100 QA Algebra Lessons 1 2 3 4 5

# 100 QA Algebra Lessons 1 2 3 4 5

393k points

Lesson 1

1. (9/15)/(27/30)

2. The cost of two baseball bats is \$360. If the aluminum one costs \$40 more than the wood one, find the cost of the aluminum bat.

3. Graph the following set on a number line: {x | x ≤ -1}.

4. Write the numeral 0.0284 x 10^4 in scientific notation.

5. 3/26 - 9/13

6. Solve the following equation for q: (2q+3)/3+(3q-4)/6 = (q-2)/2

7. Simplify the expression -3^2

8. Solve the following equation for x: 5(x-4) = 10

9. Simplify the expression [ (3xy^(-3))/(5x^(-2)y^(2))]^2

10. If the sum of the measures of two angles equals _______, the angles are called supplementary angles.

11. Write the numeral 0.034 in scientific notation.

12. Write the following numeral in scientific notation and perform the indicated operations: (0.006)(0.0007)/2100

13. The quotient of two real numbers with the same sign is

14. Simplify the express (-3)^2

15. Solving the following equation for z:

16. (8(2)-4(4))/(7(8)+9(1)) =

17. Solve the following equation for w:

18. Simplify the expression ((2a^5 b^2)/(4 a^5 b^(-2)))^(-4).

19. A 152-foot piece of rope is to be cut into four pieces. Each successive piece is to be 2 feet longer than the previous one. Find the length of the shortest piece.

20. 8/9 - 3/5

Lesson 2

1. On the rectangular coordinate system, plot the point (-1, -2).

2. Shifting the graph of an equation up or down is called a/an _______ translation.

3. Graph the equation y=(-1/3)x+2.

4. The slope-intercept form of the equation of a line is

5. Find the slope of the line that passes through the points (-3,-6) and (1,6)

6. Find the slope of the line determined by the equation 6x - 3y = 18.

7. Find the equation of the line perpendicular to the line x = 4 and passing through the point (4,2).

8. Which one of the following equations represents the y-axis?

9. Find the midpoint of the line segment joining (4,8) and (-2, -6).

10. Find the slope of the line joining the points A (-3, 2) and B (0, 4).

11. Find the slope-intercept equation of the line passing through (2, 1) with a slope of m = 3.

12. Find the slope of the line determined by the equation 2x = y.

13. Tell whether the following equation determines y to be a function of x:

14. Draw the graph of the following linear function and give the domain and range: h(x)=-2x+3.

15. Given g(x)=5/(x+3), find g(-3)

16. Graph the function g(x) = (x-1)^3.

17. Graph the function f(x) = x^2 -2.

18. Given f(x)=2x-8, find f(3).

19. Complete the following truth table for the equation y = x+3:

20. The function f(x)=x^3 is called the _______ function.

Lesson 3

1. Solve the inequality -6 ≤ 6x < 24. Give the result in set notation and graph it.

2. Graph the inequality 3x ≤ -4y - 4.

3. Solve the inequality 4 < -z - 4 < 11. Give the result in set notation and graph it.

4. Find the equation of the boundary line in the graph below. Then give the inequality represented by the shaded area.

5. Solve the inequality -2 (3+x) < 4x + 4 < 8x. Give the result in set notation and graph it.

6. If the edge isn't included in the graph of an inequality, you should draw it as a/an _______ line.

7. Solve the equation |x| = 7.

8. Graph the solution set of x + 2y ≤ 3, x + 2y ≤ 4

9. Solve the inequality |2x-4| < 10. Write the solution in interval notation and graph it.

10. Graph the following solution set: x + y ≤ 4, x ≥ 0, y ≥ 0

11. Graph the inequality y < 3x + 1.

12. Solve the inequality (1/4)y - 1/3 < y + 2. Give the result in set notation and graph it.

13. Graph the inequality y ≥ -3.

14. Solve the inequality 3 ≤ 4 + 3x/2 ≤ 2. Give the result in set notation and graph it.

15. Find the equation of the boundary line in the graph below. Then give the inequality represented by the shaded area.

16. Find the value of the expression -|-18|.

17. Graph the following solution set: y ≤ x - 1, y ≥ 2x

18. Solve the equation |6x+3| = 15

19. Graph the following solution set: x ≤ y^2, y ≥ x

20. Solve the inequality |5x+10| ≥ 15. Write the solution in interval notation and graph it.

Lesson 4

1. Find the value of the expression 2xy - x^2 y when x = 2 and y = 3.

2. Completely factor the expression 4q^2 + 27r^4.

3. Simplify the expression 2ab^4 - 3a^2 b^2 - ab^4 + a^2 b^2.

4. Completely factor the expression 2a^3 - 128.

5. Simplify the expression -2(4y^2 + 3z^3 + 5) + 3(2y^2 - 5z^3 + 3).

6. Completely factor the expression y^2 + 12y + 35.

7. Find the product of (x - 2y)^2.

8. Solve the equation x^2 + 4x - 45=0

9. Completely factor the expression 48u^4 v^4 - 18u^2 v^2 - 3u^8 v^5.

10. Solve the equation 3z^3 - 300z = 0.

11. Completely factor the expression a^2 + 4b - ab - 4a.

12. Graph the polynomial function f(x) = x^3 - 1.

13. Completely factor the expression 16x^4 - 81y^4.

14. Perform the indicated operations on the expression below.

15. Completely factor the expression r^2 - 2r + 1.

16. Find the product of -3a^3 b(2a^0 b^4 - 4 a^2 b^3)

17. Completely factor the expression 16t^3 - 50t^2 + 36t.

18. Find the product of (2a+3b)(2a-3b).

19. Solve the equation (1/4)a^2 + (3/4)a = 1.

20. Completely factor the expression 7(x-y) - z(x-y).

Lesson 5

1. Simplify the expression 35/55.

2. Simplify the following expression: [(b^2+5b+6)/(3bc)]/[(b^2-9)/(6bc)].

3. Solve the proportion for the variable: 3/y = 12/8

4. Simplify the following expression: (q^(-2) - r^(-2))/(q^(-1) - r^(-1))

5. Express this sentence as a formula: z varies directly with the square of s.

6. Solve the following equation: (3t-5)/(t-1) = 2 + (2t)/(1-t)

7. Perform the indicated operations and simplify the following expression: (y^2 - 6y + 9)/(-(y^2-4)) + (y^2-9)/(y^2 - 8y + 12)

8. Divide the following expression: (112a^0 b^3 c^(-4))/(48 a^3 b^0 c^3)

9. Perform the indicated operations and simplify the following expression: (5a+3)/(a^2+13a+12) - (2a - 3)/(a^2+13a + 12)

10. Divide the following expression: (27z + 23z^2 + 6z^3)/(2z+3)

11. Perform the indicated operations and simplify the following expression: (2z-1)/(z^2+z-6) - (3z-5)/(z^2 - 2z - 15) + (2z-3)/(z^2 - 7z + 10)

12. Simplify the expression (12a^2 + 26a + 12)/(6 - 5a - 6a^2).

13. Simplify the following expression: (1/c + 1/d)/(c/d - d/c)

14. Solve this proportion for the variable: (x+2)/(x+6) = (x-4)/(x-2)

15. Solve the following equation: 1/2 + 7/y = 2 + 1/y

16. Perform the indicated operations and simplify the following expression: (x+6)/(x^2-16) * (3x-12)/(3x+18)

17. Solve the following eqauation: 3/(z-3) + 5/(z-1) = 8/(z-2)

18. Perform the indicated operations and simplify the following expression: (6r^2-7r-3)/(r^2-1)+(4r^2-12r+9 )/(r^2-1) (2r^2-r-3)/(3r^2-2r-1)

19. Divide the following expression: (x^2+10x+21)/(x+7)

20. Perform the indicated operations and simplify the following expression: 9/(y+3) + 2y/(y+6)

algebra

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