A. 6x + 4y = 7 B. 3x 2y = 3 C. 6x 4y = 1 D. 3x 3y = 4 E. 3x + 2y = 5
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1 Dr Numsen High School Mathematics Practice Test February 07. Evaluate: ( 5) 0! [( 9) ] Max buys a dozen tacos, three burritos, and six tostados. Tacos cost $.5 each; burritos cost $.5 each; tostados cost $.0 each. He paid with two twenty-dollar bills. How much does he have left? $.5 $5.95 $.5 $7.5 $7.5. If (ax + )(x a) = 7x + bx + c, then b + c = Find the equation of the line shown. y x x + y = 7 x y = x y = x y = x + y = 5 5. Lisa has some lollipops. She gives 0% to Bart. Of the remaining, she then gives 5% to Milhouse. Of the remaining, she then gives % to Marge. Each of Bart, Milhouse, and Marge received the same number of lollipops. If Lisa has lollipops left, how many lollipops did she start with? How many subsets of the set {n, u, m, b, e, r} contain the element n? 7. The points (, 7), (, ), and (, k) are collinear. Find k
2 Practice Test February 07 Page. Solve for x in terms of y: x = 5y x = 9y 5y 7 x = y x = 7 y x = 5 7y x = y 9. Find the volume of the isosceles trapezoidal prism ( ) 7 = Today, a trucker drove hours minutes and covers 5 miles. Tomorrow, he needs to travel 0 miles and must arrive at 5:00pm. Assuming he breaks for 0 minutes to eat lunch, but otherwise can average the same speed as today, what time should he leave? (Round.) :am :am :5am 9:0am 9:9am. Which of the following does not represent y as a function of x? I. x = y II. x + y = III. x y = IV. x + y = All I, II, and IV II and IV I and IV II and III. If a + bi and a bi are the two complex roots of x + x + = 0, with b > 0, what is a + b? 0. The sum of the coefficients of the nd and rd terms in the expansion of (x + 5) is If k = 5 k, then k =
3 Practice Test February 07 Page. If f(x) = x + 5 and g(x) = 7x, then f ( g(x) ) + g ( f(x) ) = 0x + 0 x + x + 0 x + x Find the remainder when (x 7x + x 5x + ) is divided by (x ) A pipe is a right circular cylinder. Its diameter is inches and its height is feet. How many gallons does it hold? (Round.) Let T n be the nth triangular and S n be the nth square number. Find the value of T + T 9 + S. T S T 5 S 5 T 0. Given the circle, if m > STP = (m > PR), m > RS = m > TP, and m > PR = m > RS. Find m TQS. R P Q S T. lim x x x = does not exist. Find the range of y = sin [ π (x )] +. [ 5, ] [, ] [, ] [, 7] [ 7, 5]
4 Practice Test February 07 Page. If sin θ = and tan θ < 0, find cos( θ).. If a =, a =, a = a n + a n, for n, find a a 5 + a According to Descartes Rule of Signs, how many possible negative roots does f(x) = x 7x + 5x + 7x + have? or 0,, or 0 or. The parabola y = ax + bx + c has a vertex of (, ) and an x-intercept of. Find a + b If f(x) = x x + 7, find f (5). 7. BE CD, AB =, AC = 0, and AE =. Find E A B E 9 0 C D 9. What graph is produced by the polar equation r = sin θ? dimpled limaçon limaçon with inner loop cardioid spiral circle
5 Practice Test February 07 Page 5 0. If f(x) = x x +, then f () =. A wheel with equal sectors is spun. On the wheel are the numbers through. What is the probability of spinning two prime numbers in a row? in base is equal to what base fraction? The intersection of the medians of a scalene triangle is called the. orthocenter centroid circumcenter incenter Gergonne point. How much should be invested at.5% compounded quarterly over 5 years to have a total of $000.00? $5.9 $. $9.75 $70.50 $ What is the smallest prime q where p and q = p + are both prime, but q is not a Germain prime? Find the equation of the ellipse shown. y x 5x + y = 00 x + 5y = 00 5x + 9y = 5 9x + 5y = 5 x + 9y =
6 Practice Test February 07 Page 7. Let r and s be the roots of 5x x + 5 = 0. Find r s + r s + rs (n + )!. How many integral values of n exist such that n and 00? n! 5 9. Bob can lay 00 ft of carpet in 0 minutes. Tim can lay 0 ft of carpet in 5 minutes. How long will it take them working together to lay carpet in three rooms: ft by ft, 0 ft by 0 ft, and 5 ft by ft? (Round.). min.7 min.7 min.9 min. min 0. Find the largest angle of the triangle whose vertices are (, ), (5, 7), and (, 5). (Round.). If k 5 k = and k < 0, then k = 5 7. If log (x + ) log (x) =, then x =. Find the area bounded by the curve y = x x and the x-axis.. If A x + + B x = x x x, then A + B = 0
7 Practice Test February 07 Page 7 5. The pattern continues. Find the sum of all entries in Rows 5 through. Row : Row : Row : 5 Row : Find the directrix of the parabola (y ) = (x + 7). y = y = x = 9 x = 5 x = 7 7. The function f(x) = x x x has a removable discontinuity when x = x 7 7. The function f(x) = x x + 7 has an inflection point at (h, k). Find h If k k+ k+ = 9, find (k )/ A boat leaves port and sails. miles at a bearing of 7. Then, it turns and sails 7.9 miles at a bearing of. What bearing should the boat travel to return to port? (Round.) The dot product of the vectors, k and k, 5 is. Find the magnitude of the vector, k The center of a circle is (, ). The point (, 0) lies on the circle. Find the area of the segment of the circle above the x-axis. (Round.)
8 Practice Test February 07 Page 5. Sound intensity is power of sound per area. The basis of intensity is related to the threshold( of hearing, ) I 0 = 0 W/m I. The formula for intensity I is relative to the sound level L by L = 0 log, where I 0 L is measured in decibels. How many times more intense is a sound of level 0 db than a sound of level db? (Round.) How many zeros are at the end of the number (5!) (5!) when written out? Find the smallest positive solution to sin (x) + sin(x) + = 0. π π π 7π 5π 5. If x y = 5, find dy dx. x y x y x y x y x y 57. What is the y-intercept of the slant asymptote of f(x) = x x? x A hockey team has forwards, wingers, and 7 defensemen. Not counting the goaltender, the team can put 5 players on the ice. How many combinations of forward, wingers, and defensemen can be created? How many solutions to the equation x+y+z = 5 exist with x, y, z non-negative integers with x y z? The parabola y = x + x + is tangent to the line y = x at (h, k). Find h. 7
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