High School Algebra I Semester 1 Study Guide

High School Algebra I 

Semester 1 Study Guide 

1 Simplify . 

1´ You Try. 

1) Simplify . 

AF 1.2 

2 Evaluate if 

, and . 

2´ You Try. 

2) Evaluate if 

. 

1.0 

Page 1 of 19 MDC@ACOE (AUSD) 09/13/10



3 

Simplify . 

3´ You Try. 

3) Simplify . 

NS 1.2 

4 

Simplify . 

4´ You Try. 

4) Simplify . 

OR 

NS 1.2 




5 is an example of 

which property 

The Distributive Property. 

5´ You Try. 

5A) is an example of which 

property of equality 

5B) is an example 

of which property of equality 

1.0 

6 Give a counterexample to the statement: 

If a number is an integer, then it is a whole 

number. 

is an integer, but it is not a whole number. 

6´ You Try. 

6) Give a counterexample to the 

statement: 

The square of a number is greater than the 

number. 

24.0 

7 Write an equation that describes the following 

statement: 

3 less than a number is 8. 

“Less than” indicates subtraction and any 

variable can represent the unknown number. 

Therefore, the answer is: 

7´ You Try. 

Write an expression that describes each of the 

following: 

7A) Four subtracted from a number 

7B) Seven times a number squared 

AF 1.1 




8 

Solve . 

8´ You Try. 

8) Solve . 

5.0 

9 Solve . 

9´ You Try. 

9) Solve . 

4.0, 5.0 




10 Solve and graph the 

solutions. 

10´ You Try. 

10A) Solve and graph 

the solutions. 

10B) Solve or 

and graph the solutions. 

1 6 

5.0 

11 Solve . 

is less than 10 units from 0. 

11´ You Try. 

11A) Solve . 

11B) Solve . 

-10 0 10 

00 

and 

0 

and 

3.0 




12 

Solve . 

12´ You Try. 

12) Solve . 

OR 

4.0 




13 Find the domain and range for the set of 

ordered pairs. Then tell if the relation is a 

function. 

13´ You Try. 

13) Find the domain and range for the 

given relation. Then tell if the relation is 

a function. 

Domain: 

Range: 

This is not a function because the x- 

coordinate is paired with two different y- 

coordinates. 

17.0 

14 Find the slope of the line through the points 

and . 

14΄ You Try. 

14) Find the slope of the line through the 

points and . 

Slope 

AF 3.3 




15 Find the x- and y-intercepts of the line 

whose equation is . 

The x-intercept is the point where the line 

crosses the x-axis. All points on the x-axis 

have 0 for their y-coordinate. Therefore, 

15´ You Try. 

15) Find the x- and y-intercepts of the 

line whose equation is 

. 

The x-intercept is . 

Similarly, 

The y-intercept is . 

6.0 




16 Graph . 

“Graph” means “plot a point for all of the 

solutions.” So find some solutions: 

16´ You Try. 

16) Graph . 

One solution is 

substitute 0 for y, we’ll get 

. Similarly, if we 

. And 

is a solution. If we continue to pick all 

numbers for x, the solutions form a line. 

Therefore, the graph is: 

4 

3 

2 

1 

-5 -4 -3 -2 -1 0 1 2 3 4 5 

-1 

-2 

-3 

-4 

6.0, 7.0 




17 Write an equation for a line that passes 

through the points and . 

where is the slope and is 

the y-coordinate of the y-intercept. 

17´ You Try. 

17) Write an equation for a line that passes 

through the points and . 

Point-slope Method 

OR 

Therefore, the equation is . 

7.0 




18 Write the equation of the line passing 

through the point and parallel to the 

line . 

The line parallel to the line 

have the same slope, which is . 

will 

18΄ 

You Try. 

18) Write the equation of the line passing 

through the point and parallel to the 

line . 

OR 

The equation is . 

8.0 

19 What is the slope of a line perpendicular 

to 

The slope of is . The slope 

of a line perpendicular to 

opposite reciprocal of . That is, . 

is the 

19΄ 

You Try. 

19) What is the slope of a line 

perpendicular to 

8.0 




20 Solve the system: 

20´ You Try. 

20) Solve the system: 

Using the Substitution Method, 

Solve the first equation for : 

Substitute for 

in the second equation: 


in either equation: 

The solution is . 

9.0 




21 Solve the system: 

21´ You Try. 

21) Solve the system: 

Make the y-terms be opposites by 

multiplying the first equation by 2 and the 

second equation by 3: 

By the Addition Property of Equality: 


in either equation: 

The solution is . 

9.0 




22 Find the two numbers whose sum is 9 and 

difference is -5. 

Let 

and 

one of the numbers (the lesser one) 

the other (greater) one. 

22΄ You Try. 

22) Find the two numbers whose sum is 

12 and difference is -4. 

Then: and . 

According to the second equation, 

. Substituting for in the first 

equation gives: 

Substituting for 

in the first equation gives: 

Therefore, the numbers are 2 and 7. 

9.0 




23 Solve the system by graphing: 

23´ You Try. 

23) Solve the system by graphing: 

To graph 

, first graph 

. and solve the 

equation. All of the solutions will form the 

following line: 

The line should be dashed because we are 

graphing , not . 

The solutions to 

of and below the line (for example 

solution because ). 

are to the right 

is a 

Similarly, we graph 

. The 

solutions to the system are in the overlapping 

shaded region: 

9.0 




24 Two trains leave the same station at the same 

time, traveling in opposite directions. The 

first train travels at 80 mph and the second 

train travels at 90 mph. In how many hours 

will the trains be 425 miles apart 

First, draw a diagram. 

80 mph station 90 mph 

n 

425 mi. 

24´ You Try. 

24) An airplane flies from San Francisco 

to New York at a speed of 350 mph and 

takes x hours. The return flight is at a 

speed of 300 mph and takes y hours. The 

flight from New York to San Francisco 

takes 1 hour longer than the flight from 

San Francisco to New York. How long 

does each flight take 

The distance the first train travels plus the 

distance the second train travels is equal to 

425 miles. But distance is rate • time. And 

the trains travel for the same amount of time. 

So: 

80 mph • x hrs. + 90 mph • x hrs. = 425 

The trains will be 425 miles apart in 2½ hours. 

15.0 

End of Study Guide 




Answer Key 

Item Number Answer California Standard 

1 52 AF 1.2 

2 7 1.0 

3 NS 1.2 

4 NS 1.2 

5A Inverse Property of Addition 1.0 

5B Commutative Property of Addition 24.0 

6 Answers may vary. 0, 1, or any number 

between 0 and 1. 

AF 1.1 

7A 5.0 

7B 4.0, 5.0 

8 12 5.0 

9 3.0 

10A 5.0 

-15 

-4 

10B or 5.0 

-9 

5 


AUSD 


First Semester Study Guide 

2010-11 

11A and 3.0 

11B or 3.0 

12 4.0 

13 D 

17.0 

R 

14 AF 3.3 

15 x-intercept: 

6.0 

16 

y-intercept: 

4 

3 

6.0, 7.0 

2 

1 

-5 -4 -3 -2 -1 0 1 2 3 4 5 

-1 

-2 

-3 

-4 

17 7.0 

18 8.0 

19 8.0 

20 and 9.0 


AUSD 


First Semester Study Guide 

2010-11 

21 and 9.0 

22 and 9.0 

23 9.0 

24 S.F. to NY: hours 

NY to S.F.: hours 

15.0

High School Algebra I Semester 1 Study Guide

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?