \rightarrow a = 1\)

Q19: w = (P - 2l) / 2

Isolate term: \(P - 2l = 2w \rightarrow w = \frac{P - 2l}{2}\)

Q20: n = 50 shirts

Solve: \(320 = 5.5n + 45 \rightarrow 275 = 5.5n \rightarrow n = 50\)

SECTION 5

Proportional Patrol Keys (1–15)

Q1: \$2.40 / lb

Q2: 1.5 mph

Q3: 48 wpm

Q4: x = 25

Q5: No (\(\frac{250}{6} \neq 45\))

Q6: k = 4.5

Q7: \(y = 4.5x\)

Q8: k = 5

Q9: \(y = 3x\)

Q10: \(y = 7x\)

Q11: Unit rate is 3.5 units of y per 1 unit of x

Q12: 240 actual miles

\(\frac{2}{75} = \frac{6.4}{d} \rightarrow 2d = 480 \rightarrow d = 240\)

Q13: Store B is better (\$0.80/lb vs \$0.85/lb)

Q14: 2.5 hours

\(1800 \div 12 = 150 \text{ mins} = 2.5 \text{ hours}\)

Q15: y = 25

\(k = \frac{15}{6} = 2.5\). Then \(y = 2.5 \times 10 = 25\).

Algebra 1 Launch Pad Keys Page 4 of 4

-8 - 4 × (-3) + (-2)3

-8 - (-12) + (-8)

4 - 8

-4

Sections 2-3: Word Problems

Translating the Word Space

Stuck on the submarine diving question? Use this visual decoder:

"Dives three times" → Multiply the depth value by 3.

"Ascends 120 feet" → Add +120 to the submarine's starting depth of -450.

Sentence Starter: "The new depth of the submarine after ascending is ____________. After multiplying by 3, the final depth is ____________."

Algebra 1 Launch Pad Accommodations Booklet Page 2 of 4

EQUATIONS & PROPORTIONS DEFENDER

Part 1 Scaffold

The Scale of Balance: Equation solving is like keeping a space station balanced. Whatever you do to the left side, you must also do to the right side to prevent falling out of orbit.

Section 4: Solving Equations

The Multi-Step Equation Balance Scale Guide

Use this framework for two-step equations like: \( 3x + 12 = 36 \)

Step 1: Undo Constant Addition/Subtraction

Subtract 12 from both sides of the balance equation scale.

\( 3x + 12 - 12 = 36 - 12 \)

Step 2: Undo Variable Multiplication/Division

Divide 3 on both sides to isolate the variable \( x \).

\( \frac{3x}{3} = \frac{24}{3} \)

"To isolate the variable \( x \) in the equation, first I undo the constant of ____________________ (addition / subtraction) by ____________________ (adding / subtracting) that value on both sides. Next, I undo the coefficient by ____________________ (multiplying / dividing). The final isolated value of the variable is \( x = \) ____________________."

Section 5: Proportional Patrol

Identifying Proportions & The Constant of Proportionality

Checking Tables

"I check each row in the table by dividing the dependent coordinate \( y \) by the independent coordinate \( x \) (\( y \div x \)). Because every single ratio evaluates to ____________________ (the same value / different values), this table represents a proportional relationship. The constant of proportionality is \( k = \) ________."

Checking Graphs

"When reviewing the graph on my worksheet, I can immediately tell that the relationship is proportional because the plotted line is completely ____________________ (straight / curved) and goes directly through the coordinates (0, 0), which is the ____________________ (origin / y-intercept)."

Algebra 1 Launch Pad Accommodations Booklet Page 3 of 4

LINEAR SCOUTS & ESCAPE CLUES

Part 2 Support

Section 7: Linear Slope Directions

Rocket Slope Guide

POSITIVE

Rocket goes UP from left to right

NEGATIVE

Rocket goes DOWN from left to right

ZERO

Rocket flies horizontal and FLAT

UNDEFINED

Rocket blasts vertical straight UP

"Looking at the graph, the line is ____________________ (going up / going down) from left to right, which means its slope is ____________________ (positive / negative). The rise is ______ and the run is ______, which gives us a slope of \( m = \) ______."

Final Mission Support

Escape Room Decoder Sentence Guide

Use this checklist to break down locks and explain codes without writing long paragraphs:

🔐 LOCK 1: Integer Vault

"We cracked the vault because we evaluated the absolute value, and found our final coordinates. This means the code coordinates are __________."

🔐 LOCK 2: Equation Code

"To isolate the override variable, we subtracted ______, then divided by ______. This gave us our final escape value of ______."

Your Mission Progress Map

1

Vault 1

2

Equation

3

Linear

4

Unlock!

Algebra 1 Launch Pad Accommodations Booklet Page 4 of 4

PATTERN PILOT • STAGE 2

Identifying Functions

STAGE 2

Identifying Functions (Questions 6–10)

QUESTION 6 1 Point

Does the following set of ordered pairs represent a function? Explain why or why not.

\(\{(-2, 5), (3, -1), (0, 4), (-2, 8)\}\)

Explanation: Ans: ______

QUESTION 7 1 Point

Does this mapping diagram represent a function? Explain.

X -1 →
2 →
5 →

Y 4
-3
7

Explanation: Ans: ______

QUESTION 8 1 Point

Which of the following tables represents a function? (Every inputs maps to 1 output)

Table A

Table B

Workspace: Choice (A or B): ______

QUESTION 9 1 Point

If the relation \(\{(1, a), (2, 5), (3, -2)\}\) is a function, which of the following values is NOT a possible value for \(a\)?

(A) 5       (B) -2       (C) 0       (D) None of these (all are possible)

Workspace: Choice: ______

QUESTION 10 2 Points

Describe the Vertical Line Test and how it is used to determine if a graph is a function.

Explain in your own words:

Algebra 1 Launch Pad Packet Page 2 of 3

PATTERN PILOT • STAGE 3

Writing Rules & Equations

STAGE 3

Writing Rules from Sequences & Word Problems (Questions 11–15)

QUESTION 11 2 Points

Write a function rule (equation) that represents the pattern in this input-output table:

Observe constant rate of change

Equation: y = ________________

QUESTION 12 2 Points

Write a function rule (equation) for the following sequence: 5, 9, 13, 17, 21, ... (Let \(x = 1\) represent the first term).

Workspace

Equation: y = ________________

QUESTION 13 2 Points

A taxi ride costs a flat fee of \$3.50 plus \$2.00 per mile driven. Write a function rule where \(C\) is the total cost in dollars, and \(m\) is the number of miles driven.

Workspace

Rule: C = ________________

QUESTION 14 2 Points

Using the taxi ride rule in Q13, what is the total cost of riding in a taxi for 12.5 miles?

Substitute m = 12.5 into rule

Total Cost: \$________________

QUESTION 15 2 Points

A bacteriological culture starts with 100 bacteria and doubles every hour. Write a function rule that represents the total bacteria count (\(B\)) after \(h\) hours.

Observe pattern: 100, 200, 400...

Rule: B = ________________

Section 6 Complete!

Page 3 of 3

QUESTION 10 2 Points

Find the slope of the linear function represented by this table:

Select any two coordinates to calculate rate: m = ______

Algebra 1 Launch Pad Packet Page 2 of 3

LINEAR SCOUT • STAGE 3

Equations & Intercepts

STAGE 3

Graphing Concepts & Slope-Intercept Forms (Questions 11–15)

QUESTION 11 2 Points

Find the y-intercept (\(b\)) of the line that passes through \((0, -3)\) and \((4, 5)\).

Intercept is point where \(x = 0\) b = ________________

QUESTION 12 2 Points

Write the equation of the line in slope-intercept form (\(y = mx + b\)) that has a slope of \(-3\) and passes through coordinate \((0, 7)\).

Identify m and b Equation: ________________

QUESTION 13 2 Points

State the slope (\(m\)) and the y-intercept (\(b\)) of the line represented by the equation:
\(2y - 4x = 12\)

Isolate y to match slope-intercept form first m = ______     b = ______

QUESTION 14 2 Points

Write the equation of the line represented by the coordinates: \((1, 5)\) and \((3, 11)\).

Find m first, then substitute to find b Equation: ________________

QUESTION 15 3 Points

Are the lines represented by \(y = 2x + 5\) and \(2y - 4x = 8\) parallel, perpendicular, or neither? Explain with mathematical justification.

Compare the slopes of both lines: Answer: _______________________

Section 7 Complete!

Page 3 of 3

Formula: \(V = \pi r^2 h\): V = ______ \(\pi\) cu in

QUESTION 8 2 Points

A container shaped like a rectangular prism is filled with water. Its dimensions are \(12 \text{ in} \times 8 \text{ in} \times 10 \text{ in}\). If it is \(\frac{3}{4}\) full, what volume of water is inside?

Find full volume first, then multiply by \(\frac{3}{4}\): V = ______ cu in

Algebra 1 Launch Pad Packet Page 2 of 3

GEOMETRY FOUNDATIONS • STAGE 3

Algebraic Angles

STAGE 3

Solving Angle Equations (Questions 9–12)

QUESTION 9 2 Points

Two angles are complementary. One angle measures \(3x + 10\) degrees, and the other measures \(x + 20\) degrees. Write and solve an equation to find the value of \(x\).

Set sum of both expressions equal to 90: x = ________________

QUESTION 10 2 Points

Two angles are supplementary. One angle measures \(5x - 20\) degrees, and the other measures \(2x + 15\) degrees. Find the measure of the smaller angle in degrees.

Set sum equal to 180, solve for x, then substitute back: Smaller Angle = ________________ degrees

QUESTION 11 2 Points

Two intersecting lines form vertical angles measured as \(2x + 45\) and \(4x - 15\) degrees. Find the value of \(x\).

Set expressions equal to each other: x = ________________

QUESTION 12 2 Points

The three interior angles of a triangle are represented by \(2x\), \(3x\), and \(x + 10\) degrees. Find the value of the largest angle in the triangle.

Triangle interior sum is 180 degrees: Largest Angle = ________________ degrees

Section 8 Complete!

Page 3 of 3

Calculate P(Odd) × P(Tails): Probability = ______

QUESTION 8 2 Points

A spinner is divided into 4 equal sectors numbered 1 to 4. If you spin it twice, what is the probability of spinning a number greater than 2 on both spins?

Find P(>2) for Spin 1, and multiply by Spin 2: Probability = ______

Algebra 1 Launch Pad Packet Page 2 of 3

STATS & PROBABILITY • STAGE 3

Advanced Probability

STAGE 3

Box Plots & Dependent Probability (Questions 9–12)

QUESTION 9 2 Points

In a box plot representation, what does the rightmost vertical boundary of the central "box" (the upper quartile or Q3) represent? What percent of the data points lie at or below this value?

Conceptual box plot breakdown: Percent = ________________ %

QUESTION 10 2 Points

A deck has cards numbered 1 to 10. You select one card, keep it out (without replacement), and then select a second card. What is the probability that both cards are prime numbers (2, 3, 5, 7)?

Find P(Prime) for Card 1, and multiply by updated P(Prime) for Card 2: P(Both Prime) = ________________

QUESTION 11 2 Points

Class A has a mean test score of 82 with a MAD of 3. Class B has a mean test score of 82 with a MAD of 8. In which class are the individual scores more consistent? Explain.

Relate MAD to the spread of values: Class: _______________________

QUESTION 12 2 Points

What is the sample space size (total number of possible unique outcomes) if you roll a standard six-sided die, flip a coin, and draw one card from a deck of 52 cards?

Apply the Fundamental Counting Principle (multiply options): Total Outcomes = ________________

Section 9 Complete!

Page 3 of 3

Algebra 1 Launch Pad Packet Page 2 of 3

ALGEBRA PREVIEW • STAGE 3

Exponential & Growth

STAGE 3

Exponential Growth & Classifying Relations (Questions 8–10)

QUESTION 8 2 Points

A population of butterflies starts with 50 butterflies and triples every year. This is represented by the exponential rule:
\(P = 50(3)^t\) where \(t\) is time in years. Find the butterfly population after 4 years.

Substitute t = 4: Butterflies = ________________

QUESTION 9 2 Points

Classify each equation as Linear, Quadratic (nonlinear), or Exponential (nonlinear):

Equation 1
\(y = 3x^2 - 5\)
________________

Equation 2
\(y = \frac{2}{3}x + 8\)
________________

Equation 3
\(y = 4(2)^x\)
________________

QUESTION 10 2 Points

Which type of relationship represents a constant additive rate of change, and which type represents a constant multiplicative rate of change? Select the correct terms (Linear vs. Exponential).

Match term to growth behavior: Additive: ___________________      Multiplicative: ___________________

Algebra 1 Preview Complete!

Page 3 of 3

Sum area of rectangle (\(lw\)) and triangle (\(\frac{1}{2}bh\)).

Workspace: Code 8: ____________ sq cm

Algebra 1 Launch Pad Packet Page 2 of 3

ESCAPE CHALLENGE • LAUNCH SECTOR

Launch Overrides

GATE 9: STELLAR CODES 10 Points

Decrypt the shared system coordinate solution to unlock sector 9. The coordinate's \(y\) value is the code:

\(2x + y = 12\)
\(y = 4x\)

Substitute y = 4x into the first equation, solve for x, then find y.

Code 9 (y value): ______

GATE 10: ALGEBRA MASTER 10 Points

Find the value of \(x\) that satisfies this algebraic inequality. The positive integer boundary is code 10:

\(-2(3x - 4) \ge -16\)

Distribute carefully, isolate x. Don't forget to flip inequality when dividing by negative!

Code 10: x ≤ ______

System Overrides Console Logs

Gate 1: _______

Gate 2: _______

Gate 3: _______

Gate 4: _______

Gate 5: _______

Gate 6: _______

Gate 7: _______

Gate 8: _______

Gate 9: _______

Gate 10: _______

Algebra 1 Readiness Core Matrix

Calculate your score: Each bypass code is worth 10 points. Sum the bypassed points to identify your state of readiness.

90–100 Points Algebra 1 Ready

80–89 Points Almost Ready

70–79 Points Keep Practicing

Below 70 Points Review Key Skills

Mission Operations Complete!

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\(V_{\text{full}} = 12 \times 8 \times 10 = 960\). \(960 \times \frac{3}{4} = 720\)

Q9: x = 15

\(3x+10+x+20 = 90 \rightarrow 4x+30 = 90 \rightarrow x = 15\)

Q10: 65 degrees

\(7x-5=180 \rightarrow x=25\). Angles: \(105°\) and \(65°\).

Q11: x = 30

\(2x+45 = 4x-15 \rightarrow 60 = 2x \rightarrow x = 30\)

Q12: 85 degrees

\(6x+10=180 \rightarrow x=28.3\). Wait, \(2(28.3)=56.6, 3(28.3)=85\).

SECTION 9

Stats & Probability Solutions

Q1: 12 (Sum = 72. Divide by 6 = 12)

Q2: 12 (Sorted: 4, 9, 11, 12, 15, 18, 25)

Q3: \(\frac{1}{4}\) (5/20 = 1/4)

Q4: \(\frac{3}{5}\) (12/20 = 3/5)

Q5: 2.4 (Distances: 4, 2, 4, 0, 2. Average = 12/5 = 2.4)

Q6: Smaller MAD indicates data is more grouped & consistent.

Q7: \(\frac{1}{4}\) (\(\frac{3}{6} \times \frac{1}{2} = \frac{1}{4}\))

Q8: \(\frac{1}{4}\) (\(\frac{2}{4} \times \frac{2}{4} = \frac{1}{4}\))

Q9: Represents upper quartile (Q3). 75% of values are below.

Q10: \(\frac{2}{15}\) (\(\frac{4}{10} \times \frac{3}{9} = \frac{12}{90} = \frac{2}{15}\))

Q11: Class A (Smaller MAD value means closer to mean).

Q12: 624 (\(6 \times 2 \times 52 = 624\))

Algebra 1 Launch Pad Keys Page 2 of 4

ALGEBRA PREVIEW KEY

Section 10 Answers

SECTION 10

Algebra 1 Preview Solutions

Q1: x ≤ 6

Subtract 7: \(2x \le 12 \rightarrow x \le 6\)

Q2: x > -5

Add 5: \(-3x < 15 \rightarrow\) Divide by -3 and flip the inequality sign: \(x > -5\)

Q3: x ≤ -9

Expand: \(5x - 10 \ge 3x + 8 \rightarrow 2x \ge 18 \rightarrow x \ge 9\). (Wait, in workbook: \(5(x - 2) \ge 3x + 8\). Yes, \(2x \ge 18 \rightarrow x \ge 9\))

Q4: No

Substitute \(x = -5\): \(-4(-5) + 2 = 20 + 2 = 22\). Is \(22 \le 18\)? No, false statement.

Q5: (3, 8)

Substitute: \(2x + (3x - 1) = 14 \rightarrow 5x - 1 = 14 \rightarrow 5x = 15 \rightarrow x = 3\). Then \(y = 3(3) - 1 = 8\).

Q6: (7, 3)

Add equations: \(2x = 14 \rightarrow x = 7\). Then \(7 + y = 10 \rightarrow y = 3\).

Q7: Yes

Eq 1: \(5 = 2(2) + 1\) (True). Eq 2: \(3(2) + 5 = 11\) (True). Since it works in both, it is a valid solution.

Q8: 4,050 butterflies

Solve: \(P = 50(3)^4 = 50(81) = 4,050\)

Q9 & Q10: See rules

Q9: Eq 1 is Quadratic (Nonlinear), Eq 2 is Linear, Eq 3 is Exponential (Nonlinear). Q10: Additive is Linear; Multiplicative is Exponential.

Algebra 1 Launch Pad Keys Page 3 of 4

ESCAPE CHALLENGE ANSWER KEY

Mission Overrides

BYPASS CODES

Gates 1–10 Master Solutions

GATE 1 CODE: -47

\(-12 + (-20) - 15 = -47\)

GATE 2 CODE: 4

Substitute \(x = 6\): \(y = -3(6) + 22 = -18 + 22 = 4\)

GATE 3 CODE: 9

Unit rate is 4 units of thrust per liter. \(36 \div 4 = 9 \text{ liters}\).

GATE 4 CODE: -22

Simplified expression: \(2x - 16\). Substituting \(x = -3 \rightarrow 2(-3) - 16 = -22\)

GATE 5 CODE: 3

Rise over Run: \(\frac{10 - (-8)}{1 - (-5)} = \frac{18}{6} = 3\)

GATE 6 CODE: 16

\(6w - 12 = 4w + 20 \rightarrow 2w = 32 \rightarrow w = 16\)

GATE 7 CODE: 20

\(45 + 85 + 2x + 10 = 180 \rightarrow 2x + 140 = 180 \rightarrow 2x = 40 \rightarrow x = 20\)

GATE 8 CODE: 52

Rectangle area: \(40\). Triangle area: \(\frac{1}{2}(4)(6) = 12\). Total: \(52\)

GATE 9 CODE: 8

\(2x + (4x) = 12 \rightarrow 6x = 12 \rightarrow x = 2\). Then \(y = 4(2) = 8\).

GATE 10 CODE: 4

Divide by -2 and flip: \(3x - 4 \le 8 \rightarrow 3x \le 12 \rightarrow x \le 4\).

Algebra 1 Launch Pad Keys Page 4 of 4