SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I...Arlington Public Schools, 2017 Page 3 SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I WEEK 3 1. Find the length of the shortest side

Arlington Public Schools, 2017 Page 1

SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I WEEK 1

1. Write the slope-intercept form of an equation of a

line with a slope of 11

7, and a y-intercept of –3.

2. Write a definition of slope.

3. You want to place a buried treasure chest halfway

between a tree at (25, 175) and a large boulder at

(200, 75). Use the midpoint formula to find the

coordinates of the treasure chest.

4. Solve for x: x

x + 4 =

2

x

5. Use the FOIL pattern to multiply (4x 2)(x + 3). 6. Simplify using exponent rules: (6x3)(2x)3

7. Graph the linear system to determine the number of

solutions. 3x + y = 6

x 1

3 y = 2

8. Draw a line with the given slope:

a) positive b) negative

c) zero d) undefined

9. Solve for r: r – 8 = 7 10. Write an equation of the line that passes through

(8, 9) and (10, 3).

2,

2

2121 yyxx



1. Given triangle ABC. The measure of angle A is x,

the measure of angle B is three times as much as

the measure of angle A, and the measure of angle C

is twice as much as the measure of angle A. Find

the measure of each angle if the sum of the

measures of the three angles is 180° .

2. Evaluate the expressions if m = 2, n = 1

2 , and p =

2

3

without a calculator

a) pn m

b) 1

4 m2

3. The following table shows the relationship between

dog years and human years.

Dog Years Human Years

1 15

2 24

3 28

4 32

5 37

6 42

a) Draw a scatter plot. Set up an appropriate scale

and label your axes.

b) Draw the line that best fits the data.

c) Find the equation of the line.

4. Rewrite each expression in simplest radical form:

a) 3 125

b) 3 16

c) 249x

d) yx650

5. The lengths of the sides of a rectangular prism are

shown below. Write a polynomial expression for the

volume.

(V=lwh).

6. Find the equation of the line through the points

(1, 1) and (0, 2) in slope-intercept form.

7. Describe the line through the point (1, 4) with the

slope m = 0. Write the equation of the line.

8. Solve for L: P = 2L + 2W

9. Factor completely: 5x2 125 10. Find an equation of the line parallel to 4x + 3y = 9

that passes through the point (10, 5).

(Hint: Parallel Lines have the same slope.)

B

A

C

3 in

x in (x+2) in



1. Find the length of the shortest side given that the

perimeter is 31 inches.

2. The sum of two complementary angles is 90°. The

picture below represents two complementary angles.

Set up an equation and solve for the value of n.

3. Write an equation to represent the diagram. Solve

the equation to find x.

4. Solve the linear system:

x + y = 5

2x + y = 8

5. At 2:15, a parachutist is 4500 ft. above the ground.

At 2:28, she is 2200 ft. above the ground. Find the

average rate of change in feet per minute.

6. Graph the quadratic equation y = x2 2x 3. Label

the coordinates of the vertex, y-intercept, and x-

intercepts.

7. A 10-foot ladder is leaning against a wall. If the

base of the ladder is 6 feet from the wall, how high

does the ladder reach up the wall?

(Hint: The Pythagorean Theorem is a2 + b2 = c2)

8. Multiply (2x + 5)(3x 4).

9. A six-foot man casts a 5-foot shadow. If a tree

casts a 40-foot shadow, how tall is the tree?

10. What mistake was made when this problem was

solved?

3 2x = 15

3 3

2x

2 =

18

2

x = 9

What should be the correct answer?

x

2x - 7

x + 2

22

n

18x 42

96

c = 10

a = 6



1. Write an algebraic expression for each:

a) Five less than twice a number

b) A number divided by six

a) Three times a number less 5

2. The table shows the number of students each year at your

high school.

(You may use the regression feature on a graphing

calculator instead of completing parts a and b, if you

prefer).

a) Construct a scatter plot. Set up an appropriate scale

and label your axes. Let t = 0 represent 1990.

b) Draw the line that best fits the data.

c) Write the equation of the line that best fits the data.

d) How many students would you expect there to have

been in the year 2000?

Year # Students

1990 1000

1992 1125

1994 1275

1996 1350

3. Graph the linear equation 3x + y = 6 using the x- and

y-intercepts.

4. Which fraction is equivalent to T + N

N ?

a) T

N + N b) T

c) T

N + 1 d) T2 + 1

5. Solve the linear system by linear combinations:

4x + 5y = 7

6x 2y = 18

6. Find the surface area and the volume of the figure.

(S.A.= 2(lw+lh+wh) and V=lwh)

7. A jacket costs $89 plus tax. The total cost, C, is

given by the equation 89 + 89t = C, where t is the

tax rate. Solve the equation for t.

8. What is the next number in the sequence?

1, 5, 9, 13, …

9. Find x. (Remember a2 + b2 = c2)

10. Write the equation of the line in slope-intercept

form if (3, 1

2) and (4,

3

2) are points on the line.

2 ft

3 ft

1 ft

200

4x

3x



1. The following quadratic model describes the path of

a certain basketball in motion. The balls’ height (in

feet) is a function of time in flight (in seconds),

modeled by the equation: 43616 2 tth

After how many seconds would the basketball’s

height be 12 feet? Round your answer to the

nearest hundredth of a second.

2. The sum of the measures of the three angles in a

triangle is 180°. Write an equation and solve for x.

3. Solve the inequality for x:

3 2x 1. 4. Solve the literal equation for x: z =

x m

s

5. The area of the triangle is 36 square centimeters.

Find the length of the base x. (A = ½ bh)

6. Solve for x: 1

2(8 + 6x) = 10 + x.

7. Find the slope of the line which passes through the

points (3, 7) and (3, 5).

8. What is wrong with this picture?

9. Solve the system algebraically. Check your answer

by graphing.

3x + 2y = 2

5x 2y = 18

10. Explain the difference between X + X and X X.

3x 3

2x 4 x 5

8 cm

x

6 cm 6 cm

6 cm

6.25 cm



1. Solve: 6(x + 2) = 4x 5

2. Find the slope of the line that is represented with

the equation 2x + 2y = 4.

3. Write the equation of the vertical line that passes

through the point (2,-3).

4. A rectangle has a width 14 inches less than its

length. If the area of the rectangle is 176 inches,

what is the length and width of the rectangle?

5. Which of the following is equivalent to 6x2y

3xy3 ?

a) x

2y2 b) 2x

y2

c) 2x3

y4 d) x3

2y4

6. You are riding your bike at an average speed of 25

miles per hour. The number of miles you ride, d, during

t hours is given by d = 25t.

a) Does the situation represent a direct variation?

b) Draw a graph of the relation to support your

answer.

7. Plot the points given. Is there a pattern? If yes,

write an equation that represents the points.

(0, 1) (1, 2) (1, 4) (5, 16) (8, 23)

8. Your parents have given you $90 to buy lunches at

school. On average, you spend $2.50 per lunch per

day. How long before you run out of money? That

is, how many lunches are you able to buy? Write an

equation and solve.

9. A classmate brings a box of 24 cookies for the class

to share to share fairly with all students who want

cookies. If all 12 students in the class want cookies,

each student would get 2 cookies (12, 2). If only 8

people want cookies, each of these students could

get 3 cookies (8, 3).

a) Is this relation between the number of students

who would like cookies (x) and the number of

cookies each would get (y) a direct or inverse

variation?

b) Write an equation for the variation, using x and

y as defined in part (a).

10. Solve and graph: 1553

10 yx



1. How much non-overlapping wrapping paper would you

need to wrap a cube? The sides of the cube are 3

inches each. (The formula for finding the surface

area of a cube is SA=6s2 where s represents the

length of a side).

2. Find the domain and range of the quadratic function

3. Which would be the best method of solving the

linear system below? Explain your choice. Then

solve the system.

3x 2y = 11

y = 4 + x

4. Find the slope of the line shown.

-5

5

-5 5

5. The length of a rectangle is (x – 8) and the width is

(x + 5), Express the area of the rectangle as a

polynomial in simplest form. (A = lw)

6. Write the equation of the line that passes through

the points (7, 4) and (8, 3).

7. Find the volume of the cone. V = 1

3 r2h

8. Simplify the expression.

5xy0

2y3 12x2y7

5x

9. A recipe calls for 3½ cups of flour to make 20

muffins. How much flour is needed to make 50

muffins?

10. Find the solution(s) of the equation x2 – 2x = 0.

h=6 in

r=3 in



1. Factor each polynomial.

a) x2 – 9

b) x2 – 2x – 3

c) 2x2 + 5x + 3

2. The volume of a cube is 64 units3. What is the

length of one edge of the cube?

3. Jenny has a $100 clothing allowance to buy

skirts and blouses. If blouses cost $25 and

skirts are $30, write an equation that models

how she can spend her money.

4. A formula for changing temperature from

Fahrenheit to Celsius is C = 5

9 (F 32). Find the

Celsius equivalent of 77F.

5. Solve for a: 2ax + 3 = b

6. A weather balloon in the shape of a sphere has a

surface area of 160 square meters. If the

formula for the surface area of a sphere is

S.A.= 4πr2, to the nearest tenth of a meter,

what is the radius of the balloon?

7. Point B divides segment AC into two equal

sections.

5w 20 2w + 16.

a) Find the value of w.

b) Find the measure of AB and BC.

8. A car uses 10 gallons of gasoline to travel 290

miles. How much gasoline will the car use to

travel 400 miles?

9. Find the equation of a line that is parallel to the

line y = 4x 2 and passes through the point (5,

3).

(Hint: parallel lines have the same slope.)

10. Bob bought 3 apples and 2 tomatoes for $3.00

at the fruit stand. Maria bought 5 apples and 1

tomato at the same stand for $3.25. How much

did each apple and each tomato cost?

A B C



1. The perimeter of the triangle is 34 cm. Find the

measure of each side.

2. Evaluate 3x3 + 5x when x = 2.

3. Rewrite the expressions in simplest radical form:

a) 210144 yx

b) 6563 yx

c) 3 1000

d) 3 65250 yx

4. The area of a circle is 36 inches2. Find the radius

of the circle. (A = r2)

5. Solve: 2x + 4y = 8

2x 2y = 4

6. Find the slope and the y-intercept of the line

2y 4 = 8x.

7. Translate the following verbal phrase into an

algebraic inequality: “Three more than twice a

number is less than four times the number.”

8. Solve: 3x 2(6x 4) = 5x + 10.

9. A rectangle has coordinates

A(4, -3), B(-1, -3), C(-1, 2), and D(?, ?).

Find the missing coordinates, D, needed to complete

the rectangle.

10. Using the rectangle ABCD in the previous problem,

find the slopes of BCand,AD,CD,AB .

5x 6x

6x



1. What is the solution to

12 - d = 17?

2. The volume of a can is 42.4 inches3. Its diameter is

3 inches. Find the height. (V = r2h)

3. Parallel lines (lines that never intersect) have the

same slope. Find the equation of a line parallel to

y = ¼x + 7 that passes through the point (0, 2).

4. Rewrite the following equation in slope-intercept

form: 3x + 4y = 12.

5. You are driving to Aunt Sally’s house, which is 220

miles away. It takes 4 hours to get there. What is

your average speed?

6. Write the simplest expression for the area and

perimeter of the rectangle:

7. A page in a school yearbook is 8½ in. by 11 in. The

left margin is 1 in. and the right is 2½ in. The space

between two pictures is ¼ in. How wide should each

picture be to fit three across the page?

8. Ski Tours offers a one-day package deal, which

charges $75 for the first person and $55 for each

additional person. A person tries to get a group of

friends together who will split the entire cost

evenly. Complete the table:

Persons Group Cost Individual Cost

1

2

3

4

5

9. Sketch the graph of the line which contains the

point (0, 3) and whose slope is 2/3.

10. Solve and graph on a number line:

2x + 1 7.

8

1

10x 1

3x


SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I ANSWER KEY

WEEK 1 – ANSWERS

1. y = 7

11 x 3

2. Slope is the rate

of change in y for

every unit change

in x.

3. (112.5, 125)

4. x = 4 or 2

5. 4x2 + 10x 6

6. 48x6

7. Both equations represent the

same line. There are an infinite

number of solutions.

9. r = 15

10. y = 2

3x +

11

3

8.

c)

d)

a)

b)

WEEK 2 - ANSWERS

1. A = 30, B = 90, C = 60

2. a) 2 1

3 b) 1

4. a) 5 b) 3 22

c) 7x d) yx 25 3

5. 3x2 + 6x

6. y = x + 2

7. horizontal line; y=4

8. L = P 2W

2

9. 5(x + 5)(x 5)

10. y = 3

55

3

4 x

4x + 3y =55

WEEK 3 – ANSWERS

1. 9 inches

2. n = 68. Complementary

3. 18x + 42 = 96 x = 3

4. x=3, y=2

5. 176.92 ft/minute

7. 8 feet

8. 6x2 + 7x 20

9. 48 feet

10. The student lost the negative sign on 2x. x = +9

6.

-10

10

-5 5

x-int (3, 0)x-int (-1, 0)

y-int (0,-3)vertex (1, -4)

WEEK 4 - ANSWERS

1. a) 2x-5 b) 6

x c) 3x-5

2. c) y = 60x + 1007.5 d) About 1608 students

3. x-intercept = (2, 0) and y-intercept = (0, 6)

4. c

5. x = 2 and y = 3

6. Surface Area = 22 square feet, Volume = 6 cubic feet

7. t = C - 89

89

8. 17

9. 2 2

10. y = 2

7 x

5

14

WEEK 5 - ANSWERS

1. 0.25 seconds and 2 seconds

2. x = 32 degrees

3. x > -1

4. x = sz + m

5. 9 cm

6. x = 7

7. 2

8. The hypotenuse should be longer than the legs.

9. x = 2, y = 4

10. x + x = 2x

x . x = x2

Sample Equation y = 5.1x + 11.9

0

10

20

30

40

50

0 2 4 6Dog Years

Hum

an Y

ears

3.

Slope is around 5.


WEEK 6 - ANSWERS

1. x= -2

17

2. slope is 1

3. x = 2

4. l= 22, w= 8

5. b

6. a) Yes because it has a constant

rate of change and goes through

the origin.

b)

0

50

100

0 1 2 3

7. y = 3x + 1

8. 2.50x = 90 x = 36 days

9. a) inverse b) xy = 24

10. Y < (-2/3)x + 3; on graph, line

is dotted and the shading is

below the dotted line.

WEEK 7 - ANSWERS

1. 54 square inches

2. Domain: {x: x is real}; Range: {y: y > -4}

3. Substitution Method, x = 19, y = 23

4. m= -2

3

5. x2 – 3x - 40

6. y = 7x 53

7. V = 18 cubic inches 56.54 cubic inches

8. 6 x2 y4

9. 8.75 or 8¾ cups

10. x = 0 x = 2

WEEK 8 – ANSWERS

1. a) (x + 3) ( x – 3) b) (x -3) (x + 1)

c) (2 x + 3) (x + 1)

2. 4 units

3. 25b + 30s < 100 where b = number of blouses and s =

number of skirts

4. 25 C

5. a = b 3

2x

6. r = 3.57

7. a) w = 12 b) Each segment is 40 units.

8. x = 13.79 gallons

9. y = 4x + 23

10. Tomatoes cost 75 cents and Apples cost 50 cents

WEEK 9 – ANSWERS

1. 10cm, 12cm, 12cm

2. 14

3. a) 12x5y b) xx 73 2

c) 10 d) 3 22 2)5( xxy

4. Radius = 6 inches

5. x = 0 and y = 2

6. slope = 4; y-intercept = 2

7. 2x + 3 < 4x

8. x = 1/7

9. D (4,2)

10. Slopes of AB and CD = 0

Slopes of AD and BC are

undefined

WEEK 10 – ANSWERS

1. d = - 40

2. h 6 inches

3. y = 4

1x+2

4. y = - ¾x + 3

5. 55 mph

6. Area = 30x 3x Perimeter =

26x 2

7. 1.5 inches

8. Persons Individual

Cost

Group

Cost

1 $75.00 $75

2 $65.00 $130

3 $61.67 $185

4 $60.00 $240

5 $59.00 $295

10. x > 3

0 3

-5

5

-5 5

7.

9.

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SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I...Arlington Public Schools, 2017 Page 3 SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I WEEK 3 1. Find the length of the shortest side