Algebra - Practice Problems
What is the x intercept 4x-3y=12
(3,0)
Simplify the following expression. (-1/5)^3
-1/125
Simplify the following expression. -4(p - (-5))
-4p - 20
Solve the absolute value equation | x - 3 | - 6 = 2
-5, 11
Solve the absolute value equation | 2x - 4 | = 22
-9, 13
Write an equation for the sentence & then solve for w. The difference of 12w and -9 is -22.
12w - (-9) = -22 OR 12w + 9 = -22 w = -31/12
Evaluate the following expression for the given values of the variables: (3x)^2 - (x^3 - y^2); x = -3; y = -5
133
Simplify the following expression. 6n^2 - 5n^2
1n^2 or n^2
Simplify the following expression: 36 ÷ (4 + 2^3)
3
Evaluate the following expression for the given values of the variables: 5m + 6n^2 - n^3; m = 2 and n =4
42
Simplify the following expression. -(-5 + 10x)
5 - 10x
Write an algebraic expression for the following phrase: a number t times 6
6t
Simplify the following expression: 14 + (9^3 - 5^2)
718
Write an algebraic expression for the following phrase: 13 more than the product of 9 and n
9n + 13
Solve 6 - 2x - 1 = 4x + 8 - 6x - 3
All Real Numbers
Identify the domain and range X Y -1 1 -2 1 -3 1 -4 1 -5 1 -6 1 -7 1
D: {-1.-2,-3,-4,-5,-6,-7} R: {1} Notice that you do NOT write any values more than once!
Identify the domain and range (-2, 3), (4, 5), (-1, 6), (2, 3), (1, 3), (4, 7), (-3, 0)
D: {-3, -2, -1, 1, 2, 4} R: { 0, 3, 5, 6, 7}
y = 5x is what kind of an equation?
Direct Variation
Slope = -2
Identify the slope of the line by counting the rise/run
Slope = -1/2
Identify the slope of the line by counting the rise/run - (find where the line crosses in the corner of the box)
Order the following numbers from least to greatest. -7/3, 3/4, 4/3, and -2 1/4
Least --> Greatest -2 1/4, -7/4, 3/4, 4/3
Tell whether the graph is Linear or Nonlinear AND Function or Not a function
Linear - Function
What kind of slope is shown?
Negative Slope
Is the ordered pair (2 , 1) a solution to the following equation? 4x - 2y = 5
No
Is this relation a function? Why or why not? X Y -2 3 4 5 -1 6 2 3 1 3 4 7 -3 0
No - because 4 is repeated in the x values
Solve 8x + 6 - 9x = 2 - x - 15
No solution
Is (-3,9) (9,-3) (7,0) (-3,6) a function? Explain.
No, an input (x) value is repeated.
Tell whether the graph is Linear or Nonlinear AND Function or Not a function
Nonlinear - Function
Tell whether the graphs in the second column are Linear or Nonlinear AND Function or Not a function
Nonlinear - not a function
What kind of slope is shown?
Positive Slope
Graph the equation f(x) = 3x + 4 if the domain is -3, -2, 0, 1
Steps: *make an input/output table *remember that f(x) is the same thing as y *make ordered pairs after making the chart *graph ordered pairs Your ordered pairs should be: (-3, -5), (-2, -2), (0, 4), (1, 7)
Direct Variation
What kind of graph is this?
Undefined Slope
What kind of slope is shown?
Is (1,3) (2,3) (3,3) (4,3) a function?
Yes
Is it a function? (-1, 1), (-2, 1), (-3, 1), (-4, 1), (-5, 1), (-6, 1), (-7, 1)
Yes
Is the ordered pair (-2 , 2) a solution to the following equation? 2 + 6x = -5y
Yes
What kind of slope is shown?
Zero slope
Solve: -2(x - 5) = 10 - 2x
all real number/identity/infinite solutions
Solve: ( b/3) - 1=5
b = 18
f(x) = x squared - 3, Find f(-4)
f(-4)=13
f(x)=3/4x - 1, Find f(8)
f(8) = 5
G(x) = - x squared -6, Find g(-3)
g(-3) = -15
Solve: 4k - 5k = 10 + k
k = -5
The perimeter of a rectangle is 82 cm. If the length is one more than three times the width, write an equation and solve it to find the length and the width.
length = 3w + 1 width = w 2L + 2w = 82 2(3w+1) + 2w = 82 6w + 2 + 2w = 82 w = 10 cm l = 31 cm
Find the slope of the line that passes through these 2 points (-3,-4) (2, -6)
m = -2/5
Find the slope of the line that passes through these 2 points (-1,3) (5,3)
m = 0 Because 0/6 is not simplified
Find the slope of the line that passes through these 2 points (-6,2) (-6-9)
m = undefined Because -11/0 is not simplified
Solve: 3(x - 3) = 3x - 6
no solution
-3z + 2w -p = -2z, solve for p
p= z+2w
Solve and graph the inequalities -4(3 - x) > 5(x + 1)
x < -17
Solve -2(x + 3) = 4x - 3
x = - 1/2
Find the x and y intercepts and graph -5y + 2x = -10
x = -5 y = 2 (-5,0) (0,2)
Solve 4x + 12 = 2x - 6
x = -9
Solve: 6(2x + 10) = 10(x + 6)
x = 0
Find the x and y intercepts and graph 6x + 3y = 12
x = 2 y = 4 (2,0) (0,4)
Solve and graph the inequalities -3x < 10 - x
x > -5
Translate and solve: 4 less than 3 times a number is -16
x= -4
Write an equation in slope-intercept form using the point-slope formula m = -1/3 (-3,8)
y = -1/3x + 7
Write an equation in slope-intercept form using the point-slope formula m = -4 (1,5)
y = -4x + 9
Rearrange the equation into slope-intercept form 2x - 3y = 9
y = 2/3x - 3
Rearrange the equation into slope-intercept form 4x = 2y - 8
y = 2x + 4
