Home > KYOTE College Algebra Practice Exam 3 1. Simplify. x2(x3 − 7x) − (7x − 9x3) A) x5 + 2x3 − 7x B) x6 + 2x3 − 7x C) x5 D

# KYOTE College Algebra Practice Exam 3 1. Simplify. x2(x3 − 7x) − (7x − 9x3) A) x5 + 2x3 − 7x B) x6 + 2x3 − 7x C) x5 D

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KYOTE College Algebra Practice Exam 3 1. Simplify. x2(x3 7x) (7x − 9x3) A) x5 + 2x3 7x B) x6 + 2x3 7x C) x5 9x3 14x D) x5 16x3 7x E) x6 + 9x3 14x 2. A man invests 10,000 dollars in two accounts, the first yielding 4 percent annual interest and the second, 5 percent. If x dollars is invested in the first account, how much annual interest does the man earn on his investement? A) 900.0 B) 0.09x C) 9x D) −x + 50000 E) 0.01x + 500.0 3. What is the set of all values of x for which the expression x + 6 x2 2x − 8 is not defined? A) {−6,−4,2} B) {−6,−2,4} C) {−4,2} D) {−2,4} E) {−6} 4. If x and y satisfy both 9x + 2y = 14 and 7x + 2y = 2, then y =?. A) 44 B) 40 C) 6 D) 20 E) 22 5. Simplify. 2 x − 8 3 x A) 6x + 24 x(x − 8) B) −x − 16 x(x − 8) C) −x − 24 x(x − 8) D) 6 x(x − 8) E) −x + 24 x(x − 8) 6. The line with equation 5x − 4y = 3 is perpendicular to A) y =5 4 x B) y = 4 5 x C) y = 5 4 x D) y =4 5 x E) y =4 3 x 1

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7. Expand and simplify. (7x − 6y)2 A) 49x2 + 36y2 B) 49x2 84xy − 36y2 C) 49x2 36y2 D) 49x2 84xy + 36y2 E) 49x2 42xy + 36y2 8. Simplify. (x15 y12)2z x5(y4 z2)2 A) x6 y3 z2 B) x6 y3 z3 C) x25 y16 z3 D) x25 y16 z2 E) x6 y6 z3 9. Simplify. x2 + x − 6 x2 4x + 4 A) x + 3 x − 2 B) x + 6 x − 2 C) x + 2 x − 2 D) x − 3 x − 2 E) x − 6 x − 2 10. Solve 1 x − 1 4 7 = 5 for x. A)46 39 B)39 46 C)39 38 D) 8 13 E)38 39 11. A rectangle has length 21 inches and width 16 inches. What is the length of a diagonal from one corner to the opposite corner, rounded to the nearest inch? A) 28 B) 24 C) 26 D) 27 E) 25 12. If a line has slope 2 and passes through the point (3,2), what is the y-coordinate of the point on the line whose x-coordinate is 5? A) 2 B) 5 C) 6 D) 3 E) 4 2

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13. Simplify. ( 7x x
-4
)
-2
A)1 49x6 B) 7x6 C)1 49 x6 D)7 x10 E)1 49x10 14. A rectangular field is enclosed by 320 feet of fencing. If the length of the field is 6 feet more than its width, what is its length, in feet? A) 80 B) 83 C) 77 D) 157 E) 163 15. What is F in the formula L =3 5 F − 5 when L = 8? A)55 3 B) 5 C)9 5 D)39 5 E)65 3 16. Which of the following is the equation of the parabola whose graph is shown below? A) y = (x − 5) (x + 1) B) y = (x + 5) (x − 1) 10 C) y =2(x − 5) (x + 1) D) y =2(x + 5) (x − 1) E) y = (x − 5) (x + 1) 10
–5 5 –1
17. Find �� x3 y2 when x = 2 and y = 7. A)2 �� 2 7 B)4 49 C)2 �� 2 49 D) 2 �� 2 7 E) ��2 �� 2 7 3

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18. Simplify. 3 �� 8x27 + x12 A) 2x4 3 �� x15 + 1 B) 8x9 + x4 C) 2x24 + x4 D) 2x9 + x4 E) x4 3 �� 8x15 + 1 19. If f (x)=2x + 9, and f(a) = 7, then a =? A) 9 B) 23 C) 1 D) 7 E) 8 20. One solution of 2x2 = −x + 6 is A) 2 B)2 3 C)3 2 D) 1 E) 3 2 21. One of the factors of 3x2 + 18x + 24 is A) 3x + 2 B) x + 4 C) x + 8 D) x + 24 E) 3x + 4 22. Solvex − s 7= y − t 5for x. A)7 5 y + 7 5 t − s B)5 7 y + 1 7 t + 1 7 s C)7 5 y + 1 5 t +1 5 s D)5 7 y + 5 7 t + s E)7 5 y + 7 5 t + s 4

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23. Solve 4x +4= 6+3x for x. A) 2 7 B) 10 C) 5 D)7 10 E)10 7 24. Find x2 x − y when x = 3 and y = 4 A) 9 B) 9 7 C)9 7 D) 9 E) 3 4 25. Solve 7x<x + 5 and express the solution in interval notation. A) (−��, 6 5) B) (5 8 ,��) C) (8 5 ,��) D) (5 6 ,��) E) (−��, 5 8) 5

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Key: KYOTE12CART3
1) A 2) E 3) D 4) D 5) E 6) B 7) D 8) C 9) A 10) A 11) C 12) A 13) E 14) B 15) E 16) A 17) A 18) E 19) C 20) C 21) B 22) E 23) E 24) D 25) B
Standards Table
Standard Problems Max Score KYOTECA.01.3: 17,24 2 KYOTECA.02.3: 1,7 2 KYOTECA.03.3: 8,13 2 KYOTECA.04.3: 18 1 KYOTECA.05.3: 21 1 KYOTECA.06.3: 5 1 KYOTECA.07.3: 9 1 KYOTECA.08.3: 15,23 2 KYOTECA.09.3: 22 1 KYOTECA.10.3: 25 1 KYOTECA.11.3: 20 1 KYOTECA.12.3: 10 1 KYOTECA.13.3: 4 1 KYOTECA.14.3: 2,14 2 KYOTECA.15.3: 11 1 KYOTECA.16.3: 6,12 2 KYOTECA.17.3: 16 1 KYOTECA.18.3: 3,19 2
Description of Standards
1. KYOTECA.01.3: Evaluate algebraic expressions at specified values of their variables using signed numbers, rational exponents, order of operations and parentheses. 2. KYOTECA.02.3: Add, subtract and multiply polynomials. 3. KYOTECA.03.3: Simplify algebraic expressions involving integer exponents. 4. KYOTECA.04.3: Simplify algebraic expressions involving square roots and cube roots. 5. KYOTECA.05.3: Factor a polynomial in one or more variables by factoring out its greatest common factor. Factor a trinomial. Factor the difference of squares. 6. KYOTECA.06.3: Add, subtract, multiply and divide simple rational expressions. 7. KYOTECA.07.3: Simplify a rational expression. 8. KYOTECA.08.3: Solve a linear equation. 9. KYOTECA.09.3: Solve a multivariable equation for one of its variables. 10. KYOTECA.10.3: Solve a linear inequality in one variable. 6

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11. KYOTECA.11.3: Solve a quadratic equation. 12. KYOTECA.12.3: Solve an equation involving a radical, a rational or an absolute value expression. 13. KYOTECA.13.3: Solve a system of two linear equations in two variables. 14. KYOTECA.14.3: Solve problems that can be modeled using a linear or quadratic equation or expression. 15. KYOTECA.15.3: Solve geometry problems using the Pythagorean theorem and the properties of similar triangles. 16. KYOTECA.16.3: Understand and apply the relationship between the properties of a graph of a line and its equation. 17. KYOTECA.17.3: Find the intercepts and the graph of a parabola given its equation. Find an equation of a parabola given its graph. 18. KYOTECA.18.3: Evaluate a function at a number in its domain. Find the domain of a rational function or the square root of a linear function. 7