Math 50 Final Exam Sample Problems

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1 Math 50 Final Eam Sample Problems Note: These review eercises are intended as general practice for Mt. SAC Math 50 students. Please consult with your Math 50 professor to find out if there are additional topics and/or types of problems that might be on your particular Math 50 Final Eam. I. True/False A. 7 4 = 6 B. The sum of two negative numbers is a positive number. C. The median of, 5, 5, 06 and 87 is 0. D. The point ( -, 7 ) is located in QIII. E. The ordered pair ( -, 6 ) represents a solution to y = -. F. An equation in the form a c b = is called a ratio. d 5 G. The following is a monomial: yz. 4 0 H. The degree of 5 is 4. I. The following number is written in scientific notation:. 0 J. 0 = 0 II. A. Simplify the following numerical epressions:. 4 ( 6) (). ( 5 + ) 6. + [ ( 54 ( ) ) ( ) ] ( ) (.4) B. Translate to a numerical epression and simplify. Negative two added to the sum of -8 and. The difference between 4 and -8. Twelve less than the difference between 8 and The sum of 5 and -, divided by the product of 4 and - C.. Convert to Standard Form: Page

2 Math 50 Final Eam Sample Problems III. Algebraic Epressions A. Simplify the following algebraic epressions: ( ). ( ) 0... ( ) (. 8 ) 4y y 8 y 5 5 t (..0) ( ) ( ) ( + )( 4 ) ( ) 7 4. n n ( ) ( + 6 ) 6. ( 4 + ) 4 7. ( ) ( 0.5) B. Translate to an algebraic epression using as the variable. five less than twice a number. the product of negative seven and a number. the sum of eight and half a number 4. the difference of a number and 8 the quotient of three times a number and 7 6. seven times a number, subtracted from times the number C. Evaluate each algebraic epression. ( y) when = and y =. + y when = 5 and y = 4 Page

3 Math 50 Final Eam Sample Problems IV. A. Write the Prime Factorization of 40 B. Is 5 prime or composite? C. Is divisible by 7? D. Greatest Common Factor. Find the GCF of 4, 40 and 64. Find the GCF of y, 6 y and 0z E. Least Common Multiple. Find the LCM of 6, 4 and 40.. Find the LCM of 6 and 4. Find the LCM of 8y and 6 y z F. Factor out the GCF a + 0a a V. Equations A. Solve the following equations:. 5 + (-) - =. 8 = = ( -.) = ( 8) = ( + 8) = ( ) = 7( + ) = [ ( )] 7 B. Translate the equations and solve:. Five more than the product of 5 and a number is 80.. Four times a number decreased by 8 is 4.. Seven times a number increased by is decreased by twice the number. 4. The product of 7 and a number is 4. The quotient of a number and, increased by 5 is Fourteen less than a number is 5 times the number. 7. The difference of a number and 7 is Four times the difference of a number and seven is equal to eleven plus seven times the number. Page

4 Math 50 Final Eam Sample Problems VI. Ratios, Proportions, Percents and Conversions A. Ratios. On a map ¼ inch = 50 miles. How far apart in miles are two cities if they are ½ inches apart on the map?. Write as a fraction and reduce 800 stereos to 000 houses.. Write as a unit ratio 5 pizzas to 6 people. B. Percents. Epress as a percent: 5. Epress as a decimal: 6 4 %. Epress as a decimal: 0 4. Epress as a reduced fraction: % of is what number? 6. is what percent of 60? 7. % of what number is 4.4? C. Percent Applications State the answer in a complete sentence.. The cost of a dinner is $8.. If you pay 8% in ta and leave a 5% tip on the cost of dinner only, what is the total cost of your meal?. Miriam and Jose Camacho bought a house for $0,000. Their down-payment was % of the selling price. What was the amount of the down-payment?. Mary earns 5% of her sales in commission. If her commission was $0 what were her sales? 4. In preparing a miture of concrete, John uses 00 lbs. of gravel, 00 lbs. of cement and 00 lbs. of sands. What percent of the miture is gravel? D. Conversions. Convert 0 inches to feet. Convert 7 days to minutes VII. Applications State the answer in a complete sentence. A. Alfred worked 4.5 hours on Monday, 75 hours on Tuesday, and 8.5 hours on Wednesday. His hourly pay is $60. How much money did he earn for his days on the job? B. Four new babies weighed 7 lbs., 6 lbs., 8 8 lbs., and 8 lbs. at birth. What was their total weight? 7 C. An omelet recipe calls for 4 lbs. of cheese. You have 8 lbs. of cheese. How many omelets can be made from this cheese? D. You will use 0 ft of fencing to fence a rectangular plot of land. The length is 0 more than the width. What are the dimensions of the rectangular plot? E. Which is the better buy? Show your work by determining the unit price for each. Option A: $.4 for a 0-oz. bag of carrots, or Option B: $. for a 45-oz. bag of carrots F. Joe s new salary is $75,000 after he receives a 6% raise. What was his old salary? Page 4

5 Math 50 Final Eam Sample Problems VIII. Geometry Label all numerical answers with the appropriate unit of measurement. A.. Find the Circumference and Area of a circle with a diameter of 6.0 m. Use.4 for π.. Find the Perimeter and Area of the following parallelogram. ft ft 8 ft. Find the Perimeter and Area. 40 in. 60 in. 45 in. 0 in. 4. Find the Volume.. m 4.7 m 0. m Find the length of side. 5 m m 6. Find the length of side. Round the answer to the nearest tenths. 8 in 6 in Page 5

6 Math 50 Final Eam Sample Problems 7. Find a simplified epression for the Perimeter and Area Find the Area. 4 in. 8 in.. Find the Area. (Note: the top curve is a semicircle.) cm 0 cm 8 cm 0 cm B. Rectangular Coordinate System. Find the midpoint of (, -6 ) and (, 4 ).. Find the -intercept and the y-intercept of 4y = 8. Epress the answers as ordered pairs.. Find solutions of each linear equation then graph. a. y = 4 b. y = + c. y = 4 d. = Page 6

7 Math 50 Final Eam Sample Problems Solutions: I. A. true B. false C. false D. false E. false F. false G. true H. false I. false J. false II. A ½ B C.. 5,00,000 III. A y 4 5 y 6t n+ 6 n B translate: 7 simplify: 5 C.. 0. IV. A. 4 5 B. composite C. yes D.. 8. E y z F.. 4 ( 5 6). 4a ( a + 5a 8) V. A.. = 5. = 5. = = 4 4 = 0 6. = 7. = 8 8. = 4 4 B = 80, = = 4, = =, = 4. 7 = 4, = = 6, = 6. 4 = 5, = = 4, = ( 7) = + 7, = Page 7

8 Math 50 Final Eam Sample Problems VI. A.. The cities are 500 miles apart.. 4 stereos 5 houses..5 pizzas person B.. 40% % 7. 5 C.. The total cost of the meal is $.06. The down-payment paid by the Camacho s was $,80.. Mary s sales were $ The miture is 50% gravel. D feet. 0,080 minutes VII. A. Alfred earned $0.60 for his days on the job. 7 B. The total weight for the 4 babies was 0 pounds. 4 C. You can make omelets from the cheese. D. The rectangular plot of land is 45 feet by 65 feet. E. Option B would be the better buy. F. Joe s old salary was $70, VIII. A.. Circumference = 8.84 m Area = 8.6 m. Perimeter = ft Area = 7 ft. Perimeter = 60 in Area = 6000 in 4. Volume =.7 m = m 6. in 7. Perimeter = 0 Area = Area = 8 in 64. Area = 04.5 cm B.. ( 5, - ). -intercept: ( 8, 0 ) y-intercept: ( 0, - ). a. b. c. d. Authored by: Beydler, Johnson, Kirchgraber, Rivers, Terreri - June 0(revised June 05) Page 8

Math 074 Final Exam Review. REVIEW FOR NO CALCULATOR PART OF THE EXAM (Questions 1-14)

Math 074 Final Exam Review. REVIEW FOR NO CALCULATOR PART OF THE EXAM (Questions 1-14) Math 074 Final Exam Review REVIEW FOR NO CALCULATOR PART OF THE EXAM (Questions -4) I. Can you add, subtract, multiply and divide fractions and mixed numbers?. Perform the indicated operations. Be sure