Early Start: Worksheet #1 No calculator/phone use I. Perform the operations; simplify completely. a) 8 ( + 4) ( 7) + ( 1) b) (11 16) (17 10) c) 7 14 6 d) 1 6 5 e) 4 1 + f) 6 9() 10 + 5 5 1 5 4 g) 9 9 + h) 9 + 6 i) 5 5 6 1 j) 8. 4.6 +.05 k) 0.(1.4) + (0.) l) 6.7
II. Operations with Integer Exponents: Perform the operations; simplify completely. a) 4 10 b) 8 6 0 ( 6 4 c) ) 9 4 d) 6 ( 9) e) 1 0 + f) 10(7 + 5) 1 III. Simplify the expressions; solve the equations. 60 5 1 a) y [5 (6 4 y)] + y b) n = c) 6( 0 r) + 4(1r+ 0) = 9 6 1 d) a ab + ab + a e).4n n 0.17 = 0.4 f) 0.c+ 0.06c 1. + 0.5 5 4 10 8 15
IV. Evaluate the formula at the given values. V. Evaluate the expression at the given values. C = 5 ( F ) ; 9 c d d cd; c =, d = 6 i) F = 68 ii) C = 15 VI. Evaluate each function at the given value. Write result as an (Ordered, Pair). 4 a) f( x) = x x + 17 ; x = b) gx ( ) = 4x+ ; x = c) f( x) = x 4x ; x = 0. 5 b ± b 4ac VII. Solve and simplify. Use the Quadratic Formula: If ax + bx + c = 0, then x =. a a) 5x 10x+ 1 = 0 b) x + 8x = 0
Early Start: Worksheet # No calculator/phone use I. Divide: a) Write result as a mixed number. b) Write result as a decimal rounded to tenths. i) 57 1 = ii) 0.07 5 7.5 = i) = ii) 0.8 = c) Write as a decimal number. i) 7 100 01 8 8 = ii) 14 = iii) = iv) 7 = 1000 10,000 d) Write as a decimal with a repeat bar. e) Write as: simplified fraction; per cent. i) 4 11 = ii) 11 = i) 0.08= % 6 10 = fr. ii) 4.45 = % = fr. II. Divide the polynomials; when appropriate, write with a rational remainder. a) 1y y+ 6 y b) a 7a 11 a +
III. Write each as a decimal. i) 0.04% = ii) 50 = iii) 6 4 % = iv) IV. Convert to a %: a) 7 b) with a fractional remainder. 9 00 = = (tenth of a %) i) 5 16 = ii) 41 = = (nearest %) 1 c) Convert 1 % to a simplified fraction. V. In an office of 6 employees, 15 are men. Eighteen of the 4 employees who are lawyers are women. a) How many women work in the office? b) How many male lawyers are there? c) What simplified fraction of the: i) employees is female? ii) lawyers is male? d) What percent of the: i) men are lawyers? ii) lawyers are women? 5 e) What percent of the employees is male? (Express as mixed number %, e.g., 7 6 % ) f) What percent of the women are not lawyers? (Round % to nearest tenth. e.g., 1.% ) Do work on back! VI. Find each percent by moving the decimal point; do as much mentally as possible! $4: 100% = 10% = 1% = % = 0% = 0.1% = 00% = 50% = VII. Assume the standard tip at a restaurant is 15%. Round the bill, then estimate a tip. Bill = $7.84 a) Round bill to nearest ten dollars. b) Round bill to nearest dollar. tip = $ tip = $
VIII. a) A clothing store pays its supplier $8 per shirt. Find the retail price if the store desires a markup of: i) $10 ii) 10% iii) 5% b) Decrease $0 by a % using Mental Math skills. 10% 50% 100% 1% c) Cynthia earns $,600/month. Determine her take-home pay if she pays % in state taxes, 1% in federal taxes, and $450 for health insurance. [Hint: Deduct taxes first, then the cost of health insurance.] IX. Multiply/Divide by moving the decimal point avoid arithmetic! a) 100(0.0416) b) 94. 10 c).479 4 d) 851 10 0.01 X. Graph each set, then express solution in [Interval, Notation). 9 1) x < 1.8 ) w 0.4 ) c 8 5 0 1 0 1 0 1 XI. a) Round 75,49 to the nearest: ten thousand hundred ten thousand ten million million hundred thousand b) Ralph wants to purchase six tacos at 89 cents/each, two bean burritos at 69 cents/each, and a medium drink at $1.49. If sales tax is 9%, can he afford this bountiful buffet if he has only $10? SHOW! XII. a) Round the measurements of the rectangular room to the nearest unit. Then, estimate: 1.7 feet i) Perimeter ii) Area 8. b) Suppose the floor shall be covered with tile that costs $.79 per square foot and sales tax is 9%. Estimate the tile cost by rounding the tile price to the nearest dollar and the sales tax to the nearest unit. Do you think this estimate is higher or lower than the actual amount? Explain!
Early Start: Worksheet # No calculator/phone use Divisibility Rules the most common cases A number is divisible by: if it is even (i.e., it ends with 0,, 4, 6 or 8) 6 if divides number and divides number if divides the sum of the number s digits 8 if 8 divides the number s first three digits 4 if 4 divides the number s first two digits 9 if 9 divides the sum of the number s digits 5 if the number ends with 0 or 5 10 if the number ends with 0 I. a) Determine the divisibility of each number. b) Find the Prime factorization of each number. i) 70 Circle divisors: 4 5 6 8 9 10 ii) 40 Circle divisors: 4 5 6 8 9 10 Prime factorization = Prime factorization = iii) 784 Circle divisors: 4 5 6 8 9 10 iv) 1,485 Circle divisors: 4 5 6 8 9 10 Prime factorization = Prime factorization = v) 97 Circle divisors: 4 5 6 8 9 10 c) Simplify the fractions. i) 40 70 ii) 784 40 Prime factorization =
II. a) Determine the Least Common Multiple of each collection of numbers by listing multiples. i) 1, ii) 0, 16, 6,, 45, b) Use the above results and the fact that the LCM = LCD to simplify the expressions. i) 5 1 + 7 ii) 7 + 8 11 16 1 0 45 6 III. i) Prime factor the given numbers; iii) Determine the LCD; simplify the expression. ii) Determine the GCF; simplify the fraction. a) i) 6 = 60 = ; i) 48 = 7 = ; 6 ii) GCF = 60 = ii) GCF = 7 48 = iii) LCD = iii) LCD = 7 11 5 17 + 60 6 48 7 IV. Determine the LCD, then simplify the expression. a) LCD = x x y 4 x + + y 16 1
b) LCD = c) LCD = 1 8 7 1 a 7 + 6 6w 45w 0w 4a 8 a 4a V. Determine the LCD, then use it to solve the equation. a) LCD = b) LCD = c) LCD = x x= 1.5c 6 0.1c=.4 0.01 a (0.a 1) = 8.5 7 1 0 8 4 d) LCD = e) LCD = f) LCD = 5 1 7 y 7 1 + = = 6v 1 8v 4y+ 16 y + 4y 4y r 8 r 8 = 0 18 45
Early Start: Worksheet #4 No calculator/phone use Addition Key terms in translation Subtraction 1.45 more than a number 1.45 + x six less than r r 6 eight plus some number 8 + n a number minus five t 5 K increased by K + seven decreased by x 7 x 75 added to H H + 75 y reduced by three y the sum of two numbers a+ b a subtracted from 10 10 a the total of w and 14 w + 14 the difference of 1 and m 1 m Multiplication Division the product of d and 0.4 0.4d the quotient of 18 and x six multiplied by y 6 y F divided by,000 a number times 76 76r the ratio of two numbers 17% of some number Two-thirds of n 17 0.17 100 p or p n 18 or x F 000 a b 18 x I. Translate each sentence fragment into an algebraic expression. 1) 100 more than A 6) the square of 4% of a number ) a number reduced by 40 7) the sum of three times a number and two ) 15 less than a number 8) three times the sum of a number and two 4) a number increased by nine 9) the quotient of 5 more than a number and the number 5) 4% of a squared number 10) the quotient of a number and 5 more than the number II. Translate then simplify each expression. i) the difference of a number increased by eight ii) the total of a number decreased by 1 and 10 less than twice the number and the number subtracted from six iii) eight decreased by 0% iv) a number increased by 5%
v) one-sixth a cubed number added to nine-tenths vi) one-half the square root of B subtracted from the cubed number five-eighths the square root of B Terminology Common to Inequalities Sara has more than $8,000 in her 401K account. x > 8000 The population of Elbow, Nevada is at most 68. P 68 Fewer than seven clients called during lunchtime. C < 7 Thirty or more students chose the CR/NC option. S 0 The temperature was no more than 90 F. t 90 Dinner costs at least $15, but less than $5. 15 t < 5 III. Translate each sentence to an equation or inequality; solve. i) Nine added to twice a number is fifteen. ii) Seven less than two-thirds a number is at most 11. iii) The difference of a number and six is iv) Four percent of some number is less than 1.. is three-fifths the number. v) The quotient of eight more than twice a number vi) A number decreased by 40% is greater than 6. and the number decreased by one is nine halves. IV. a) Perform the operation; write result in feet, inches. Facts: 1 inches = 1 foot; feet = 1 yard i) ( feet, 8 inches) + (6 feet, inches) ii) ( feet, 9 inches) + ( feet, 7 inches) + (4 feet, 11 inches) iii) (8 feet, 10 inches) - ( feet, 6 inches) iv) (6 feet, inches) - ( feet, 4 inches)
b) Calculate the sum; convert to the desired unit type. When necessary, express as a mixed number. 87 inches + 4 feet + yards i) inches = ii) feet = iii) yards = c) A rectangular poster measures 0 inches by 0 inches. Find the poster s: i) perimeter in inches; convert that to ii) area in square inches; convert that to feet (express as a mixed number). ft (express as a mixed number). V. Convert the Rates of Change. Facts: ounces = 1 quart = pints a) 45 feet inches = b) 15 feet = min. sec. 4 hours yards day c) 1 oz. quarts = e) 16 pint s = quarts 10 sec. min. 5 min. hour VI. Find the perimeter and area of each rectangle. Use correct units. 0.6 cm a) b) 0.
c) The perimeter is 106 cm. d) The perimeter is 10 in. i) Find x. i) Find n. ii) Find area of rectangle. ii) Find area of rectangle. VII. A living room floor plan is pictured. i) Find: a = ; b = ii) Find the perimeter and area. Use correct units. a) Area = b) Perimeter = 18 ft. 1 ft. a b 14 ft. 10 ft. VIII. 1.5 6 4 feet a) Find the volume of the box (in feet): c) Find the surface area of the box (in feet): SA = (Use correct units!) V = (Use correct units!) b) Convert the volume to cubic yards. d) Convert the surface area to square yards. Write the result as a mixed number. Write the result as a mixed number.