Algebra 1 Final Exam 2026 2027: 80 Practice
Questions with Answers | Factoring,
Radicals, Quadratics & Logarithms
Description:
Prepare for your Algebra 1 final exam 2026/2027 with 80 comprehensive practice questions
covering factoring, radicals, quadratic equations, logarithms, and word problems.
Each question includes a correct answer and step-by-step explanation.
Download the full 2026/2027 exam paper now and pass with confidence.
, Algebra 1 Final Exam 2026 2027 Practice Test
Section A: Properties of Real Numbers (4 marks)
Question 1 (1 mark)
Which of the following equations demonstrates the commutative property of addition?
A) (a+b)+c=a+(b+c)(a+b)+c=a+(b+c)
B) a+b=b+aa+b=b+a
C) a(b+c)=ab+aca(b+c)=ab+ac
D) a+0=aa+0=a
Answer: B
Explanation: The commutative property of addition states that changing the order of
addends does not change the sum, expressed as a+b=b+aa+b=b+a.
Question 2 (1 mark)
The equation (ab)c=a(bc)(ab)c=a(bc) illustrates which property?
A) Commutative property of multiplication
B) Associative property of multiplication
C) Distributive property
D) Identity property of multiplication
Answer: B
Explanation: The associative property of multiplication states that the grouping of factors
does not affect the product, written as (ab)c=a(bc)(ab)c=a(bc).
Question 3 (2 marks)
Use the distributive property to expand 4x(2x2−5y+3)4x(2x2−5y+3). Simplify your answer.
A) 8x3−20xy+12x8x3−20xy+12x
B) 8x2−20xy+12x8x2−20xy+12x
C) 8x3−20x2y+12x8x3−20x2y+12x
D) 8x3−20xy+128x3−20xy+12
, Answer: A
Explanation: Multiply each term inside the parentheses
by 4x4x: 4x⋅2x2=8x34x⋅2x2=8x3, 4x⋅(−5y)=−20xy4x⋅(−5y)=−20xy, and 4x⋅3=12x4x⋅3=12x.
No further simplification is possible.
Section B: Rational Exponents and Simplification (12 marks)
Question 4 (2 marks)
Simplify (x4y−4)−5(2x−3y2)−2(x4y−4)−5(2x−3y2)−2. Express your answer with positive
exponents only.
A) y164x144x14y16
B) 4x4y16y164x4
C) y122x62x6y12
D) 2y8x10x102y8
Answer: A
Explanation: First term: (x4y−4)−5=x−20y20(x4y−4)−5=x−20y20. Second
term: (2x−3y2)−2=2−2x6y−4=14x6y−4(2x−3y2)−2=2−2x6y−4=41x6y−4.
Multiply: x−20+6y20−4=x−14y16x−20+6y20−4=x−14y16. Then multiply by 1441 to
get y164x144x14y16.
Question 5 (2 marks)
Simplify (ab−2c−3a2b3c−4)−4(a2b3c−4ab−2c−3)−4.
A) a4b20c4c4a4b20
B) a4b20c4b20c4a4
C) b20a4c4a4c4b20
D) a4b4c4a4b4c4
Answer: A
Explanation: Simplify inside parentheses
first: a1−2=a−1a1−2=a−1, b−2−3=b−5b−2−3=b−5, c−3−(−4)=c1c−3−(−4)=c1. So inside
= a−1b−5c1a−1b−5c1. Raise to the power of -4: a4b20c−4=a4b20c4a4b20c−4=c4a4b20.
Questions with Answers | Factoring,
Radicals, Quadratics & Logarithms
Description:
Prepare for your Algebra 1 final exam 2026/2027 with 80 comprehensive practice questions
covering factoring, radicals, quadratic equations, logarithms, and word problems.
Each question includes a correct answer and step-by-step explanation.
Download the full 2026/2027 exam paper now and pass with confidence.
, Algebra 1 Final Exam 2026 2027 Practice Test
Section A: Properties of Real Numbers (4 marks)
Question 1 (1 mark)
Which of the following equations demonstrates the commutative property of addition?
A) (a+b)+c=a+(b+c)(a+b)+c=a+(b+c)
B) a+b=b+aa+b=b+a
C) a(b+c)=ab+aca(b+c)=ab+ac
D) a+0=aa+0=a
Answer: B
Explanation: The commutative property of addition states that changing the order of
addends does not change the sum, expressed as a+b=b+aa+b=b+a.
Question 2 (1 mark)
The equation (ab)c=a(bc)(ab)c=a(bc) illustrates which property?
A) Commutative property of multiplication
B) Associative property of multiplication
C) Distributive property
D) Identity property of multiplication
Answer: B
Explanation: The associative property of multiplication states that the grouping of factors
does not affect the product, written as (ab)c=a(bc)(ab)c=a(bc).
Question 3 (2 marks)
Use the distributive property to expand 4x(2x2−5y+3)4x(2x2−5y+3). Simplify your answer.
A) 8x3−20xy+12x8x3−20xy+12x
B) 8x2−20xy+12x8x2−20xy+12x
C) 8x3−20x2y+12x8x3−20x2y+12x
D) 8x3−20xy+128x3−20xy+12
, Answer: A
Explanation: Multiply each term inside the parentheses
by 4x4x: 4x⋅2x2=8x34x⋅2x2=8x3, 4x⋅(−5y)=−20xy4x⋅(−5y)=−20xy, and 4x⋅3=12x4x⋅3=12x.
No further simplification is possible.
Section B: Rational Exponents and Simplification (12 marks)
Question 4 (2 marks)
Simplify (x4y−4)−5(2x−3y2)−2(x4y−4)−5(2x−3y2)−2. Express your answer with positive
exponents only.
A) y164x144x14y16
B) 4x4y16y164x4
C) y122x62x6y12
D) 2y8x10x102y8
Answer: A
Explanation: First term: (x4y−4)−5=x−20y20(x4y−4)−5=x−20y20. Second
term: (2x−3y2)−2=2−2x6y−4=14x6y−4(2x−3y2)−2=2−2x6y−4=41x6y−4.
Multiply: x−20+6y20−4=x−14y16x−20+6y20−4=x−14y16. Then multiply by 1441 to
get y164x144x14y16.
Question 5 (2 marks)
Simplify (ab−2c−3a2b3c−4)−4(a2b3c−4ab−2c−3)−4.
A) a4b20c4c4a4b20
B) a4b20c4b20c4a4
C) b20a4c4a4c4b20
D) a4b4c4a4b4c4
Answer: A
Explanation: Simplify inside parentheses
first: a1−2=a−1a1−2=a−1, b−2−3=b−5b−2−3=b−5, c−3−(−4)=c1c−3−(−4)=c1. So inside
= a−1b−5c1a−1b−5c1. Raise to the power of -4: a4b20c−4=a4b20c4a4b20c−4=c4a4b20.
