This document provides a review for algebra sections on various topics including: 1) Solving word problems involving equations with one unknown variable. 2) Finding sums, differences, and ratios of numbers. 3) Representing word problems using tables and equations. 4) Solving uniform motion problems using tables, diagrams, and the appropriate equation based on the type of motion described. 5) Graphing linear equations and finding slopes of lines from equations or two points. 6) Writing equations of lines in different forms given information like slopes, intercepts, or two points.

1. LOURDES SCHOOL QUEZON CITY
High School Department
ALGEBRA
FOR ALL SECTIONS
REVIEWER
Directions: Read each problem carefully and solve what is asked. Do not forget to represent
your unknown. Three times a number increased by nine is eighty-one. Find the number.
1. Find three consecutive integers whose sum is 318.
2. Find two consecutive even integers whose sum is 90.
3. The sum of two numbers is 100. If the larger number is equal to two times the smaller
number increased by twenty-two, find the smaller number.
4. Find three consecutive integers such that the sum of thrice the first and four times the
second is equal to three times the third increased by two.
5. Rico is six years older than Tita. The sum of their ages is 54. How old is each?
let x – Age of Tita
x + 6 – Age of Rico
(W. E.) x + (x + 6) = 54
2x = 48
x = 24
Tita is 24 while Rico is 30 years old.
We can also use tables in representing the data:
PRESENT AGE W. E.
TITA x x (x + 6) = 54
RICO x+6
6. The sum of the ages of Anne and Rose is 60. Nine years ago, Anne was twice as old as
Rose. Find their present ages.
7. Poldo is now five times as old as Robert. In ten years, Poldo will be three times as old as
Robert. How old is each?
 Using a table how are you going to represent the given?
 What should we include in the table/
 What will be your working equation?
 How are you going to look back and check your answer?
8. Two trains left a station at the same time traveling in opposite directions. Train A
traveled at a rate of 135 kph while Train B traveled at a rate of 65 kph. How long did it
take before they were 500 kms apart?
a. You may draw a diagram to visualize the problem.
STATIO
TRAIN A
TRAIN B
500 km

2. b. Draw a table
RATE TIME DISTANCE
Train A 135kph x 135x
Train B 165 kph x 165x
Total Distance 500 km
c. Identify what type of UMP (Uniform Motion Problem) was given and write a
working equation.
(OPPOSITE DIRECTIONS!!! d1 + d2 = dT)
(W. E.) 135x + 165x = 500
… Solving for x,
300x = 500
x = 1 2/3 hours or 1 hour and 40 minutes
d. Check
My UMP Checklist
As you learn this lesson, I understand that there are so many things that you should
remember, so to help you with that, I suggest that we make a Uniform Motion Checklist…
remember to use this every time you answer uniform motion problemsWhat are the things
that we should remember in answering uniform Motion problems?
1. Identify the given facts in the problem then visualize… draw it!
2. Make a table… remember, RT=D
3. W. E. – to write a working equation, identify the type of UMP
4. OPPOSITE DIRECTIONS (d1 + d2 = dT)
5. TOWARDS EACH OTHER (same)
6. SAME DIRECTION (d1 = d2)
7. UNIT – after you solve for the answer, do not forget to write the unit, remember, it
should be appropriate to what is asked.
9. Two cars start from the same point at the same time. The faster car travels northwest 12kph
faster than the other that travels southeast. If after 6 hours they are 648km apart, find the rate of
each car.
CARTESIAN PLANE
I. Identify the x and y-coordinate in the given points below:
1. W (- 8, 6)
2. E1 (1/2, 3)
3. L (-6, -1)
4. (0, -3)
5. V (2, -7)
6. E2 (-0.75, 0)
7. M (4, 1/3)
8. A (-8.2, -1.5)
9. T (-3, 0)
10. H (0.25, -2/3)
II. Identify the location of the given points in I. Write Q1 for first quadrant, Q2 for second
quadrant, Q3 for third quadrant, Q4 for fourth quadrant, x for x-axis, y for y-axis and o for
origin.
III. To plot a point means to graph it on a Cartesian Plane. Plot the points on Exercise I on a
Cartesian plane. Label the points.
IV. In the given sets below, identify the domain and range.
1. {(0, 0), (-1, 1), (-2, 2), (-3, 3)}
2. {(1,1), (2,4), (3,9), (4,16)}
3. {(-2,-2), (-1,-2), (0,-2)}
V. Identify the type of relation given in Exercise I.

3. VI. Identify whether the relation in Exercise I is a function or not a function.
VII. Let the domain be {-2, -1, 0, 1, 2}, use tables to list the ordered pairs in the given
equations below:
1. y=2x
2. y=4x-1
3. y=-2x+4
VIII. Make a solution table then graph the equation:
1) x = y + 3 Domain {-5, -2, 0, 3, 10}
2) 2x – y = 4 Domain {-8, -4, 0, 4, 12}
IX. The average membership fee in IT Log Computer Shop is Php25 plus Php15 for every
hour of computer use. The total fee can be expressed by the equation F = 25 + 15h where
F is the total fee and h is the number of hours of using the computer in their shop.
Complete the table:
h 1 2 3
F 40 ? ?
Graph the solutions given in the table. Label the x-axis as d and the y-axis as F. Connect
the points with a line.
Use the graph to estimate the fee for a new member who wants to use a computer for 6
hours.
Ino, a transferee from Lourdes School was asked by his friend to join him at the ITLog
Computer Shop. Since he is new in the school and knows no one yet but that friend, he
decided to join him for fun. Ino has decided to spend not more than Php200. How long will
Ino stay in the computer shop?
SLOPES
I. FinD the slope (m) of each line in the Cartesian Plane below:
1. Line 1: m=
2. Line 2: m=
3. Line 3: m=
4. Line 4: m=
5. Line 5: m=
6. Line 6: m=
II. Complete the sentences below:

4. 1. If the line is increasing the slope is _________________.
2. If the line decreasing, the slope is ________________.
3. If the line is horizontal, the slope is _________________.
4. If the line is vertical, the slope is ________________.
III. Find the slope of a line that contains the given points. Identify whether the graph
leans to the right (R), leans to the left (L), vertical (V) or horizontal (H). Show
your complete solution.
1. M (1,3) , N (2,3) 6. A (4,7) , B (3,7)
2. J (-3,10) , K (-3,2) 7. A(3,2) , B (3,7)
3. X (0,5) , Y (3,5) 8. S(-2,1) , T (3,-5)
4. P (-5,2) , R (-5,1) 9. G(5,-2) , H (4,3)
2 2
5. B (2,1) , C (0,1) 10. E( ,5) ; L( ,2)
3 3
y=mx+b and x and y-intercepts
I. Identify the slope and y-intercepts of the following equations:
1. 4y = x
2. 2y + 3x = 10
3. y–x=3
4. 2x – 5y = -15
II. Identify the x and y-intercepts of the following equations:
1. x+y=9
2. 2x + 3y = 6
3. 5y – 3x = -15
4. 2a + 3b = 7
THE EQUATION OF A LINE
3 important RULES
1. The equation should always be in standard form.
2. The x-term should always be positive.
3. The numerical coefficient of x and y, the constant term should always be a whole
number. (no fractions)
3 forms of equations
1. y= mx+b  use this if you have a slope and a y-intercept
2. y − y1 = m( x − x1 )  the generic form of equation, it may be used anytime but remember
y1 − y2
that m = .
x1 − x2
x y
3. + = 1  use this if you have the x and y-intercept.
a b
Write the equation of a line in standard form given the slope and the y-intercept.
1) m = - 2 ; b = 3
2) m = 6 ; b = 2
3) m = -4 ; b = - 7
4) m = -1/4 ; b = 5
5) m = 2/5 ; b = 1/3
Write the equation of a line in standard form given the x and y-intercepts:

5. 1) Q(0,3) ; A(3,0)
2) G(0,7) ; N(4,0)
3) E(0,5) ; G(-3,0)
4) G(0,-6) ; E(5,0)
2
5) E(0,5) ; L( ,0)
3
Write the equation of a line in standard form given two points:
1) Q(5,3) ; A(3, 2)
2) G(-2,7) ; N(4,-3)
3) E(0,5) ; G(-3,2)
4) G(10,-6) ; E(5,-6)
2 2
5) E( ,5) ; L( ,2)
3 3
Derive the equation of a line in standard form given a slope and a point:
1. m = 3 ; A (4 , 2)
2. m = - 5 ; N (- 3 , 6)
3. m = 1/3 ; G (-4 , -1)
4. m = 3/5 ; E (-1/2, 11)
5. m = 3/4 ; L (1/3 , ¼)
6. m = 1 ; I (2, 3)
7. m = -6 ; N(1, 1)
8. m = -4/7 ; A(5, 2)
9. m = 2/5 ; M (-1/2, -4/3)
10. m = -7/2 ; L (2/3, ½)
Synthesis:
Fact: Parallel lines have equal slopes.
Challenge: Write the equation of a line that is parallel to the graph of y = 2x – 1 and passes
through the point (1, - 2).