1. The document provides a review for a midterm exam in Mathematics 17 covering topics like simplifying expressions, properties of sets, graphing functions, solving equations and word problems. 2. The review contains 6 sections with multiple parts testing skills in algebra, functions, coordinate geometry, and problem solving. 3. Questions range from simplifying expressions and determining true/false statements to graphing functions, finding intersections of graphs, and solving rate and time word problems.

1. Diliman Learning Resource Center
Mathematics 17 Midterm Exam Review
Second 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−3 b 2 c 5 8a 12 b−9 c 27
  x 3− y 3
 2y

−
3
1. ⋅ 1−
7
a bc
−1 6 3 3
a b c x 3 y 3 x y
2.
2xy
1 2 2
x −xy  y
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 a 2  ab then a  b
3. 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 −3k 1 x 2−k −2 x1=0 will not intersect the x-axis.
x
III. Consider the functions f  x  =  7−x , g  x = ∣2x−3∣ and hx =
x−1
f °g
1. Find
h
f °g
2. Find the domain of f , g , h ,
h
IV. Consider the functions f  x  = −3x9 and g  x = x 2− 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 x5 =  x1 x 2x1 3x5
3. 2
− 2 =
2x −5x−3 x −x−6 2x 2 5x2
2 3 2x−3
− = 7 4.  1
x y 2
x −2x−3
1 10
2.  = −5
y z
1 4 5
−  = 2
x y z
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.