50+ algebra worksheets for 11th Grade on Quizizz | Free & Printable - Free Printable

Let’s solve each question one by one with clear explanations.

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1. What is the product of (3x² + 2)(2x + 2)?

Use the distributive property (FOIL or box method):

= 3x²·2x + 3x²·2 + 2·2x + 2·2
= 6x³ + 6x² + 4x + 4

✔ Answer: C. 6x³ + 6x² + 4x + 4

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2. Determine the equation of the line passing through (2,3) and (-1,-6)

First, find slope (m):

m = (y₂ - y₁)/(x₂ - x₁) = (-6 - 3)/(-1 - 2) = (-9)/(-3) = 3

Now use point-slope form: y - y₁ = m(x - x₁)

Using point (2,3):

y - 3 = 3(x - 2)
y = 3x - 6 + 3
y = 3x - 3

✔ Answer: C. y = 3x - 3

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3. Factor completely: 2x² + 13x + 15

We need two numbers that multiply to 2×15 = 30 and add to 13 → 10 and 3.

Split middle term:

2x² + 10x + 3x + 15
= 2x(x + 5) + 3(x + 5)
= (2x + 3)(x + 5)

✔ Answer: D. (2x + 3)(x + 5)

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4. Choose the function described: Absolute value shifted vertically up 3 units and horizontally left 2 units.

Parent function: f(x) = |x|

- Shift left 2 → replace x with (x + 2) → |x + 2|
- Shift up 3 → add 3 → |x + 2| + 3

✔ Answer: B. f(x) = |x + 2| + 3

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5. Describe end behavior of f(x) = x⁹ + 6x⁷ + 3x⁵ + 2x³ + x + 1

This is a polynomial of odd degree (9) with positive leading coefficient (1).

End behavior for odd degree, positive leading coefficient:

- As x → ∞, f(x) → ∞ → Right Up
- As x → -∞, f(x) → -∞ → Left Down

The question asks to “describe the end behavior” — typically, multiple choice will refer to both ends, but here options are single phrases. Since “Right Up” is an option and matches the right end, and it’s the most commonly asked part, we go with that.

But let’s check the options:

A. Left Down
B. Right Down
C. Right Up
D. Left Up

Since the function goes up on the right, correct answer is C. Right Up

(Also, A is true too — but since only one can be selected, and “Right Up” is listed, and often the right end is emphasized, C is correct.)

✔ Answer: C. Right Up

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6. Solve the system:

Equations:

(1) -2x + 2y + z = 14
(2) 3x - 2y + z = -5
(3) -x + y - 2z = -8

Let’s eliminate variables step by step.

Step 1: Eliminate z using equations (1) and (2)

Subtract (1) from (2):

(3x - 2y + z) - (-2x + 2y + z) = -5 - 14
→ 3x - 2y + z + 2x - 2y - z = -19
→ 5x - 4y = -19 → Equation (A)

Step 2: Eliminate z using equations (1) and (3)

Multiply equation (3) by 1, and equation (1) by 2 to align z coefficients:

Eq (1): -2x + 2y + z = 14
Multiply Eq (3) by 1: -x + y - 2z = -8

To eliminate z, multiply Eq (1) by 2:

→ -4x + 4y + 2z = 28
Add to Eq (3): -x + y - 2z = -8

Add them:

(-4x - x) + (4y + y) + (2z - 2z) = 28 - 8
→ -5x + 5y = 20 → divide by 5: -x + y = 4 → y = x + 4 → Equation (B)

Step 3: Plug (B) into (A)

From (A): 5x - 4y = -19
Substitute y = x + 4:

5x - 4(x + 4) = -19
5x - 4x - 16 = -19
x - 16 = -19
x = -3

Then y = x + 4 = -3 + 4 = 1

Now plug x = -3, y = 1 into any original equation to find z.

Use Eq (1): -2(-3) + 2(1) + z = 14
→ 6 + 2 + z = 14
→ 8 + z = 14
→ z = 6

✔ Solution: (-3, 1, 6)

✔ Answer: A. (-3, 1, 6)

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✔ Final Answers:

1. C
2. C
3. D
4. B
5. C
6. A

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