Diliman Learning Resource CenterMathematics 17 Midterm Exam ReviewSecond Semester AY 2010-2011 January 17, 2011, Monday

General Directions. Do as indicated. Write your answers clearly and legibly. Show your complete solutions, if necessary, and box your final answer. Use black or blue ink only. Answer as many problems as you can. Good luck!

I. Simplify the following expressions.

1. 64a−3b2 c5

a7bc−1⋅8a12b−9 c27a6b3 c3 −

13

2. x3− y3x3 y3 1− 2y

x y 1 2xyx2−xy y2

II. Do the following as indicated.1. TRUE or FALSE. The set {bi | b∈ℝ and i=−1} is closed under multiplication.2. TRUE or FLASE. For any real numbers a and b that are not zero, if a2 ab then a b3. TRUE or FALSE. The set S = { x , y | x=∣y∣} denotes a function.4. Determine the equation of a line perpendicular to x - 2y = 4 and passing through the midpoint of (4,7) and (-8,3).5. Obtain an equation of a circle in center-radius form if the points (3,-1) and (-5,3) are the endpoints of the diameter of

the circle.6. Find the value(s) of k such that the equation −3k1 x2−k−2 x1=0 will not intersect the x-axis.

III. Consider the functions f x = 7−x , g x =∣2x−3∣ and h x = xx−1

1. Find f °gh

2. Find the domain of f , g , h , f °ghIV. Consider the functions f x =−3x9 and g x = x2− x−6

1. Find the zeros of f(x) and g(x)2. Solve for the y-intercepts of f(x) and g(x)3. Obtain algebraically the points of intersection of f(x) and g(x)4. Find the vertex of g(x)5. Sketch the graphs of f(x) and g(x) on the same coordinate plane.

V. Determine the solution sets of the following.1. 2x x5 = x1

2.

2x− 3y

= 7

1y 10z

= −5

1x− 4y 5z

= 2

3.x

2x2−5x−3− 2x1x 2−x−6

= 3x52x25x2

4.2x−3

x2−2x−3 1

VI. Solve the following word problems. Clearly indicate the quantities your variables represent. Be sure to include the units of the quantities involved in your final answer.1. Working alone, Maria can complete a task in 100 minutes. Jean can complete the same task in two hours. Maria and

Jean work together for 30 minutes when Ralph, the new employee, joins and begins helping. They finish the task 20 minutes later. How long would it take Ralph to complete the task alone?

2. Two persons simultaneously leave cities A and B and travel towards each other. The first person travels 2kph faster than the second and arrives in B one hour before the second arrives in A. If A and B are 24 km apart, determine the rate of each person.