SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I
WEEK 1
1.
Write the slope-intercept form of an equation of a
2. Write a definition of slope.
7
line with a slope of
, and a y-intercept of –3.
11
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
2
=
x+4 x
 x1  x 2 y1  y 2 
,


2 
 2
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
1
x  y = 2
3
8. Draw a line with the given slope:
9. Solve for r: r – 8 = 7
Arlington Public Schools, 2016
a) positive
b) negative
c) zero
d) undefined
10. Write an equation of the line that passes through
(8, 9) and (10, 3).
Page 1
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I
WEEK 2
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° .
A
2. Evaluate the expressions if m = 2, n =
without a calculator
a) pn  m
b)
B
1
2
, and p =
2
3
1 2
m
4
C
3. The following table shows the relationship between
dog years and human years.
Dog Years
1
2
3
4
5
6
Human Years
15
24
28
32
37
42
4. Rewrite each expression in simplest radical form:
a)
3
125
b)
3
16
c)
49x 2
d)
50 x 6 y
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.
5. The lengths of the sides of a rectangular prism are
shown below. Write a polynomial expression for the
volume.
(V=lwh).
3 in
(x+2) in
6. Find the equation of the line through the points
(1, 1) and (0, 2) in slope-intercept form.
x in
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.)
Arlington Public Schools, 2016
Page 2
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I
WEEK 3
1.
Find the length of the shortest side given that the
perimeter is 31 inches.
x+2
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.
x
2x - 7
n
22
3. Write an equation to represent the diagram. Solve
the equation to find x.
18x
42
4. Solve the linear system:
x+y=5
2x + y = 8
96
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 xintercepts.
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 a 2 + b2 = c2)
8. Multiply (2x + 5)(3x  4).
c = 10
a=6
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
18
=
2
2
x = 9
What should be the correct answer?
Arlington Public Schools, 2016
Page 3
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I
WEEK 4
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
3. Graph the linear equation 3x + y = 6 using the x- and
y-intercepts.
5. Solve the linear system by linear combinations:
4x + 5y = 7
6x  2y = 18
1350
4. Which fraction is equivalent to
T+N
?
N
a)
T
+N
N
b) T
c)
T
+1
N
d) T2 + 1
6. Find the surface area and the volume of the figure.
(S.A.= 2(lw+lh+wh) and V=lwh)
1 ft
2 ft
3 ft
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
1
3
form if (3, ) and (4, ) are points on the line.
2
2
200
3x
4x
Arlington Public Schools, 2016
Page 4
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I
WEEK 5
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:
h  16t 2  36t  4
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.
3x  3
x5
2x  4
3. Solve the inequality for x:
3  2x  1.
4. Solve the literal equation for x:
5. The area of the triangle is 36 square centimeters.
Find the length of the base x. (A = ½ bh)
6. Solve for x:
z=
xm
s
1
(8 + 6x) = 10 + x.
2
8 cm
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?
6 cm
6 cm
6.25 cm
6 cm
9. Solve the system algebraically. Check your answer
by graphing.
3x + 2y = 2
5x  2y = 18
Arlington Public Schools, 2016
10. Explain the difference between X + X and X  X.
Page 5
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I
WEEK 6
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).
5. Which of the following is equivalent to
a)
c)
7.
x
2y2
3
2x
y4
b)
d)
6x2y
?
3xy3
2x
y2
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?
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?
3
x
2y4
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)
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).
b) Draw a graph of the relation to support your
answer.
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.
10. Solve and graph:
10
x  5 y  15
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).
Arlington Public Schools, 2016
Page 6
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I
WEEK 7
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).
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
2. Find the domain and range of the quadratic function
4. Find the slope of the line shown.
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)
7. Find the volume of the cone. V =
1
3
 r 2h
r=3 in
6.
-5
5
Write the equation of the line that passes through
the points (7, 4) and (8, 3).
8. Simplify the expression.
5xy0 12x2y7
2y3  5x
h=6 in
9. A recipe calls for 3½ cups of flour to make 20
muffins. How much flour is needed to make 50
muffins?
Arlington Public Schools, 2016
10. Find the solution(s) of the equation x2 – 2x = 0.
Page 7
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I
WEEK 8
1.
2. The volume of a cube is 64 units3. What is the
length of one edge of the cube?
Factor each polynomial.
a) x2 – 9
b) x2 – 2x – 3
c) 2x2 + 5x + 3
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.
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
B
4. A formula for changing temperature from
5
Fahrenheit to Celsius is C = (F  32). Find the
9
Celsius equivalent of 77F.
8. A car uses 10 gallons of gasoline to travel 290
miles. How much gasoline will the car use to
travel 400 miles?
C
a) Find the value of w.
b) Find the measure of AB and BC.
9. Find the equation of a line that is parallel to the
line y = 4x  2 and passes through the point (5,
3).
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?
(Hint: parallel lines have the same slope.)
Arlington Public Schools, 2016
Page 8
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I
WEEK 9
1.
The perimeter of the triangle is 34 cm. Find the
measure of each side.
2. Evaluate 3x3 + 5x when x = 2.
5x
6x
6x
3. Rewrite the expressions in simplest radical form:
4. The area of a circle is 36
of the circle. (A = r2)
a)
144 x10 y 2
b)
63x 5 y 6
c)
3
1000
d)
3
250 x 5 y 6
5. Solve:
2x + 4y = 8
2x  2y = 4
 inches2. Find the radius
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(?, ?).
10. Using the rectangle ABCD in the previous problem,
find the slopes of AB, CD, AD, and BC .
Find the missing coordinates, D, needed to complete
the rectangle.
Arlington Public Schools, 2016
Page 9
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I
WEEK 10
1.
2. The volume of a can is 42.4 inches3. Its diameter is
What is the solution to
12 -
1 d = 17?
8
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:
10x  1
3x
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
1
2
3
4
5
9. Sketch the graph of the line which contains the
point (0, 3) and whose slope is 2/3.
Arlington Public Schools, 2016
Group Cost
Individual Cost
10. Solve and graph on a numberline:
2x + 1  7.
Page 10
SUMMER REVIEW FOR STUDENTS COMPLETING ALGEBRA I
ANSWER KEY
4.
5.
6.
7.
x = 4 or 2
4x2 + 10x  6
48x6
Both equations represent the
same line. There are an infinite
number of solutions.
9. r = 15
2
11
10. y = x +
3
3
WEEK 2 - ANSWERS
1. A = 30, B = 90, C = 60
1
2. a) 2
b) 1
3
4. a) 5
b)
c) 7x
23 2
3
d) 5 x 2 y
5. 3x2 + 6x
6. y = x + 2
8.
a)
c)
horizontal line; y=4 3.
50
P  2W
40
8. L =
2
30
9. 5(x + 5)(x  5)
20
4
55
10
10. y =  x 
3
3
0
4x + 3y =55
7.
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
d)
b)
Sample Equation y = 5.1x + 11.9
Human Years
WEEK 1 – ANSWERS
7
1. y =
x3
11
2. Slope is the rate
of change in y for
every unit change
in x.
3. (112.5, 125)
Slope is around 5.
0
2
Dog Years
4
6
6.
10
x-i nt (3, 0)
x-i nt (-1, 0)
-5
y-i nt (0,-3)
-10
5
vertex (1, -4)
WEEK 4 - ANSWERS
b)
x
6
1.
a) 2x-5
c) 3x-5
2.
3.
4.
5.
6.
c) y = 60x + 1007.5 d) About 1608 students
x-intercept = (2, 0) and y-intercept = (0, 6)
c
x = 2 and y = 3
Surface Area = 22 square feet, Volume = 6 cubic feet
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.
Arlington Public Schools, 2016
7. t =
C - 89
89
8. 17
9. 2
2
2
5
10. y = x 
7
14
9. x = 2, y = 4
10. x + x = 2x
x . x = x2
Page 11
WEEK 6 - ANSWERS
6.
17
2
1.
x= -
2.
3.
4.
5.
slope is 1
x=2
l= 22, w= 8
b
a) Yes because it has a constant
rate of change and goes through
the origin.
b)
100
50
0
0
1
2
WEEK 7 - ANSWERS
1. 54 square inches
2.
3.
Domain: {x: x is real}; Range: {y: y > -4}
Substitution Method, x = 19, y = 23
4.
m= -
5.
6.
x2 – 3x - 40
y = 7x  53
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
WEEK 9 – ANSWERS
1. 10cm, 12cm, 12cm
2. 14
3. a) 12x5y
b)
3x 2 7 x
c) 10
d)
(5 xy 2 )3 2 x 2
4.
5.
6.
7.
8.
9.
Radius = 6 inches
3. y =
1
x+2
4
4. y = - ¾x + 3
5. 55 mph
6. Area = 30x  3x Perimeter =
26x  2
7. 1.5 inches
8.
Persons
Individual
Cost
Group
Cost
Arlington Public Schools, 2016
9.
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.
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
5.
a=
1
$75.00
$75
2
$65.00
$130
3
$61.67
$185
4
$60.00
$240
5
$59.00
$295
7.
x = 36 days
V = 18 cubic inches  56.54 cubic inches
6 x2 y4
8.75 or 8¾ cups
x=0 x=2
x = 0 and y = 2
slope = 4; y-intercept = 2
2x + 3 < 4x
x = 1/7
D (4,2)
WEEK 10 – ANSWERS
1. d = - 40
2. h  6 inches
y = 3x + 1
2.50x = 90
3
7.
8.
9.
10.
3
2
7.
8.
10. Slopes of AB and CD = 0
Slopes of AD and BC are
undefined
10. x > 3
3
0
5
-5
5
-5
Page 12