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Which ordered pair is the solution to the system of equations: $y = 3x - 5$ $x + y = 7$

Select one option

A) (2, 1)

B) (4, 3)

C) (3, 4)

D) (5, 2)

Simplify the expression: $(5x^2 - 3x + 1) + (2x^2 + 7x - 4)$

Select one option

A) $7x^2 + 4x - 3$

B) $7x^2 - 10x - 3$

C) $3x^2 + 4x - 3$

D) $7x^2 + 4x - 5$

Expand and simplify: $(x + 4)(x - 2)$

Select one option

A) $x^2 + 2x - 8$

B) $x^2 + 2x - 8$

C) $x^2 + 6x - 8$

D) $x^2 - 2x - 8$

Factor the greatest common factor (GCF) from the polynomial: $12a^3b^2 - 18a^2b^3$

Select one option

A) $6a^2b^2(2a - 3b)$

B) $6ab(2a^2b - 3ab^2)$

C) $6a^2b^2(2a - 3b)$

D) $3a^2b^2(4a - 6b)$

Factor the trinomial: $x^2 + 7x + 10$

Select one option

A) $(x + 5)(x + 2)$

B) $(x + 10)(x + 1)$

C) $(x + 7)(x + 3)$

D) $(x - 5)(x - 2)$

Factor the difference of squares: $49x^2 - 81y^2$

Select one option

A) $(7x - 9y)^2$

B) $(7x + 9y)^2$

C) $(49x - 81y)(49x + 81y)$

D) $(7x - 9y)(7x + 9y)$

What is the hypothesis of the conditional statement: "If a polygon has three sides, then it is a triangle"?

Select one option

A) It is a triangle.

B) A polygon has three sides.

C) If it is a triangle.

D) Then it is a triangle.

What is the converse of the statement: "If a number is even, then it is divisible by 2"?

Select one option

A) If a number is not even, then it is not divisible by 2.

B) If a number is not divisible by 2, then it is not even.

C) If a number is divisible by 2, then it is even.

D) A number is even and it is not divisible by 2.

An angle measures $110^{\circ}$ . What type of angle is it?

Select one option

A) Acute

B) Obtuse

C) Right

D) Straight

10.

In $\triangle ABC$ , if $m\angle A = 50^{\circ}$ and $m\angle B = 70^{\circ}$ , what is $m\angle C$ ?

Select one option

A) $50^{\circ}$

B) $60^{\circ}$

C) $70^{\circ}$

D) $80^{\circ}$

11.

Which set of side lengths could form a triangle?

Select one option

A) 2, 3, 6

B) 4, 4, 8

C) 5, 7, 10

D) 1, 2, 3

12.

If two angles are complementary, their sum is $90^{\circ}$ . If angle A measures $35^{\circ}$ , what is the measure of its complement?

Select one option

A) $55^{\circ}$

B) $145^{\circ}$

C) $35^{\circ}$

D) $90^{\circ}$

13.

Solve the following system of equations by substitution. Show all your work. $y = x - 5$ $2x + y = 7$

14.

Solve the following system of equations by elimination. Show all your work. $3x + y = 9$ $x - 2y = -4$

15.

Multiply and simplify the expression: $(2x - 4)(3x + 1)$ . Show all your work.

16.

Factor the quadratic expression: $x^2 + 11x + 24$ . Show all your work.

17.

In $\triangle ABC$ , $m\angle A = x^{\circ}$ , $m\angle B = (x + 10)^{\circ}$ , and $m\angle C = 70^{\circ}$ . Find the value of $x$ and the measure of $\angle B$ . Show all your work.

18.

Consider the conditional statement: "If a figure is a square, then it has four equal sides."

a) Write its converse. b) Write its inverse. c) Write its contrapositive. d) Determine the truth value of the original statement, its converse, its inverse, and its contrapositive.

Segment AB on Line AC

19.

Given points A, B, and C are collinear. Point B is between points A and C. If $AB = 5$ and $AC = 12$ , prove that $BC = 7$ . Provide a two-column proof.

Isosceles Triangle ABC

\text{AB} \text{AC}

\text{BC}

\text{Altitude}

20.

Given $\triangle ABC$ is an isosceles triangle with $AB \cong AC$ . Prove that $m\angle B = m\angle C$ . (You may also show how to find $m\angle B$ if $m\angle A$ is known). Provide a two-column proof.