Download Algebra I – Semester 1 Final Review

Algebra I – Semester 1 Final Review - 2015
Name___________________________
Foundations for Algebra
Write the expression.
1) 5 more than x
2) n less than 2
Simplify
2 7
4) 
5 10
5)
3) 4 more than twice a
3 9

4 10
6) 3  42  2  1  6 2
8) 23  (4  5)  3
7) 3.2 2.1  5.3  3.6
9) Evaluate 3x 2  2 y  z if x=-3, y=-1, z = 4
10) Fred buys 10 computers for his child’s school for a total of $5000. Each additional computer after the
first 10 costs $300. How much would Fred spend if he bought 25 computers? Use an expression to find
this.
Simplify
11)
-62
12)
14)
15) 2a – 4b + 6c – c + 5b – (-4a)
-3(x+3) –(5x-7)
(-6)2
13) (-5)2-52
16) Classify the numbers using the following options: Real, Rational, Irrational, Natural, Whole, Integer
a) 9
b)
3
4
c)
25
d)
2)
2
1 5
x 
3
4 6
e) -2
3
Equations
Solve
5
1)  x  10
8
4) 4 – 6a + 4a = -1 -5(7 – 2a)
3) -2(x – 4) = 11
5) 12x – 3 + x = 5x – 4 + 8x
6) The museum charges $5 admission plus $2 for every hour spent in the building. Write an equation to
represent this. How much would you spend if you were at the museum for 5 hours?
1
7) Solve for b: A  bh
2
8) Solve for x: xyz = -5
9) Solve for y:
ab
9
y
10) The length of a rectangle is 3cm less than 8 times the width. The perimeter is 30 cm. Find the length
and width.
11) Find three consecutive even integers whose sum is 72.
Solve for y:
12) 2x + 3y = 6
13) x – 2y = 10
14) Find four consecutive integers such that the sum of the second and twice the third is 101.
15) The sum of the angle measures of any triangle is 180⁰. Find the angle measures of a triangle if the
second angle is three times the first and the third angle is 5 more than the first.
Inequalities
Solve and graph on a number line
1) d – 5 > -7
2
2)  x  8
3
3) 2(7n – 1) < 3(5 – n)
4) Find all sets of two consecutive positive integers whose sum is no more than 5.
5) Mrs. Smith is taking herself and her 5 children to an amusement park. Tickets cost $20 per person.
Her kids want some snacks when they get there. If Mrs. Smith has $254 to spend for the whole day, how
many snacks can she buy? Snacks cost $5 each.
6) Write and solve the inequality: 2 less than 5 times a number is at least 19.
Solve and graph on a number line
7) -4 < x + 6 < 10
8) 3 < s + 9 OR 1 > s – 4
9) x  7  10  12
10) 2 x  2  18
Functions
1) State the domain and range { (1, -1), (3, 5) (3, -2), (6, -1) }
Domain:
Range:
Is it a function?
2) What is the vertical line test? Draw a sketch of a graph that would not be a function.
3) Write a function rule for:
x
1
2
3
y
1
4
9
For the function, find the indicated values.
4) f ( x)  2 x  5 , find f(-3)
5) f (b)  b2  9 , find f(-4)
6) What is the definition of a function (in your own words)?
7) Draw a graph that represents the following situation: A car accelerates and travels at a constant speed
for a period of time. The car then slows to a stop.
Linear Functions
1) Does something have to be linear in order to be a function?
Put the following into standard form.
2) y = 4x + 3
3)
1
2
y  3x 
2
3
Find the x and y intercepts. Graph.
4) -3x-2y = 12
Find the slope.
5) (3, -2) (5, 4)
6) (4, 5) (4, -10)
Put the following into slope-intercept. Graph.
8)
a) 2x – 3y = 9
b) y – 2x +5 = 0
7) (-7, 9) (-15, -5)
Write the equation of the line in slope-intercept form with the given information.
1
9) slope = -4 y-int = 17
10) slope =
through the point (5, -2)
4
11) Through the points (-6, 3) (9, 8)
12) Parallel to the line y =
1
x  9 through point (9, 1)
3
1
13) Perpendicular to the line y   x  19 through the point (-2, 3)
5
14) Write an equation of the following in point-slope form: slope = -7 through the point (-1, 3)
Systems of Equations
1) Solve the following by graphing: 2x – 5y = 20 and y  2
Solve the following by substitution.
2) y = ½ x – 3 and 2y – 3x = -2
3) 3x = 15 – 3y and 3y = 3x +1
Solve the following by elimination.
4) 5x + 6y = -11 and 3x + y = -4
5) 3x – 5y = 7 and 5x – 2y = -1
6) Tom bought 30 tickets to the symphony and spent $200. He bought a combination of regular tickets
for $5 and premium tickets for $15. Write a system of equations. How many regular and premium tickets
did Tom buy?
Graph
7) y < 3x + 4
8) 3x - 2y < 6
9) x > 4 and y < -2
10) y < ½x + 1
x+y<3