This study guide covers several topics for a math semester 1 exam, including integers, evaluating expressions, discounts/sales tax, perfect squares/square roots, the Pythagorean theorem, linear functions, systems of equations, and slope. For integers, it provides examples of representing situations with positive and negative numbers and performing operations on integers. For linear functions, it discusses translating between tables, equations, and graphs. It also includes examples of finding missing sides of triangles using the Pythagorean theorem and determining if functions are linear or nonlinear based on situations.

1. Study Guide: Math course 3 Semester 1 exam
Integers: represent a given situation with a positive or negative integer
*example: Mike lost 15 yards on the football field is represented by
the integer – 10.
Try it!
1. Crystal earned $50 babysitting. ______
2. Gerard dove 25 feet below sea level. _________
Integers: add, subtract, multiply or divide integers given a situation.
*example: I had $32 in my wallet on Monday. I spent $8 on Tuesday
and my friend gave me $10 on Wednesday. How much money do I
have in my wallet at the end of the day Wednesday?
32 – 8 + 10 = $34.
Try it!
3. I can make 3 pizzas per hour. At that rate, how long will it take me to
make 123 pizzas?
4. The high temperature for Tuesday was 7 degrees Fahrenheit and the low
temperature was -6 degrees Fahrenheit. What was the difference
between the high and low temperatures?
Evaluate Expressions: Solve the expressions below if a = 4, b = - 5, and c = 9
5.
6. 5b + 6 – 2c
7. 8 + 5a - c
Discounts and sales tax: Find a sales price after the discount or a total price
after tax is added in.
8. I went out to eat with a friend. We each got the same meal and
drink, so we each paid the same amount of money. If our bill was
$42.84 and there is a 7% sales tax on the food, how much did each of
us pay for our meal?* HINT: remember you have to split the cost
equally among 2 people!!!
9. A skateboard has a regular price of $218. The sale price is 20%
off the regular price, and you have a coupon for 5% off the sale
price. What is the final price of the sweater?
10. A pair of shoes that is $79 is on sale for 10% off. If there is a
7.5% sales tax, what is the total cost of the game?

2. Perfect squares/ square roots:
11. Find
in simplest form.
12. The square below has an area of 456 square inches. What is the
length of s, rounded to the nearest tenth?
s
s
s
s
13. Identify the following square root:
(*hint- there is an
important thing to remember when the negative sign is INSIDE the
square root symbol!)
Pythagorean Theorem: Use the formula
missing side.
a
to find the length of a
c
b
14. Find the missing side length in the triangle below.
15 in
11 in
15. Find the height of the triangle below. Round to the nearest
hundredth if necessary.
32 ft.
19 ft.

3. 16. Find the distance between points A and B.
Tables/equations/graphs of linear functions: translate from tables to
equations, from equations to graphs, and from graphs to equations.
17. Represent the following table as an equation:
X
1
2
3
4
5
Y
5
8
11
14
17
18. Look at the table below. Which equation represents the relationship
of x to y? (Notice the x and y values do not always go up by the same
amount…. You may want to use the “guess and check” strategy).
X
Y
2
17
3
25
6
49
8
65
10
81
19. Graph the following equation;
20. Graph the equation
22. Graph the equation

4. 23. Look at the graph below. Write an equation that represents the
relationship of x to y.
24. Write an equation that represents the graph of the line below.
Systems of equations: When given a graph, identify the solution to the system
of equations.
25. Write the solution to the system of equations below.

5. Slope:
26. Draw a graph that correctly shows a slope of
. (Multiple choice on
exam).
27. Deborah is buying Oreo cookies for her classes. The cookies cost
$3.50 per package. Draw a graph that correctly shows the cost per
package. (Multiple choice on exam).
28. Michael collects Pokémon cards. He has 250 unpackaged cards and c
unopened packages of cards. The total number of Pokémon cards
that Michael has is given by the formula M(c) = 12c +250, where
M(c) is the total number of Pokémon cards that Michael has. What
does the slope of this function represent?

6. Linear/Nonlinear: You will be given a situation. You will determine if the
information will give a linear or nonlinear function, and choose a graph that
best represents it (there are 3 questions like this).
29. George noticed that the price of an airline ticket was dropping every
day. He recorded the price of the ticket each day for a week and plotted his
data on a coordinate grid. George was able to write a linear function to
describe the price decrease. Which coordinate grid correctly illustrates
George’s data?
30. The price at the buffet restaurant is $8.95 per person to eat. Draw a graph
that illustrates the total price of the meal for any number of people. (This
concept will be tested as a multiple choice problem).
31. The price of a ticket for One Direction concert can cost as much as
$250, but a discount is given as you choose a seat that is further away from
the stage. A discount of $50 per section farther away from the stage is given.
Draw a graph that illustrates the price of One Direction tickets. (this concept
will be tested as a multiple choice problem)
Continuous/Discrete: You will be given a table and asked to identify the
domain or the range. Then, you will look at the table and decide if the data is
continuous or discrete. (There are 2 questions like this).