CLEP Pre-Calculus Section : Time 0 Minutes 50 Questions For each question below, choose the best answer from the choices given. An online graphing calculator (non-cas) is allowed to be used for this section.. According to the tables for f(x) and g(x) below, what is the value of [f + g]( )? (A) (B) 4 (C) 7 (D) 0 (E) x f(x) x g(x) 4 4 0 0 5 5 7 7 0. According to the graphs of f(x) and g(x) shown, what is the value of [g f]()? (A) (B) 0 (C) (D) (E) Cannot be determined Copyright 006 Peterson's CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus. Alex's grades are shown in the table below for pre-calculus tests. If each test is weighted equally, what is the lowest grade that Alex can score on the fifth and final test to have an average of at least 90%? (A) 89.5% (B) 90% (C) 90.5% (D) 9% (E) 94% Test Grade # 85% # 9% # 86% #4 94% 4. Which of the following could be an equation for the hyperbola shown? (A) (B) (C) (D) (E) ( y 5) ( x + 4) a b ( x + 4) ( y 5) a b ( y + 5) ( x 4) a b y x 5 6 ( y + 5) ( x + 4) + a b 5. Let f(x) x 6, and let g(x) 5x + 4. Which of the following is equivalent to [f g](x)? (A) 0x 8x 4 (B) 0x + (C) x (D) 0x 4 (E) 0x x - 4 Copyright 006 Peterson's CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus 6. Find S so that the sum of the areas of the three figures shown is less than 4. (A) < S < 6 (B) S < or S < 6 (C) 6 < S < (D) S < (E) Cannot be determined 7. Suppose cos( θ ). What is the value of tan( θ )? 8 (A) 7 (B) 65 (C) 7 (D) 7 (E) 8 8. Find the exact value for x if 4 x 6 4. (A) (B) (C) (D) (E) log(0) log(4) log(0) log(4) log(0) log(4) log(4) log(0) log(4) log(0) Copyright 006 Peterson's CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus 9. What is the circumference of the circle with equation (x ) + (y + ) 49? (A) (B) (C) (D) (E) 7π 4π 8π 49π 60π 0. An ellipse has an equation of ellipse? ( x ) ( y + ) +. Which statement is true about this 4 9 (A) (B) (C) (D) (E) The center is at (, ) with a horizontal major axis. The center is at (, ) with a vertical major axis. The center is at (-, ) with a horizontal major axis. The center is at (-, ) with a vertical major axis. The center is at (-, -) with a vertical major axis.. Find the range of the function h( x) + 5. x (A) (,) (B) (5, ) (C) (, ) (D) (,5) (E) (, ). Find three functions, f(x), g(x), and h(x), such that [ f g h]( x) F( x ) if F( x). cos( x) + 5 (A) (B) (C) (D) (E) f ( x), g( x) x + 5, h( x) cos( x) x f ( x) cos( x), g( x) x, h( x) x + 5 5 f ( x) cos( x), g( x) x +, h( x) x 5 f ( x), g( x) x 5, h( x) sin( x) x f ( x), g( x) x 5, h( x) cos( x) x Copyright 006 Peterson's 4 CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus. If 5x + 4y 6 and 6x y 9, what is the value of x +? 4. For each of the functions, indicate if the function is even, odd, or neither. Function Even Odd Neither f(x) 4x g(x) 5sin(θ) h(x) x x + 5 5. If x 6, what is the value of x? (A) 4 4 (B) 8 (C) 6 (D) 4 (E) 64 6. Which of the following equations has a y-intercept of? (A) y x (B) y x + (C) y x + x (D) y x + 7 (E) y sin(x) 7. Let f(x) x, and let the values of g(x) be as shown in the table: What is the value of f(g())? (A) (B) (C) 4 (D) (E) 5 x g( x ) 4 0 4 4 Copyright 006 Peterson's 5 CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus 8. If cot( θ ) p, 6 what is the value of csc(θ)? (A). (B) (C) (D) (E) 6 + p. 6 ( p + 6)( p 6) p 6 6 6 + p 6 6 p 9. Find y if 5y tan(0 ) 0. (A) (B) (C) (D) 4 (E) 6 0. The graphs of f(x) and g(x) are shown here. What is the value of g(f(0))? (A) 0 (B) (C) (D) (E) Cannot be determined Copyright 006 Peterson's 6 CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus. Which of the following could be an equation for the parabola with its vertex at the point ( 6, 8) and a vertical axis? (A) (x + 6) c(y 8) (B) (x 6) c(y + 8) (C) (y + 6) c(x 8) (D) (y 6) x(c + 8) (E) (y 6) x(c 8). Let g(x) x + x 6, and let h(x) x + 5x 8. What is g(h(x))? (A) x 4 + x x 57x + 4 (B) 4x 4 + 0x x 65x + 4 (C) x + 8x 4 (D) x 4 + x 5x 54x + 48 (E) 4x 4 + 0x x 65x + 4. If cos( θ ) z, what is the value of sin( θ )? (A) (B) (C) (D) (E) z 4 + z + z 4 z ( z)( + z) Copyright 006 Peterson's 7 CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus 4. Which of the following is true about the inverse of the function shown in the graph below? (A) (B) (C) (D) (E) The domain of the function is all real numbers. The range of the function is all positive real numbers. The inverse is not a function. The inverse is one-to-one. Both B and D 5. What is the value of sin(50 )? (A) (B) (C) (D) (E) + Copyright 006 Peterson's 8 CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus Section : Time 0 Minutes 50 Questions For each question below, choose the best answer from the choices given. No calculator is allowed for this section. 6. Which of the following is NOT true about the function represented in the table? x f(x) 0 6 0 4 6 5 9 (A) The function is increasing as x moves from 0 to 5. (B) The graph intersects the x-axis at 6. (C) The slope as x moves from 0 to 5 is. (D) Both B and C. (E) All of the above 7. Let h(x) be the function represented in the table, and let g(x) be the function shown in the graph. What is the value of g(h())? x h(x) 0 6 0 0 4 5 7 (A) 0 (B) (C) 4 (D) 5 (E) 7 Copyright 006 Peterson's 9 CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus 8. Jeffrey s job pays him $0 per hour and 5% commission on all of his sales. Last week, Jeffrey worked 40 hours and made x dollars in sales. Which of the following expresses the total amount of money that Jeffrey made last week as a function of x? (A) M 800 + 0.5x (B) M 40x + 00 (C) M 0x + 600 (D) M 800 + 5x (E) M 0 +.5x 9. Two buildings facing each other are separated by a distance of 40 feet. From the top of the first building, the angle of depression of the second building s base is 60, and the angle of depression of the top of the second building is 45. What is the height of the second building? (A) 40( ) (B) 40 (C) 40 (D) 40( ) (E) Not enough information to solve this problem 0. Let f(x) x 9x + 7, and let g(x) x 4x 0. What is the value of f(g())?. Michelle is flying a kite that is 8 feet high. If the string of the kite forms a 60 angle with the ground, and Michelle is holding the kite feet off the ground, what is the length of the string? Write your answer to the nearest hundredth of a foot. Copyright 006 Peterson's 0 CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus. According to the graphs of f(x) and g(x) below, what is the domain of [f + g](x)? (A) (, ) (B) [, ) (C) (, ) (D) (,) (E) [, ). The length of a rectangle is 4 more than times the width. Which of the following is an equation for the length of the diagonal of the rectangle in terms of the width? (A) (B) (C) d 4 + w d 4w + 6w + 6 d 5w + 6w + 6 (D) d 5w + 6w + 6 (E) d 4w + 6w + 8 4. Let f(x) x 4x 5, and let What is the value of [f g](5)? (A) 5.68 (B) 0.049 (C) 49.8 (D) 50 (E) 50. Copyright 006 Peterson's CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus 5. What is the range of the function y cos(x)? (A) [, ] (B) all real numbers (C) all rational numbers (D) [0, ] (E) [-, 0] 6. Suppose sin( θ)cos( θ ). What is the approximate value of θ? 4 (A) (B) 4 (C) 4 (D) 49 (E) 5 7. Suppose the volume of a cylinder is 0 cubic inches. Which of the following is an expression of the surface area of the cylinder in terms of its radius? (A) (B) (C) 60 S r 60 S π ( r) + r 0 S π( ) r (D) 0 S π ( r) + π( r ) (E) S π(r) 8. The sum of all three sides of the right triangle shown is. Find the lengths of its two legs. Copyright 006 Peterson's CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus f 9. According to the tables of values for f(x) and g(x), what is the value of ()? g (A) (B) (C) (D) 6 (E) 7 x f(x) g(x) 5 8 5 0 6 7 40. Find all values of q that satisfy the system of equations shown: (A) -.44,.56 (B).8, 4.07 (C) 0.56, 4.4 (D).4, 0.8 (E).44,.4 p + pq q 4 4 p + q 6 4. Let f(x) x + 6x 7, and let g(x) x 4x +. What is the value of f ()? g (A) (B) (C) (D) (E) 58 8 9 7 9 8 7 9 Copyright 006 Peterson's CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus 4. Find a range of values for p if 4 5p 4. (A) p 4 (B) 8 4 p 5 (C) p 4 or (D) 4 p (E) p 4 8 5 p 8 5 4. According to the table of values for f(x) and g(x), what is the value of [ f g ]()? (A) (B) 0 (C) (D) 4 (E) 6 x f(x) g(x) 6 8 0 4 5 6 4 0 0 4 4 6 44. A right triangle has legs of length 6 inches and 8 inches. What is the measure of the angle opposite the 6-inch leg? (A) 48.6 (B) 4.4 (C) 5. (D) 6.87 (E) Not enough information to solve Copyright 006 Peterson's 4 CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus 45. Which of the following values for x and y satisfies the system of equations shown? (A) 0 4 x, y (B) 94 0 x, y (C) 9 x, y 4 (D) 8 4 x, y (E) x -, y x + 4y 0 x 5y 6 46. A woman is walking along a straight road. She notices the top of a building subtending an angle of 0 with the ground at the point where she is standing. If the building is 50 feet tall, how far is the woman from the building? (A) (B) (C) (D) (E) 86.6 feet 8.9 feet 57.7 feet 00 feet 9. feet 47. What is the value of sin(75 )? (A) (B) (C) (D) (E) 6 + 4 8 4 6 4 Copyright 006 Peterson's 5 CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus 48. A number x is first decreased by 5%, and then the result is increased by 0%. Which of the following functions could be used to determine the final result? (A) f(x) 0.5x (B) f(x) 0.85x (C) f(x) 0.75x (D) f(x) 0.5x (E) f(x) 0.04x Copyright 006 Peterson's 6 CLEP is a registered trademark of the College Entrance Examination Board, which was not involved in the production of and does not endorse this product.
CLEP Pre-Calculus. The correct answer is C. The algebraic combination, [f + g](x), is defined as f(x) + g(x). According to the table, f( ) and g( ) 4. Now find the sum: [ f + g]( ) f ( ) + g( ) + 4. The correct answer is A. The algebraic combination [g f](x) is defined as g(x) f(x). According to the graphs, g() 0, and f(). Now subtract to find the difference: 7 [ g f ]() g() f () 0. The correct answer is D. The average is calculated by dividing the sum of the test scores by the number of tests. Let x equal the score on the fifth and final test: sum of scores Average number of tests 85 + 9 + 86 + 94 + x 5 58 + x 5 Now plug in 90 for the average and use an inequality sign to represent the situation in terms of x: 58 + x 90 5 58 + x 90(5) (5) 5 450 58 + x 450 58 58 + x 58 9 x 4. The correct answer is A. The standard form of the equation for a hyperbola centered at the ( y k) ( x h) point (h, k) and with a vertical axis is. The hyperbola shown is centered at a b ( y 5) ( x + 4) the point ( 4, 5), so an equation for the hyperbola is. a b ANSWER KEY - Page 7
Recovered Master File (08/08/04 : AM) 5. The correct answer is E. The algebraic combination [f g](x) is defined as f(x) g(x). Multiply the equation for f(x) by the equation for g(x) and combine like terms to find the simplified product: [ f g]( x) f ( x) g( x) (x 6) (5x + 4) 0x + 8x 0x 4 0x x 4 6. The correct answer is C. Write an equation for the sum of the area of the three figures. Then solve the inequality for S: Area (S)(S) + ()(S) ()(4) < 4 S S + 4S + < 4 + 4S < 0 ( S )( S + 6) < 0 In order for (S )(S + 6) to be less than zero, one of the factors must be negative, and one must be positive: ( S ) > 0 and ( S + 6) < 0 S > and S < 6 OR ( S ) < 0 and ( S + 6) > 0 S < and S > 6 Since the first solution is impossible, the value of S must lie between 6 and. 7. The correct answer is C. Since sec( θ ), use the identity tan (θ) + sec (θ): cos( θ) ANSWER KEY - Page 8
Recovered Master File (08/08/04 : AM) sec( θ ) cos( θ) tan ( θ ) + sec ( θ) tan ( θ ) + (8) tan ( θ ) + 64 8 8 tan ( θ ) 6 tan( θ ) 6 7 8. The correct answer is C. This equation can be solved using the logarithmic function: x 4 6 4 x 4 0 x log(4 ) log(0) xlog(4) log(0) x log(0) log(4) 9. The correct answer is B. The standard form for the equation of a circle centered at (h, k) and with radius r is (x h) + (y k) r. In this case, the radius of the circle is equal to or 7. Use this value for the radius to calculate the circumference: C π( r) π(7) 4π 0. The correct answer is B. The standard form of the equation for an ellipse centered at the ( x h) ( y k) point (h, k) is +. In this case, the ellipse is centered at the point (, ). a b Since the value for a is less than b, we also know that this equation has a vertical major axis.. The correct answer is B. First find the domain of the function. In order for h(x) to be a real number, x 0, so x and x 0, which means that x cannot be equal to. The ANSWER KEY - Page 9
Recovered Master File (08/08/04 : AM) domain of h(x) is (,). As x runs through (,), range of h(x) is (5, ). x takes on all positive values. The. The correct answer is A. The function F(x) consists of taking the cosine of x, adding 5, and then inverting. Set h(x) cos(x), g(x) x + 5, and f ( x). Calculate [ f g h]( x ) to be sure it x equals the function F(x):. The correct answer is 5.. Multiply the first equation through by : Multiply the second equation through by 4: [ f g h]( x) f ( g( h( x))) f ( g(cos( x))) f (cos( x) + 5) cos( x) + 5 F( x) 5x + 4y 6 (5x + 4y 6) 5x + y 48 6x y 9 4(6x y 9) 4x + y 6 Add the equations together and cancel out the y terms, which leaves a linear equation that can be solved for x: Calculate x + : 5x + y 48 4x y 6 9x 84 84 8 x 9 ANSWER KEY - Page 0
Recovered Master File (08/08/04 : AM) 8 x + + 56 + 69 5. 4. The correct answer is even, odd, and neither. Function Even Odd Neither f(x) 4x x g(x) 5sin(θ) x h(x) x x + 5 x For f(x) 4x, you can see on the coordinate plane that this graph is symmetrical about the y-axis, which means that it is an even function. For g(x) 5sin(θ), we know this is an odd function because the sine curve is symmetrical about the origin. For h(x) x x + 5, we know that this is neither odd nor even because the function is shifted and hence will not be symmetrical to the y-axis or the origin. 5. The correct answer is E. x 6 x x 8 6 x (6) x 6 ( 6 ) 4 64 ANSWER KEY - Page
Recovered Master File (08/08/04 : AM) 6. The correct answer is D. Plug x 0 into each of the equations to find which one has a y- intercept of : Equation A: Equation B: Equation A: Equation D: Equation E: y x y x y x + x x+ y 7 y sin( x) 0 (0) (0) + sin(0) (0) + (0) 7 0 0 + 0 0 7 8 7 The equation given in choice D, y x + 7 has a y-intercept of. 7. The correct answer is D. The notation f(g()) indicates that the value of g() must be determined first, and then that value must be plugged into the equation of f(x). Looking at the table, when x, g(x) 4, and g() 4. Now, plug 4 into the equation f(x): f ( x) x f (4) (4) 6 So, f(g()). 8. The correct answer is A. Use the identity + cot (θ) csc (θ) to solve for csc(θ): + cot ( θ ) csc ( θ) p + ( ) csc ( θ) 6 6 p + csc ( θ) 6 6 6 + p 6 csc( θ) 9. The correct answer is C. First, calculate the tangent of 0 : ANSWER KEY - Page
Recovered Master File (08/08/04 : AM) Plug this value into the equation and solve for y: sin θ tan θ cosθ sin 0 tan0 cos0 5y tan 0 0 5 y( ) 0 y 0 5 0. The correct answer is C. According to the graph of f(x), f(0). Now look at the graph of g(x) to find the value of g(), which is.. The correct answer is A. The standard form for a parabola with a vertical axis and its vertex at the point (h, k) is (x h) c(y k). An equation for this particular parabola is (x + 6) c(y 8).. The correct answer is B. Plug the equation for h(x) into the equation for g(x): g( h( x)) g(x + 5x 8) (x + 5x 8) + (x + 5x 8) 6 4 (4x + 0x 7x 80x + 64) + (6x + 5x 4) 6 4 4x + 0x x 65x + 4. The correct answer is E. Use the identity sin (θ) +cos (θ) : ANSWER KEY - Page
Recovered Master File (08/08/04 : AM) sin ( θ ) + cos ( θ ) z sin ( θ ) + ( ) z sin ( θ ) + 4 4 z sin ( θ ) 4 sin( θ ) ( z)( + z) 4. The correct answer is C. The inverse of a function can be found by reflecting the graph across the line y x, as shown below. Since this graph would not pass the Vertical Line Test, it cannot be a function. 5. The correct answer is E. Use the addition formula for the sine function: sin( α + β ) sin( α)cos( β ) + cos( α)sin( β) sin(50 ) sin(60 + 90 ) (0) () + 0 + 6. The correct answer is B. Consider each statement. As x moves from 0 to 5, the values of f(x) steadily increase. The statement in choice A is true. According to the table, when f(x) 0, x is equal to. The graph intersects the x-axis at. The statement in choice B is not true about the function. Calculate the slope as x goes from 0 to 5: ANSWER KEY - Page 4
Recovered Master File (08/08/04 : AM) y slope x y x 9 ( 6) 5 0 5 5 The slope on this interval is, so the statement in choice C is true. The only statement that is not true about the function is the one given in choice B. 7. The correct answer is B. Use the table to find the value of h(), which is 4. Then use the graph to find the value of g(4), which is. The value of g(h()) is. 8. The correct answer is A. Since Jeffrey worked for 40 hours at $0 per hour, he earned $800. He also made 5% of x dollars, which is equal to 0.5x. In total, Jeffrey earned $800 + 0.5x last week. 9. The correct answer is A. Draw a diagram to represent the situation: Use the trigonometric identity opposite tan( θ ) : adjacent BE tan(45 ) 40 BE 40 BE 40 Also, ANSWER KEY - Page 5
Recovered Master File (08/08/04 : AM) Notice that CD AB BE: AB tan(60 ) 40 AB 40 AB 40 CD 40 40 40( ) 0. The correct answer is 97. First determine the value of g() by plugging into the equation of g(x): Now plug 6 into the equation of f(x) for x: g( x) x 4x 0 g() () 4() 0 (4) 8 0 8 0 6 f ( x) x 9x + 7 f ( 6) ( 6) 9( 6) + 7 6 + 54 + 7 97. The correct answer is 7. feet. Draw a diagram illustrating the situation: Use the trigonometric identity opposite si n( θ ) : hypotenuse ANSWER KEY - Page 6
Recovered Master File (08/08/04 : AM) 5 sin(60 ) x x 5 x 0 0 x 7.. The correct answer is E. The domain of the algebraic combination [f + g](x) is defined as dom( f ) dom( g ). According to the graph, the domain of f(x) is all real numbers, or (, ), and the domain of g(x) is all real numbers greater than or equal to, or [, ). The intersection of the domain of f(x) and the domain of g(x) is [, ).. The correct answer is D. Let l equal the length of the rectangle, let w equal the width of the rectangle, and let d equal the length of the diagonal of the rectangle. The length is 4 more than times the width, so l 4 + w. Now use the Pythagorean Theorem to find the length of the diagonal: (4 + w) + w d 6 + 6w + 4w + w d 5w + 6w + 6 d a + b c 5w + 6w + 6 d 4. The correct answer is C. The algebraic combination [f g](x) is defined as f(x) g(x). Plug x 5 into the equation of f(x) to find f(5): f ( x) x 4x 5 f (5) (5) 4(5) 5 (5) 0 5 75 0 5 50 Now plug x 5 into the equation for g(x) to find g(5): ANSWER KEY - Page 7
Recovered Master File (08/08/04 : AM) Now subtract to find the difference: g( x) g(5) 9 5 5 5 4 + x x 4 + (5) (5) [ f g](5) f (5) g(5) 50 5 50 5 5 49 5 49.8 5. The correct answer is A. Graph the function to observe which y values have corresponding x values: The y values range from to. The range of the function is [, ]. 6. The correct answer is A. Use the double angle formula cos(θ) sin(θ)cos(θ): ANSWER KEY - Page 8
Recovered Master File (08/08/04 : AM) cos( θ ) sin( θ)cos( θ) cos( θ ) 4 cos (cos( θ )) cos ( ) 4 θ 4.4 θ 7. The correct answer is B. Use the formula for the volume to solve for h, the height, in terms of r: V π( r) h 0 π( r) h 0 h π ( r) Plug this value into the formula for the surface area: S π ( r) + π( r)( h) 0 π ( r) + π( r)( ) π( r) 60 π ( r) + r 8. The correct answer is and 4. Using the Pythagorean theorem, write an equation for x and y: a + b c ( x) + ( y) (5) 4x + 9y 5 Since the sum of the three sides is, x + y + 5. Solve this equation for either x or y: x + y + 5 x + y 7 x 7 y 7 y x ANSWER KEY - Page 9
Recovered Master File (08/08/04 : AM) Plug this value into the first equation: Solve using the quadratic formula: Plug these values into an equation for x: 7 y + y 4 9 5 (7 y) + 9y 5 49 4y + 9y + 9y 5 8y 4y + 4 0 4 ± 764 4(8)(4) y (8) 4 ± 764 78 6 4 ± 6 6 4 ± 6 6 4, Calculate the lengths of the legs of the triangle: 7 y x 7 () 4 7 x ANSWER KEY - Page 0
Recovered Master File (08/08/04 : AM) x () 4 x y () 4 y 4 The lengths of the legs of the triangle are and 4. f f ( x) 9. The correct answer is A. The algebraic combination ( x) is defined to be, g g( x) provided g(x) 0. According to the tables, f(), and g(). Now divide to find the product: f f () () g g() 40. The correct answer is E. Solve the second equation for q in terms of p: Plug this value into the first equation: p + q 6 p p + q 6 p q 6 p Solve using the quadratic formula: p + pq 4q 4 p + p(6 p) 4(6 p) 4 p + p 4 p 4(6 4 p + 4 p ) 4 p 4 p 6 p + p + 96 p 44 4 7 p + 08p 44 4 7 p + 08p 58 0 ANSWER KEY - Page
Recovered Master File (08/08/04 : AM) 08 ± 664 4( 7)( 58) p ( 7) 08 ± 664 0744 4 08 ± 90 4.8, 4.07 Plug these values into an equation for q: q 6 p 6 (.8).44 q 6 (4.07).4 f 4. The correct answer is C. The algebraic combination ( ) x is defined as f ( x ), g g( x) provided g(x) 0. Plug x into the equation for f(x), then multiply through by to find f(): f ( x) x + 6x 7 g() (()) + 6() 7) ((9)) + 8 7) (8 + 8 7) (9) 87 Now plug x into the equation for g(x), then multiply through by to find g(): g( x) x 4x + g() (()) 4() + ) ((9)) + ) (7 + ) (7) 54 Now divide to find the quotient: ANSWER KEY - Page
Recovered Master File (08/08/04 : AM) f f ( x) () g g( x) 87 54 9 8 4. The correct answer is B. Solve the inequality as if it were an equation. Remember that when dividing or multiplying by a negative number, the inequality sign changes direction: 4 5 p 4 4 5p 4 5 p 0 p 4 Since the problem involves an absolute value, there is a second inequality to solve: 4 5 p 4 5 p 8 p 4. The correct answer is A. The composition function [ f g]( x ) is defined as f(g(x)). According to the table, g () 4. Now look on the table for f(x) to find f(4), which is equal to. Thus: 8 5 [ f g]() f ( g()) f (4) 44. The correct answer is D. Draw a diagram to illustrate the situation: ANSWER KEY - Page
Recovered Master File (08/08/04 : AM) Use the trigonometric identity opposite tan( θ ) : adjacent 6 tan( θ ) 8 tan (tan( θ )) tan 4 θ 6.87 45. The correct answer is A. Multiply the first equation through by : Multiply the second equation through by : x + 4y 0 (x + 4y 0) 6x y 60 x 5y 6 (x 5y 6) 6x 0y 5 Add the two resulting equations together, canceling out the x terms. Then solve for y: 6x y 60 + 6x 0y 5 y 8 8 y 4 ANSWER KEY - Page 4
Recovered Master File (08/08/04 : AM) Plug this value into either of the original equations and solve for x: x + 4y 0 4 x + 4 0 6 0 x + 04 x 0 x 46. The correct answer is A. Draw a diagram to illustrate the situation: Use the trigonometric identity opposite tan( θ ) : adjacent 50 tan(0 ) x 50 x x 50 86.6 47. The correct answer is A. Use the addition formula for the sine function: ANSWER KEY - Page 5
Recovered Master File (08/08/04 : AM) sin( α + β ) sin( α)cos( β ) + cos( α)sin( β) sin(75 ) sin(45 + 0 ) sin(45 ) cos(0 ) + cos(45 )sin(0 ) + 6 + 4 4 6 + 4 48. The correct answer is B. The result after decreasing by 5% is equal to 0.75x. Decreasing this number by 0% is equivalent to multiplying 0.75x by., which is equal to 0.85x. ANSWER KEY - Page 6