4x = y + 3 3x 2y = 1

Transcription

1 Math 102, Ch. 3 & Ch. 4, Practice Test Note: No make-up exams will be allowed. Instead, the lowest score will be dropped. 1. Solve the system by graphing x + y = 4 2x y = 2 2. Solve the system by graphing 4x + y = 2 y = x 3. Solve the system by substitution x = 2y 3 5x 4y = 9 4. Solve the system by substitution 4x = y + 3 3x 2y = 1

2 Math 102, Chs. 3 & 4, Practice Test Page 2 5. Solve the system by elimination x + y = 4 x y = 8 6. Solve the system by elimination 2x 3y = 16 2x 5y = Solve the system by elimination 5x + y = 12 2x 2y = 0 8. Solve the system by elimination 6x + 5y = 4 4x + 2y = 8

3 Math 102, Chs. 3 & 4, Practice Test Page 3 9. A landscape designer invested a total of $6000, some at 4% and the rest at 2%. He earned $162 in interest after one year. How much did he invest at each rate? Amount invested Interest earned Equations: 4% 2% Total 10. How many pounds each of cookie dough containing 15% chocolate chips and dough containing 30% chocolate chips must be mixed to obtain 100 pounds of cookie dough containing 18% chocolate chips? Pounds of dough Pounds of chocolate chips Equations: 15% 30% 18% The amount invested at 4% is. The amount invested at 2% was. 11. Solve the system by graphing. y 0 y x 3 The no. of lbs. of 15% mixture is. The no. of lbs. of 30% mixture is. 12. Solve the system by graphing. y < 1 4 x + 3 x y < 1

4 Math 102, Chs. 3 & 4, Practice Test Page Simplify 14. Simplify completely. (a) (a) 9 1 ( 0.5) Simplify (a) Simplify. (a) 40a x 2

5 Math 102, Chs. 3 & 4, Practice Test Page Simplify. (a) 5 x Simplify. 600a 6 b 3 121c x Simplify. (a) Simplify 90a 2 b 5 125b 72 12

6 Math 102, Chs. 3 & 4, Practice Test Page Simplify. 22. Simplify. (a) (a) Simplify. 24. Simplify. Write your answers with rational exponents. 3 2 (a) 100 (a) 3 a 8 a 1 4 ( a 12 ) a 1 4 a

7 Math 102, Chs. 3 & 4, Practice Test Page Simplify using rational exponents. Then write the expression as a single radical. 6 a a 26. Solve. 8x 1 = Solve. x +12 = x 28. Find the length of the unknown side as a radical in simplest form. x 10 5

8 Math 102, Chs. 3 & 4, Practice Test Page Simplify. Write your answer in the form a + bi. (a) ( i) ( 1+ 2i) 30. Simplify. Write your answer in the form a + bi i ( 5 + 3i) ( 4 2i)

9 Math 102, Chs. 3 & 4, Practice Test Page 9 For Reference Rules for Fractions For any real numbers, a, b, c, and d, b 0, c 0, and d 0 a c + b c = a + b a c c b c = a b a c b c d = ac a bd b c d = a b d c = ad bc Properties of Equality Properties of Inequality For any real numbers, a, b, c, For any real numbers, a, b, and c > 0 For any real numbers, a, b, and c < 0 If a = b, then If a < b, then If a > b, then If a > b, then If a < b, then a + c = b + c and ac = bc a + c < b + c and ac < bc a + c > b + c and ac > bc a + c > b + c and ac < bc a + c < b + c and ac > bc Consistent systems Independent equations Dependent equations Inconsistent system The two lines intersect in a single point. The equations describe the same line. The lines are parallel. System solution set: {(2, 1)} Product Rule Rules for Exponents System solution set: {(x, y) 2x + y = 3} a m a n = a m+n Definition System solution set: Rules for Radicals (for a 0 if n is even) Quotient Rule (a 0) Power Rules (a m ) n = a mn (ab) m = a m b m (b 0) Product Rule Quotient Rules Zero Exponent a 0 = 1 (a 0) Distributive Property Negative Exponent (a 0) Definition (for a 0 if n is even) Rational Exponent (a 0 when n is even)

10 Math 102, Chs. 3 & 4, Practice Test Page 10 Power Property of Equality For any real numbers, a, b, and n, such that a n is a real number, if a = b, then a n = b n Complex numbers = {a + bi a, b, and i = 1 }. Note that i 2 = 1. Pythagorean Theorem a 2 + b 2 = c 2