Cipher Breaker Worksheet
Mission: Algebraic Evaluation
CIPHER BREAKER
LEVEL: SECURE
Agent Name
Date of Mission
Sector / Period
Briefing: Substitution Rules
Replace each variable with its designated value. Always use parentheses when substituting negative numbers to avoid sign errors. Follow order of operations: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
PART 1
Single-Variable Decryption (Positive Integers)
[01] Substitute \( x = 4 \)
\( 3x + 7 \)
Value:
[02] Substitute \( a = 5 \)
\( 12 - 2a \)
Value:
[03] Substitute \( y = 8 \)
\( 5(y - 2) \)
Value:
[04] Substitute \( m = 6 \)
\( \frac{24}{m} + 3 \)
Value:
PART 2
Multi-Variable Matrix (Negative Values & Exponents)
[05] \( a = -3, \; b = 2, \; c = -5 \)
\( ab^2 - c \)
Value:
[06] \( x = -4, \; y = -1 \)
\( 2x^2 + 3y \)
Value:
[07] \( m = -2, \; n = 5 \)
\( -3(m - n) \)
Value:
[08] \( x = -10, \; y = -2, \; z = -3 \)
\( \frac{x + y}{z} \)
Value:
ALGEBRAIC SYSTEMS & CODES MISSION CODE: EVAL-01 PAGE 1 OF 2
Mission: Advanced Operations
CIPHER BREAKER
STAGE 2 ACTIVE
PART 3
Complex PEMDAS Grid (Fractions & Absolute Values)
[09] Substitute \( a = -2, \; b = 3, \; c = -4 \)
\( |2a - 5b| + 3c^2 \)
Value:
[10] Substitute \( x = 6, \; y = -4 \)
\( \frac{x^2 - y}{2x + y} \)
Value:
[11] Substitute \( p = -2, \; q = -10 \)
\( 4[3(p + 1)^2 - q] \)
Value:
PART 4
Tactical Field Formulas (Real-World Applications)
[12] TEMPERATURE CONVERSION \( C = -15 \)
To convert Celsius to Fahrenheit, use \( F = \frac{9}{5}C + 32 \). Find the Fahrenheit temperature for a cold front of \( -15^\circ\text{C} \).
\( F = \)
[13] KINETIC ENERGY \( m = 6, \; v = -4 \)
The energy of a moving drone is given by \( E = \frac{1}{2}mv^2 \) (in Joules). Calculate the kinetic energy for a drone with mass \( m = 6\text{ kg} \) and velocity \( v = -4\text{ m/s} \).
\( E = \)
PART 5
Input Calibration (Solving for Target Variables)
[14] Find \( x \)
If \( y = 4x - 9 \) and \( y = 11 \)
\( x = \)
[15] Find \( h \)
If \( A = \frac{1}{2}bh \) and \( A = 24, \; b = 6 \)
\( h = \)
[16] Find \( w \)
If \( P = 2l + 2w \) and \( P = 36, \; l = 10 \)
\( w = \)
ALGEBRAIC SYSTEMS & CODES MISSION CODE: EVAL-02 PAGE 2 OF 2
Cipher Breaker Answer Key
Mission: Evaluation (Teacher Resource)
CIPHER BREAKER ANSWER KEY
MASTER CODE: UNLOCKED
Reference Dossier
Full Guide & Solutions
Subject Code
MATH.ALG.01
Level
Pre-Algebra / Algebra 1
PART 1 SOLUTIONS
Single-Variable Decryption (Positive Integers)
[01] Substitute \( x = 4 \)
\( 3x + 7 \)
\( 3(4) + 7 \implies 12 + 7 \) Value: 19
[02] Substitute \( a = 5 \)
\( 12 - 2a \)
\( 12 - 2(5) \implies 12 - 10 \) Value: 2
[03] Substitute \( y = 8 \)
\( 5(y - 2) \)
\( 5(8 - 2) \implies 5(6) \) Value: 30
[04] Substitute \( m = 6 \)
\( \frac{24}{m} + 3 \)
\( \frac{24}{6} + 3 \implies 4 + 3 \) Value: 7
PART 2 SOLUTIONS
Multi-Variable Matrix (Negative Values & Exponents)
[05] \( a = -3, \; b = 2, \; c = -5 \)
\( ab^2 - c \)
\( (-3)(2)^2 - (-5) \implies -12 + 5 \) Value: -7
[06] \( x = -4, \; y = -1 \)
\( 2x^2 + 3y \)
\( 2(-4)^2 + 3(-1) \implies 32 - 3 \) Value: 29
[07] \( m = -2, \; n = 5 \)
\( -3(m - n) \)
\( -3(-2 - 5) \implies -3(-7) \) Value: 21
[08] \( x = -10, \; y = -2, \; z = -3 \)
\( \frac{x + y}{z} \)
\( \frac{-10 + (-2)}{-3} \implies \frac{-12}{-3} \) Value: 4
ALGEBRAIC SOLUTIONS MASTER KEY MISSION CODE: EVAL-KEY-01 PAGE 1 OF 2
Mission: Advanced (Teacher Resource)
CIPHER BREAKER ANSWER KEY
STAGE 2 COMPLETED
PART 3 SOLUTIONS
Complex PEMDAS Grid (Fractions & Absolute Values)
[09] Substitute \( a = -2, \; b = 3, \; c = -4 \)
\( |2a - 5b| + 3c^2 \)
\( |2(-2) - 5(3)| + 3(-4)^2 \implies |-19| + 48 \) Value: 67
[10] Substitute \( x = 6, \; y = -4 \)
\( \frac{x^2 - y}{2x + y} \)
\( \frac{(6)^2 - (-4)}{2(6) + (-4)} \implies \frac{40}{8} \) Value: 5
[11] Substitute \( p = -2, \; q = -10 \)
\( 4[3(p + 1)^2 - q] \)
\( 4[3(-1)^2 - (-10)] \implies 4(3 + 10) \) Value: 52
PART 4 SOLUTIONS
Tactical Field Formulas (Real-World Applications)
[12] TEMPERATURE CONVERSION \( C = -15 \)
To convert Celsius to Fahrenheit, use \( F = \frac{9}{5}C + 32 \). Find the Fahrenheit temperature for a cold front of \( -15^\circ\text{C} \).
