LDME Unit 1 Review - Foundations of Algebra

OCS LDME Unit 1: Foundations for Algebra Review

Lesson 1: Combining Like Terms Like Terms have the same variables and the same exponents Examples: 2x and 4x 3y2 and 6y2 m3n and 8m3n Distributive Property Remember to multiply EVERYTHING inside the parentheses by the term on the outside.

Examples: a(b + c) = ab + ac 2(x + y) = 2x + 2y Order of Operations Please Excuse My Dear Aunt Sally!

Parentheses, Exponents, Multiplication, Division, Addition and Subtraction Example: 7 + (6 * 52 + 3) Start inside Parentheses, then use Exponents 7 + (6 * 25 + 3) Then Multiply 7 + (150 + 3) Then Add 7 + 153 Parentheses completed, last operation is an Add 160 Lesson 2: Adding and Subtracting Integers Rule: If the signs are the SAME, add the numbers and keep that sign.

If the signs are DIFFERENT, subtract the numbers and keep the sign of the larger number.

Example: -4 - 3 = -7 -8 + 9 = 1 Multiplying and Dividing Integers Rule: If the signs are the same, the answer is positive.

If the signs are different, the answer is negative.

Example: (-3)(-4) = 12 (-5)(2) = -10 Lesson 3: Multiplying with Exponents Rule: If the base is the same, add the exponents.

OCS LDME Unit 1: Foundations for Algebra Review Example: (x2)(x3) = x5 Dividing with Exponents Rule: If the base is the same, subtract the exponents.

Example: x8 = x4 x4 Raising and Power to a Power Rule: When raising a power to a power, multiply the exponents.

Example: (x4y3)2 = x8y6 Simplifying Expressions with Zero Rule: Anything to the power of zero is equal to one.

Example: (4x3y7)0 = 1 Simplifying Expressions with Negative Exponents Rule: If you have a negative exponent on the top, move the term to the bottom to make the exponent positive.

If the negative exponent is on the bottom, move the exponent to the bottom.

Examples: 2x2 = 2x2y3 y-3 x-3 = 1 = 1 2 3 x x *x2 x5 Simplifying Expressions with Radicals The square root of a number is whatever you multiply times itself to get that number.

The cube root is the number that you multiply times itself three times to get that number.

Examples: √36 = x 3 √8 = 2 71/2 = √7 x1/3 = 3√x

OCS LDME Unit 1: Foundations for Algebra Review

Multiple Choice Questions 1. 5x2y + xy – 2x2y a. 8x2y b. 7x4y3 c. 3x2y + xy 2. x(2 + 3x + y) a. 2x + 3x2 + xy b. 2 + 3x2 + y c. 5x2 + xy 3. (2 + 6 * 2 + 2 – 4) * 2 a. 24 b. 28 c. 18 4. – 9 + 12 a. -21 b. 3 c. -3 5. (-5)(-3) a. 15 b. -8 c. -2 6. (x4y2)(xy3) a. x4y5 b. x5y5 c. x3y5 7. 3x3y5 xy3 a. 3x4y8 b. 3x2y c. 3x2y2 8. (12xy4z)0 a. 12xy4z b. xy4z c. 1

OCS LDME Unit 1: Foundations for Algebra Review

9. 4x-1y a. 4xy b. 4y x c. 4y 10. 641/3 a. 8 b. 2 c. 4 Free Response Questions Simplify problems 11-18 11. 12xy2z + 3xyz3 – 8xy2z + 3xyz3 12. 2x(x + yz) + 3(x + 3yz) 13. 10 – (-10) – 7 – 5 14. (-3)(3)(-3)(-3) 15. (x2y3)2 xy2 16. (3xy)0 + (2x2)2 17. 8x-1y 18. 1251/3 19. A roller coaster begins at 90 feet above ground level. Then it descends 105 feet.

Find the height of the coaster after the first descent.

20. Eric plays a card game. He scores 289 points in the first round and scores 137 points in the second round. How many points does he have?

21. Grace scores 15 points fewer than Payton, who scores 35 points. Alex scores half as many points as Grace. How many points does Alex score?

22. Jackson plans to buy three boxes of popcorn at the movies for himself and two friends. If each box costs $1.95, how much change will he receive when he pays with a ten-dollar bill?