Nallari Math 8 Class : Mid-Term Review Study Guide Name Date P. Part I: Patterns, Functions & Algebra (Midterm) SOL 8.15: Match the algebraic terms to their correct definitions Expression Term Coefficient Variable Constant Equation Inequality 1 - - A term that does not contain a variable: e.g., the #2 in 4x 3 2 = 23. 2 - - Any number, variable, or the product of a number and a variable: for example, in 7x (-9y) both 7x and (-9y). 3 - - A numerical factor combined with a variable. E.g., in 2x + 3y - 16, the of x is 2 & of y is 3 4 - a mathematical phrase containing numbers, variables and operations (but with no equal sign): 2n (3+2) 2 5 - - a letter or other symbol that stands for a number. 6 - - a math sentence that contains a sign like <,,, or >. 7 - - A math sentence with an equal sign: 2x 5 = 15. SOL 8.15: Label the equation below with the correct terms from the word bank. Term Coefficient Variable Constant Inequality 4 > 3x + 1 SOL 8.15: Translate the following expressions or equations: 1. Eighteen more than a number. 2. Five less than a number. 3. The difference of seven and a number. 4. Sixteen less than twice a number. 5. Five times the sum of a number and four. 6. The quotient of a number and six equals 12. 7. A number divided by three plus two is 16. 8.15: EQUATIONS - Solve and check the equations that follow 2-step: 1.!!!!12!!2! =!!10 2.!!!! 26 = 3! 11
3.!!!!!!!15 =!!10 4.!!!!!!19 =!!!! +!7 Multi-Step: 5. 7 + 3h = -1 5h 6. x + 12 = -4-3x 7. 4(x -4) = -28 8. -3(-5x -2) = 21x 9. 3 = 3(6t 9) 8t 9. 2 ( x 7 ) = 30 9x Inequalities: Solve 1.) 2x 5 < 23 Graph Check 2.) ½ b + 30 > 10 3.) -2x + x -24 4.) -3x + 5-23
8.16: Linear Equations: Fill in X, solve and graph. Given Equation: y = 8 2x x y = y ( x, y ) Identify 3 sets of ordered pairs along the line, then ID the equation that belongs to the graph! 1. Y = X Y SOL 8.14: Determine whether the tables or graphs below represent functions. Explain your decision. 1. 2. X Y 1 2 2 3 3 4 1 5 3. 4. X Y -7 1-5 2-3 3-1 4
SOL 8.14: Use the tables of value below to determine the rules of the functions. 1. 2. 3. 4. X Y -2-4 0 0 2 4 4 8 X Y 12 4 9 3 6 2 3 1 X Y 0 4-1 3-2 2-3 1 X Y 10 8 6 4 4 2 2 0 SOL 8.17: Domain & Range. 1. Find the domain and range: {(6,9), (-4,-2), (5,4), (-1,2)} D R 2. Circle the independent and square the dependent variables in the following equations: y = 2x y = 3x -6 u = m!2 23 = y + 2x 3 3. Given the function of x defined by y = -x + (-2), if the input is { -1, 0, 1}, what is the output? Part II - Computation and Estimation (Midterm) SOL 8.3: Use proportions to find %... Percent is a ratio with a denominator of. 1.) What is 15% of 115? 3.) 18 is 60% of what number? 2.) 45 is what percent of 180? 4.) What is 12.5% of $80.80? SOL 8.3: Finding % change between two values 1) A necklace was originally priced at $7.45, and is 2) A pair of tennis shoes was originally priced at marked down to $4.70. What is the percentage decrease in price? $6.98, and is marked down to $4.58. What is the percentage decrease in price?
SOL 8.3a: Use proportions to solve the following problems: 1. 2. 3. 12 = x 5 15 n = 10 50 20 5 = 15 9 k 4. A display case of ties are marked 59 for $8. If Nate has $56, how many ties can Nate get? (Assume no tax or other fees.) 5. To make a fruit salad, Kenny uses 60 grapes for every 13 people. How many people will be served if Kenny is using 240 grapes? 6. A display case of gold chains are marked 9 for $49. If Betty wants to buy 63 gold chains, how much will Betty spend (not including tax)? 7. To make a fruit salad, Fiona uses 31 star fruits for every 3 people. If Fiona wants to serve 24 people, how many star fruits will Fiona SOL 8.3b: Calculate the tax, tip or discount in the following problems: 1) In Minnesota, sales tax is 6.0%. What is the tax on items that total $17.50? 2) In Kansas, sales tax is 5.0%. What is the total (including tax) on items that total $180? 3) You and your friends order a meal for $138. How much tip should you leave if you want to leave a 15% tip? 4) You and your friends order a meal for $50.50. How much will you pay (including tip) if you want to leave a 20% tip? 5) While shopping for a gift, you find the perfect jacket on sale for 40% off it's original $38.00 price. How much will be the discount? 6) A shirt is marked with a sale sticker saying it is 11% off. The original price is $29.00. What is the total sale price?
SOL 8.3b: Solve I, P, R or T in the questions below 1) What is the interested earned if $7500 is invested over 4 years at an interest rate of 3%? 2) If you invest $2500 in an account that earns 5% annual simple interest for 10 years, what will the total value of the account be? 3) Bill borrows $490 at 4.9% simple interest per year. When Bill pays the loan back 5 years later, how much interest does Bill pay? 4) Evan borrows $3300 at 2.5% simple interest per month. When Evan pays the loan back 10 years later, how much interest will he have to pay? 5) A) What is the interest earned if $17500 is invested over 10 years at an interest rate of 0.5%? B) What is the total amount that would be in the bank? 6) If you earned $1250 interest from an account that earns 5% annual simple interest over 10 years, how much did you invest? 7) Bill borrows $490 at and pays back $120.05 in simple interest over 5 years. What was the interest rate for Bill s loan? 8) Evan borrows $3300 at 2.5% simple interest per year and ended up paying $825 in interest over the course of the loan. How many years did Evan take to pay back the loan?
SOL 8.4: Order of Operations (PEMDAS) & Expressions. 1.!![!"!!!! ]!!!! 16 2. 6 2 (3 + 9) + 2(5+3) 3. 6(2 + 5) 3(7) Substitute the given value for the variable and evaluate the expression. x = - 4, y = 3, m = ½, p = 2/3. 4. mxy + 2( x+ y) 2 5. 6p + (2y + 5x) 6. 2x 2 + y 3 Part III: Number & Number Sense (Midterm) SOL 8.1: Conversions of Dec., Percent, & Fractions. Picture form Fraction Decimal Percent 1. 88% 2. 2.17 3. 3/8 4.
SOL 8.2: Scientific Notation & Square Roots. Rewrite the numbers in standard form. 1. 7 x 10-6 = 2. 4 x 10 4 3. 7 x 10 5 4. 8 x 10-5 5. 9.9 x 10 7 6. 2.21 x 10-9 Find the square root OR two roots between which the square root falls. 1. 225 2. 400 3. 576 4. 81 5. 133 6. 43 7. 380 8. 324 SOL 8.1: Compare & Order Dec., %, Fractions & Scientific Notation in ascending order. 1. 3/4, 57%, 0.68 2. 65%, 0.321, 3.2 x 10², 12/12 3. 24.5, 1.2 x 10², ½, 99% 4. 9.3, 3 x 10², 1/4, 22.3% SOL 8.2: Identify the subset(s) of Real Numbers represented by each set of # s. Irrational # s, Rational # s, Integers, Whole # s, Natural # s 1) 0, -1, 8 Irrational, Rational, Integers, Whole, Natural 2) 1.5, -1.23, 7.2 Irrational, Rational, Integers, Whole, Natural 3) 0, 1, 3, 5 Irrational, Rational, Integers, Whole, Natural 4) 1.123456, Irrational, Rational, Integers, Whole, Natural 5) 3.14, 3.33, -0.66 Irrational, Rational, Integers, Whole, Natural 6) 1, 2, 3 Irrational, Rational, Integers, Whole, Natural
SOL 8.1a: Properties of Rational Numbers Match the properties below to the correct variable and numerical example: Match the correct letter below Variable Form Numerical Example 1. Commutative Property of Addition 2. Commutative Property of Mult. 3. Associative Property of Addition 4. Associative Property of Multiplication 5. Distributive Property 6. Additive Identity Property 7. Multiplicative Identity Property 8. Additive Inverse Property 9. Multiplicative Inverse Property 10. Multiplicative Property of Zero A~ a + ( b + c ) = ( a + b ) + c B~ a + b = b + a C~ a + ( -a ) = 0 D~ a ( b + c ) = a b + a c E~ a b = b a F~ a 1 = a G~ a ( b c ) = ( a b ) c H~ a + 0 = a I~ a 0 = 0 A~ 3 0 = 0 B~ 2 + 3 = 3 + 2 C~ 2 ( 3 + 4 ) = 2 3 + 2 4 D~ 2 ( 3 ) = 3 ( 2 ) E~ F~ 2 + ( 3 + 4 ) = ( 2 + 3 ) + 4 G~ 3 + (-3) = 0 H~ 3 + 0 = 3 I~ 2 ( 3 4 ) = ( 2 3 ) 4 J~ J~ 3 1 = 3