Ready to ace your Algebra 1 Chapter 4 Test? Jump into our free pre algebra chapter 4 test and challenge your skills with a comprehensive divisibility factorization quiz and solving equations quiz. This chapter 4 test algebra 1 review is perfect for students prepping for midterms or anyone wanting extra practice. Kickstart your study with our detailed algebra 1 chapter 4 test and explore more problems in our algebra test collection. Embrace the challenge, boost your confidence, and click to begin - let's conquer those equations together! Plus, receive instant feedback to track your progress.
What is the greatest common factor (GCF) of 18 and 24?
6
12
3
9
The GCF is the largest integer that divides both numbers without leaving a remainder. The divisors of 18 are 1, 2, 3, 6, 9, 18 and of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The greatest common divisor they share is 6. Learn more at Math is Fun.
Which of the following numbers is divisible by 3?
123
124
125
127
A number is divisible by 3 if the sum of its digits is divisible by 3. For 123, the digits sum to 1 + 2 + 3 = 6, which is divisible by 3. Therefore 123 is divisible by 3. More on divisibility rules at Math is Fun.
Simplify the expression: 4(2x + 3).
8x + 12
8x + 3
2x + 3
4x + 12
Use the distributive property: multiply 4 by each term inside the parentheses. 4×2x gives 8x, and 4×3 gives 12, so the result is 8x + 12. This is a foundational algebra skill. See more at Khan Academy.
Factor the quadratic expression: x² – 5x – 6.
(x - 6)(x + 1)
(x - 2)(x + 3)
(x - 3)(x + 2)
(x + 6)(x - 1)
To factor x² - 5x - 6, find two numbers whose product is -6 and whose sum is -5. These numbers are -6 and 1, giving factors (x - 6)(x + 1). Factoring quadratics is covered at Math is Fun.
Solve the equation: x + 7 = 12.
5
-5
19
-19
Subtract 7 from both sides: x = 12 - 7 = 5. This is a simple one-step linear equation. Practice more at Khan Academy.
What is the least common multiple (LCM) of 4 and 6?
12
2
24
18
The LCM is the smallest positive number divisible by both given numbers. Multiples of 4 are 4, 8, 12, … and of 6 are 6, 12, … The first common multiple is 12. More at Math is Fun.
Which of these numbers is prime?
11
12
15
21
A prime number has exactly two distinct positive divisors: 1 and itself. 11 is only divisible by 1 and 11, making it prime. Composite examples are explained at Math is Fun.
Evaluate the expression 3x² – 1 for x = 2.
11
5
12
7
Substitute x = 2 into 3x² – 1: 3×(2²) – 1 = 3×4 – 1 = 12 – 1 = 11. This demonstrates evaluation of algebraic expressions. See more at Khan Academy.
Factor the quadratic trinomial: 6x² – 13x – 5.
(3x + 1)(2x - 5)
(2x + 1)(3x - 5)
(6x + 1)(x - 5)
(3x - 1)(2x + 5)
Look for a pair of factors of 6×(-5) = -30 that add to -13. Those are -15 and +2. Rewriting the middle term and factoring by grouping gives (3x + 1)(2x - 5). Learn more at Khan Academy.
Solve for y: 2(y - 3) + 4 = 10.
6
4
8
2
Expand the left: 2y - 6 + 4 = 10, so 2y - 2 = 10. Add 2: 2y = 12, then divide by 2: y = 6. See similar problems at Khan Academy.
Factor by grouping: x³ + 3x² + 2x + 6.
(x + 3)(x² + 2)
(x + 2)(x² + 3)
(x + 1)(x² + 6)
(x + 6)(x² + 1)
Group terms: x²(x + 3) + 2(x + 3). Factor out (x + 3) to get (x + 3)(x² + 2). Grouping is illustrated at Math is Fun.
Simplify the product: (x + 2)(x - 2).
x² - 4
x² + 4
x² - 2
x² + 2
This is a difference of squares: (a + b)(a - b) = a² - b². Here a = x and b = 2, so the product is x² - 4. See details at Math is Fun.
Solve for x: x/4 + 3 = 8.
20
5
32
1
Subtract 3: x/4 = 5. Multiply both sides by 4: x = 20. This demonstrates solving a one-step equation with fractions. More practice at Khan Academy.
Factor the perfect square trinomial: 4x² – 12x + 9.
(2x - 3)²
(4x - 3)²
(2x + 3)²
(x - 3)²
A perfect square trinomial a² - 2ab + b² factors as (a - b)². Here a = 2x and b = 3, giving (2x - 3)². Learn more at Math is Fun.
What is the least common denominator for the fractions 1/2 and 1/3?
6
5
4
3
The least common denominator (LCD) is the LCM of the denominators. LCM of 2 and 3 is 6, so the LCD is 6. More at Math is Fun.
Determine whether 2349 is divisible by 9.
True
False
A number is divisible by 9 if the sum of its digits is a multiple of 9. For 2349: 2 + 3 + 4 + 9 = 18, which is divisible by 9. Therefore, 2349 is divisible by 9. See the rule at Math is Fun.
What are the solutions to the quadratic equation 2x² – x – 3 = 0?
x = 3/2 or x = -1
x = 1/2 or x = -3
x = 1 or x = -3/2
x = 2 or x = -3/2
Use the quadratic formula: x = [1 ± ?(1 + 24)]/4 = [1 ± 5]/4, giving x = 6/4 = 3/2 or x = -4/4 = -1. This method works for any quadratic. Read more at Khan Academy.
Factor completely: x³ – x² – x + 1.
(x - 1)²(x + 1)
(x - 1)(x² + 1)
(x + 1)²(x - 1)
(x - 1)(x - 1)(x - 1)
Group: x²(x - 1) - 1(x - 1) = (x - 1)(x² - 1). Then factor x² - 1 as (x - 1)(x + 1) to get (x - 1)²(x + 1). See grouping at Math is Fun.
Solve for x: 3(x - 2)/4 = 6.
10
8
6
4
Multiply both sides by 4: 3(x - 2) = 24, then divide by 3: x - 2 = 8, so x = 10. This tackles fractional coefficients. See examples at Khan Academy.
If a and b are relatively prime, what is the least common multiple of ab and b²?
ab²
a²b
ab
b
When gcd(a,b)=1, lcm(ab, b²) = (ab·b²)/gcd(ab,b²) = a b². The formula for LCM of two numbers ab over their GCD gives this result. More at Wikipedia.
Solve the equation: (x - 3)(x + 2) = x² - 9.
3
-3
0
9
Expand: x² - x - 6 = x² - 9. Subtract x²: -x - 6 = -9, so -x = -3, giving x = 3. This checks understanding of algebraic expansion. See practice at Khan Academy.
If a number is divisible by both 4 and 6, it must also be divisible by which of the following?
12
2
9
24
A number divisible by both 4 and 6 is divisible by their LCM, which is 12. Divisibility by the LCM ensures divisibility by each factor. Learn more at Math is Fun.
Solve for x: 5/(x + 1) = 2/(x - 1).
7/3
3/7
-7/3
7/2
Cross-multiply: 5(x - 1) = 2(x + 1) ? 5x - 5 = 2x + 2 ? 3x = 7 ? x = 7/3. This requires solving a rational equation. See techniques at Khan Academy.
Which integer values of x between 0 and 20 make 3x + 5 divisible by 7?
3, 10, 17
2, 9, 16
4, 11, 18
1, 8, 15
We need 3x + 5 ? 0 (mod 7) ? 3x ? 2 (mod 7). Multiply both sides by 5 (the inverse of 3 mod 7) to get x ? 10 ? 3 (mod 7). Solutions in [0,20]: 3, 10, 17. See modular arithmetic at Wikipedia.
Solve the system of equations: 2x + 3y = 7 and x - y = 4.
x = 19/5, y = -1/5
x = 3, y = -1
x = 1, y = -3
x = 4, y = 0
From x - y = 4, x = 4 + y. Substitute into 2x + 3y = 7: 2(4+y) + 3y = 7 ? 8 + 2y + 3y = 7 ? 5y = -1 ? y = -1/5, then x = 4 - 1/5 = 19/5. Practice at Khan Academy.
0
{"name":"What is the greatest common factor (GCF) of 18 and 24?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"What is the greatest common factor (GCF) of 18 and 24?, Which of the following numbers is divisible by 3?, Simplify the expression: 4(2x + 3).","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}
Study Outcomes
Analyze Divisibility Rules -
Identify and apply the rules of divisibility for common integers to quickly determine if numbers are divisible without long division.
Apply Factorization Techniques -
Break down algebraic expressions into their prime factors and factored forms, reinforcing your skills with monomials and polynomials.
Solve Linear Equations -
Work through one- and two-step equations with confidence, using inverse operations to find the correct solution in each problem.
Interpret Immediate Feedback -
Use instant quiz results to pinpoint errors, understand misconceptions, and adjust your approach for better accuracy.
Identify Strengths and Weaknesses -
Assess your mastery of Chapter 4 topics - divisibility, factorization, and equation solving - to target areas needing further practice.
Build Assessment Confidence -
Gain practice and proficiency in pre-algebra concepts, preparing you for quizzes, tests, and classroom challenges.
Cheat Sheet
Divisibility Rules -
As you prep for the Algebra 1 Chapter 4 Test, mastery of divisibility rules speeds up factor checks: a number is divisible by 2 if it's even, by 3 if its digits sum to a multiple of 3, by 5 if it ends in 0 or 5, by 9 if the digit sum is a multiple of 9, and by 11 if the alternating sum of digits is a multiple of 11. For example, 198 has digits summing to 18, so it's divisible by 9. These quick checks, taught in university-level arithmetic reviews, cut down computation time on quizzes.
Prime Factorization & GCF -
Breaking numbers into primes helps find the greatest common factor (GCF) and least common multiple (LCM) efficiently: use a factor tree to express each number as a product of primes, then take common primes for the GCF. For instance, 48=2³·3 and 180=2²·3², so GCF=2²·3=12. This systematic approach, endorsed by leading math resources, prevents errors on factorization quizzes.
Factoring Simple Trinomials -
To factor x²+bx+c, find two numbers that multiply to c and add to b; this "product-sum" strategy is central for chapter 4 test Algebra 1 problems. For example, x² - x - 12 factors into (x - 4)(x+3) because - 4·3= - 12 and - 4+3= - 1. Practicing with varied c and b values boosts your speed and accuracy.
Difference of Squares -
Recognize expressions of the form a² - b² and apply the identity a² - b²=(a - b)(a+b) to factor instantly. For example, 49y² - 25=(7y - 5)(7y+5) simplifies complex problems in a flash. This pattern, featured in standardized algebra exams, eliminates guesswork.
Solving Linear Equations -
Master the balance method by undoing operations in reverse order: first eliminate constants, then isolate the variable by dividing or multiplying. In 3x+5=20, subtract 5 to get 3x=15, then divide by 3 to find x=5. This clear, two-step approach underpins every pre algebra chapter 4 test and builds confidence for more advanced equations.
