Algebra 1 Honors Review Notes
Algebra 1 Honors Review for Final (1st 9 Weeks)
Simplifications
Problem 1: Simplify the expression $16 rac{1}{8.22}$.
Problem 2: Simplify $2(17+2.4)$, then calculate $62 - 11$.
Problem 3: Calculate $-32 (-2)^{2} - 4$.
Problem 4: For the expression $b^{2} - 2c^{2}$ over $a + c - b$, substitute $a = 12$, $b = 9$, and $c = 4$ to find the result:
- Result: $8$.
Problem 5: Simplify the expression $16a^{2} + 7b^{2} + 36 - 2a^{2}$.
Problem 6: Simplify $2(2x^{2} - x) + (-10x^{2} - 15x)$.
Problem 7: Simplify $9 imes 2(3 + 2a) - 1$. The result provided: $14a^{2} - 762 + 36$ leads to $-8x$.
Solving for Variables
Problem 8: Solve for $a$ from the equation $19a - 4 = 0$.
- Result: $a = 23$.
Problem 9: Solve $5 imes 3p = 17$.
- Result: $p = -4/3$.
Problem 10: Solve for $x$ in $-x - 2 = -8$.
- Result: $x = 8$.
Problem 11: Solve $7 (-4x) = -4x + 8$.
Problem 12: Solve $x + 1 = - rac{1}{3}$.
Problem 13: Solve for $x$ in $4(x + 2) = 0$.
- Result: $x = -2$.
Problem 14: Solve the equation $2(x + 2) + 8(16x) = 4$.
Problem 15: Solve $-(6 - 2x) = 6$.
- Result: $x = 0$.
Problem 16: Solve for $x$ in $x - 1 = rac{3}{0.5}$.
- Result: $x = 11$.
Problem 17: Solve the equation $24a - 8 - 10a = -2(4-7a)$.
Problem 18: Solve $4|x5| = 24$.
- Result: All real numbers.
Specific Variable Solving
Problem 20: Given $A = rac{1}{2} bh$, solve for $h$:
- Result: $h = rac{2A}{b}$.
Problem 19: Solve $9 |1 + 3x - 1| = -37$,
- Result: $x = 1$.
Problem 21: For $m - 4a = 6x$, solve for $m$.
- Result: $m = 9x + 6a$.
Inequalities
Problem 22: Solve the inequality from the statement of $-3 < -2 < -1 < 0 < 2 < 3$.
Problem 27: Solve $-(6x - 9) + 2 > -(6x + 2)$.
Problem 30: Solve and graph the inequalities $-6 < 2x + 4 < 6$.
Problem 32: Solve the inequality $3x + 4 > -11$.
Problem 35: Solve $3(2x + 9) < 4(-x + 3)$.
Algebraic Products and Expressions
Problem 50: Find the product of $(2x - 5)$ and $(3x + 4)$.
Problem 55: Multiply $(x - 3)$ and $(x^{2} - 2x + 5)$.
Problem 59: Simplify $(x + 9)(x - 6)$.
- Result: $x^{2} + 3x - 54$.
Problem 60: Find the product $(2a + 3b)^{2}$.
- Result: $4a^{2} + 12ab + 9b^{2}$.
Problem 63: Factor $6x^{2} + 9xy + 2$.
- Result: $3x(2x + 3y)$.
Problem 66: Factor $15x^{2} + 8x$.
- Result: $-(x - 5)(x - 3)$.
Evaluations and Functions
Problem 75: Evaluate $g(x)=x-5$ for $g(-6)$.
- Result: $g(-6) = -9$.
Problem 76: For $f(x) = x^{2} - 2x + 1$, calculate $f(-1)$.
- Result: $f(-1) = 4$.
Problem 78: Mr. Glass's budget problem.
- Total possible notebooks: 10 / 0.85
ightarrow x ext{ (Possible numbers)}. - Condition derived: $x ext{ must be under } 11.76…$.
- Total possible notebooks: 10 / 0.85
Problem 80: Create an expression for Company A's costs ($4.50 x + 25$) and Company B's ($4 x + 75$).
- Write the inequality for costs: $4.50x + 25 < 4x + 75$.
- Solve to find $x < 100$.