Algebra Practice Quiz: College Readiness Test

1) How many minutes will it take a man to walk 4320 feet if he walks at 2 feet per second?

18

36

54

72

Speed is distance divided by time. The man walks 2 feet every second and needs to cover 4320 feet. First find the time in seconds: 4320 ÷ 2 = 2160 seconds. Then convert seconds to minutes: 2160 ÷ 60 = 36 minutes. So, walking at a constant rate, he needs 36 minutes to complete the distance. This uses a simple rate formula of distance, speed, and time.

Explanation

Speed is distance divided by time. The man walks 2 feet every second and needs to cover 4320 feet. First find the time in seconds: 4320 ÷ 2 = 2160 seconds. Then convert seconds to minutes: 2160 ÷ 60 = 36 minutes. So, walking at a constant rate, he needs 36 minutes to complete the distance. This uses a simple rate formula of distance, speed, and time.

2) Solve for x: 56 − 7x = 2.

8

54/7

58/7

−54/7

Start with 56 − 7x = 2. Subtract 56 from both sides to move constants together: −7x = 2 − 56 = −54. Now isolate x by dividing both sides by −7: x = −54 ÷ (−7) = 54/7. Keeping the answer as an improper fraction is fine here and shows the exact solution. None of the integer options would satisfy the original equation if substituted back.

Explanation

Start with 56 − 7x = 2. Subtract 56 from both sides to move constants together: −7x = 2 − 56 = −54. Now isolate x by dividing both sides by −7: x = −54 ÷ (−7) = 54/7. Keeping the answer as an improper fraction is fine here and shows the exact solution. None of the integer options would satisfy the original equation if substituted back.

3) Simplify 2(4x + 2)(x − 1).

8x^2 − 4x − 4

8x^2 − 12x − 4

16x^2 − 8x − 8

8x^2 − 4

Begin with 2(4x + 2)(x − 1). First expand (4x + 2)(x − 1). Multiply: 4x·x = 4x^2, 4x·(−1) = −4x, 2·x = 2x, and 2·(−1) = −2. Combine like terms: 4x^2 − 4x + 2x − 2 = 4x^2 − 2x − 2. Now multiply this by 2: 2(4x^2 − 2x − 2) = 8x^2 − 4x − 4.

Explanation

Begin with 2(4x + 2)(x − 1). First expand (4x + 2)(x − 1). Multiply: 4x·x = 4x^2, 4x·(−1) = −4x, 2·x = 2x, and 2·(−1) = −2. Combine like terms: 4x^2 − 4x + 2x − 2 = 4x^2 − 2x − 2. Now multiply this by 2: 2(4x^2 − 2x − 2) = 8x^2 − 4x − 4.

4) A line has slope 3 and passes through (0, 10). What is the y-coordinate when x = 2?

13

16

6

32

A line with slope 3 passing through (0, 10) has equation y = 3x + 10, because when x = 0, y equals the y-intercept 10. To find the y-coordinate when x = 2, substitute x = 2: y = 3(2) + 10 = 6 + 10 = 16. This uses the slope-intercept form y = mx + b, where m is slope and b is the intercept.

Explanation

A line with slope 3 passing through (0, 10) has equation y = 3x + 10, because when x = 0, y equals the y-intercept 10. To find the y-coordinate when x = 2, substitute x = 2: y = 3(2) + 10 = 6 + 10 = 16. This uses the slope-intercept form y = mx + b, where m is slope and b is the intercept.

5) Simplify the expression 3x^6 − 1.

3x^6 − 1

6x^8 − 1

3x^4 − 1

3x^6 − 2x^2

The expression 3x^6 − 1 consists of two unlike terms: 3x^6 and −1. There are no like terms to combine, because one term has x^6 and the other is a constant. Over the real numbers, we do not get a simple factorization with integer coefficients that is expected at this level. So the expression is already in its simplest polynomial form and remains written as 3x^6 − 1.

Explanation

The expression 3x^6 − 1 consists of two unlike terms: 3x^6 and −1. There are no like terms to combine, because one term has x^6 and the other is a constant. Over the real numbers, we do not get a simple factorization with integer coefficients that is expected at this level. So the expression is already in its simplest polynomial form and remains written as 3x^6 − 1.

6) Add the mixed numbers 5 2/3 and 4 3/14.

9 37/42

10 5/42

9 5/7

8 11/42

Convert both mixed numbers to improper fractions. First, 5 2/3 = (5 × 3 + 2)/3 = 17/3. Next, 4 3/14 = (4 × 14 + 3)/14 = 59/14. To add, use a common denominator. The least common multiple of 3 and 14 is 42. Convert: 17/3 = 238/42 and 59/14 = 177/42. Add: 238/42 + 177/42 = 415/42. Convert back to a mixed number: 415 ÷ 42 = 9 remainder 37, so 9 37/42.

Explanation

Convert both mixed numbers to improper fractions. First, 5 2/3 = (5 × 3 + 2)/3 = 17/3. Next, 4 3/14 = (4 × 14 + 3)/14 = 59/14. To add, use a common denominator. The least common multiple of 3 and 14 is 42. Convert: 17/3 = 238/42 and 59/14 = 177/42. Add: 238/42 + 177/42 = 415/42. Convert back to a mixed number: 415 ÷ 42 = 9 remainder 37, so 9 37/42.

7) What is the greatest common factor of 6x^3y^2 and 9x^2y^4?

3x^2y^2

6x^2y^2

3x^3y^4

X^2y^2

To find the greatest common factor of 6x^3y^2 and 9x^2y^4, look at numbers and variables separately. For coefficients, GCF of 6 and 9 is 3. For x, the smaller exponent is x^2 (from x^3 and x^2). For y, the smaller exponent is y^2 (from y^2 and y^4). Combine them: 3x^2y^2. This is the largest expression dividing both terms without leaving any remainder.

Explanation

To find the greatest common factor of 6x^3y^2 and 9x^2y^4, look at numbers and variables separately. For coefficients, GCF of 6 and 9 is 3. For x, the smaller exponent is x^2 (from x^3 and x^2). For y, the smaller exponent is y^2 (from y^2 and y^4). Combine them: 3x^2y^2. This is the largest expression dividing both terms without leaving any remainder.

8) The lines y = 4 and 9x − 2y = 55 intersect at a point. What is the x-coordinate of the point?

4

−4

7

9

The intersection of y = 4 and 9x − 2y = 55 occurs where both equations are true at the same time. Since y = 4, substitute this into 9x − 2y = 55. That gives 9x − 2(4) = 55, so 9x − 8 = 55. Add 8 to both sides: 9x = 63. Divide both sides by 9: x = 63 ÷ 9 = 7. So, the x-coordinate is 7.

Explanation

The intersection of y = 4 and 9x − 2y = 55 occurs where both equations are true at the same time. Since y = 4, substitute this into 9x − 2y = 55. That gives 9x − 2(4) = 55, so 9x − 8 = 55. Add 8 to both sides: 9x = 63. Divide both sides by 9: x = 63 ÷ 9 = 7. So, the x-coordinate is 7.

9) Simplify (1 / (9x^6))^2.

1 / (81x^12)

1 / (18x^12)

1 / (9x^12)

1 / (81x^6)

The expression is (1 / (9x^6))^2. When squaring a fraction, square the numerator and the denominator separately. The numerator 1 becomes 1^2 = 1. The denominator 9x^6 becomes (9x^6)^2 = 9^2 · (x^6)^2 = 81x^12. So the result is 1 / (81x^12). This shows careful use of exponent rules: (a^m)^n = a^(m·n) and squaring a product multiplies exponents appropriately.

Explanation

The expression is (1 / (9x^6))^2. When squaring a fraction, square the numerator and the denominator separately. The numerator 1 becomes 1^2 = 1. The denominator 9x^6 becomes (9x^6)^2 = 9^2 · (x^6)^2 = 81x^12. So the result is 1 / (81x^12). This shows careful use of exponent rules: (a^m)^n = a^(m·n) and squaring a product multiplies exponents appropriately.

10) Solve for x: 3(x − 4) = 2x + 5.

11

17

−17

3

Start with 3(x − 4) = 2x + 5. Distribute the 3 on the left: 3x − 12 = 2x + 5. Move the x-terms to one side by subtracting 2x from both sides: x − 12 = 5. Then add 12 to both sides to isolate x: x = 5 + 12 = 17. Substituting x = 17 back into the original equation confirms both sides equal, so 17 is correct.

Explanation

Start with 3(x − 4) = 2x + 5. Distribute the 3 on the left: 3x − 12 = 2x + 5. Move the x-terms to one side by subtracting 2x from both sides: x − 12 = 5. Then add 12 to both sides to isolate x: x = 5 + 12 = 17. Substituting x = 17 back into the original equation confirms both sides equal, so 17 is correct.

Algebra Practice Quiz For Students