This math review document provides answers and explanations for various math problems involving converting between number systems, identifying patterns and rules, calculating areas and perimeters of shapes, working with expressions and equations, and evaluating expressions. It includes converting between Egyptian, Chinese, and Mayan numerals; matching number sequences to their rules; finding areas and perimeters of rectangles and triangles; calculating interest; writing algebraic expressions; and evaluating expressions with variables.
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Final Exam Name___________________________________Si.docxcharlottej5
Final Exam Name___________________________________
Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE.
Solve the absolute value inequality. Write your answer
in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set.
Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in
interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation.
4) 4x + 9 = 2x + 7
Solve the compound inequality.
5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write
your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in
interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities.
8) 2x + 8y ≥ -4
y < - 3
2
x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix.
9) 10 5
0 -4
Use Cramer's rule to solve the system of linear
equations.
10) 6x + 5y = -12
2x - 2y = -4
Write a system that models the situation. Then solve the
system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips,
and soft drinks. A customer buys 3 hot dogs,
4 bags of potato chips, and 5 soft drinks for
$14.00. The price of a hot dog is $0.25 more
than the price of a bag of potato chips. The
cost of a soft drink is $1.25 less than the price
of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system.
12) x + y + z = 3
x - y + 4z = 11
5x + y + z = -9
2
Find the domain of f. Write your answer in interval
notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables
exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression.
15) 100-1/2
A) 1
1000
B) 1
10
C) 1
100
D) 1
10
Write the expression in standard form.
16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are
positive.
17) 5 t
5
z10
Solve the equation.
18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i
5 + 3i
3
Write the equation in vertex form.
20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve
ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
Solve the equation. Write complex solutions in standard
form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1
3
x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions.
24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem.
25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square
inches, what is its length?
4
Solve the equation..
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Final Exam Name___________________________________Si.docxcharlottej5
Final Exam Name___________________________________
Silva Math 96 Spring 2020
YOU MUST SHOW ALL WORK AND BOX YOUR ANSWERS FOR CREDIT. WORK ALONE.
Solve the absolute value inequality. Write your answer
in interval notation.
1) |2x - 12 |> 2
Solve the compound inequality. Graph the solution set.
Write your answer in interval notation.
2) -4x > -8 and x + 4 > 3
Solve the three-part inequality. Write your answer in
interval notation.
3) -1 < 3x + 2 < 14
Solve the absolute value equation.
4) 4x + 9 = 2x + 7
Solve the compound inequality.
5) 3( x + 4 ) ≥ 0 or 4 ( x + 4 ) ≤ 4
Solve the inequality. Graph the solution set and write
your answer in interval notation.
6) |5k + 8| > -6
Solve the inequality graphically. Write your answer in
interval notation .
7) x + 3 ≥ 1
x-8 -6 -4 -2 2
y
8
6
4
2
x-8 -6 -4 -2 2
y
8
6
4
2
1
Graph the system of inequalities.
8) 2x + 8y ≥ -4
y < - 3
2
x + 6
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
x-10 -8 -6 -4 -2 2 4 6 8 10
y
10
8
6
4
2
-2
-4
-6
-8
-10
Find the determinant of the given matrix.
9) 10 5
0 -4
Use Cramer's rule to solve the system of linear
equations.
10) 6x + 5y = -12
2x - 2y = -4
Write a system that models the situation. Then solve the
system using any method. Must show work for credit.
11)A vendor sells hot dogs, bags of potato chips,
and soft drinks. A customer buys 3 hot dogs,
4 bags of potato chips, and 5 soft drinks for
$14.00. The price of a hot dog is $0.25 more
than the price of a bag of potato chips. The
cost of a soft drink is $1.25 less than the price
of two hot dogs. Find the cost of each item.
Use row reduced echelon form to solve the system.
12) x + y + z = 3
x - y + 4z = 11
5x + y + z = -9
2
Find the domain of f. Write your answer in interval
notation.
13) f(x) = 13 - 9x
If possible, simplify the expression. If any variables
exist, assume that they are positive.
14) 2x + 6 32x + 6 8x
Match to the equivalent expression.
15) 100-1/2
A) 1
1000
B) 1
10
C) 1
100
D) 1
10
Write the expression in standard form.
16) (5 + 8i) - (-3 + i)
Simplify the expression. Assume that all variables are
positive.
17) 5 t
5
z10
Solve the equation.
18) 3x + 1 = 3 + x - 4
Write the expression in standard form.
19) 3 + 3i
5 + 3i
3
Write the equation in vertex form.
20) y = x2 + 5x + 2
The graph of ax2 + bx + c is given. Use this graph to solve
ax2 + bx + c = 0, if possible.
21)
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
x-5 5 10
y
50
40
30
20
10
-10
-20
-30
-40
-50
Solve the equation. Write complex solutions in standard
form.
22) 4x2 + 5x + 5 = 0
Graph the quadratic function by its properties.
23) f(x) = 1
3
x2 - 2x + 3
x
y
x
y
Solve the equation. Find all real solutions.
24) 2(x - 1)2 + 11(x - 1) + 12 = 0
Solve the problem.
25) The length of a table is 12 inches more than its
width. If the area of the table is 2668 square
inches, what is its length?
4
Solve the equation..
Q1. Determine, without graphing, whether the given quadratic funct.docxamrit47
Q1. Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = x2 - 2x - 5
a. maximum; 1
b. minimum; 1
c. maximum; - 6
d. minimum; - 6
Q2. Find the domain of the rational function.
g(x) =
a. all real numbers
b. {x|x ≠ -7, x ≠ 7, x ≠ -5}
c. {x|x ≠ -7, x ≠ 7}
d. {x|x ≠ 0, x ≠ -49}
Q3. Solve the inequality.
(x - 5)(x2 + x + 1) > 0
a. (-∞, -1) or (1, ∞)
b. (-1, 1)
c. (-∞, 5)
d. (5, ∞)
Q4. Find the domain of the rational function.
f(x) =
a. {x|x ≠ -3, x ≠ 5}
b. {x|x ≠ 3, x ≠ -5}
c. all real numbers
d. {x|x ≠ 3, x ≠ -3, x ≠ -5}
Q5. Solve the equation in the real number system.
x3 + 9x2 + 26x + 24 = 0
a. {-4, -2, -3}
b. {2, 4}
c. {3, 2, 4}
d. {-4, -2}
Q6. Find k such that f(x) = x4 + kx3 + 2 has the factor x + 1.
a. -3
b. -2
c. 3
d. 2
Q7. Use the Theorem for bounds on zeros to find a bound on the real zeros of the polynomial function.
f(x) = x4 + 2x2 - 3
a. -4 and 4
b. -3 and 3
c. -6 and 6
d. -5 and 5
Q8. Find all zeros of the function and write the polynomial as a product of linear factors.
f(x) = 3x4 + 4x3 + 13x2 + 16x + 4
a. f(x) = (3x - 1)(x - 1)(x + 2)(x - 2)
b. f(x) = (3x + 1)(x + 1)(x + 2i)(x - 2i)
c. f(x) = (3x - 1)(x - 1)(x + 2i)(x - 2i)
d. f(x) = (3x + 1)(x + 1)(x + 2)(x - 2)
Q9. Find the power function that the graph of f resembles for large values of |x|.
f(x) = -x2(x + 4)3(x2 - 1)
a. y = x7
b. y = -x7
c. y = x3
d. y = x2
Q10. Use the Factor Theorem to determine whether x - c is a factor of f(x).
8x3 + 36x2 - 19x - 5; x + 5
a. Yes
b. No
Q11. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
f(x) = 9x3 + 8x2 - 6
a. No; the last term has no variable
b. Yes; degree 5
c. Yes; degree 3
d. Yes; degree 6
Q12. Solve the equation in the real number system.
x4 - 3x3 + 5x2 - x - 10 = 0
a. {-1, -2}
b. {1, 2}
c. {-1, 2}
d. {-2, 1}
Q13. A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 320 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?
a. 25,600 ft2
b. 19,200 ft2
c. 12,800 ft2
d. 6400 ft2
Q14. State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not.
f(x) =
a. Yes; degree 3
b. No; x is a negative term
c. No; it is a ratio
d. Yes; degree 1
Q15. Give the equation of the oblique asymptote, if any, of the function.
h(x) =
a. y = 4x
b. y = 4
c. y = x + 4
d. no oblique asymptote
Q16. Find all of the real zeros of the polynomial function, then use the real zeros to factor f over the real numbers.
f(x) = 3x4 - 6x3 + 4x2 - 2x + 1
a. no real roots; f(x) = (x2 + 1)(3x2 + 1)
b. 1, multiplicity 2; f(x) = (x - 1)2(3x2 + 1)
c. -1, 1; f( ...
1. Answers for Math Review for Period Exam
Note: This is just a review, you need to study every lesson (from fractal and algebra
book and notes from notebook) seen during class.
Answer
Convert the following numbers to Egyptian numerals.
a) 12 b) 101 c) 1011
Convert the following numbers to Chinese numerals.
a) 12
c) 1011
b) 255
Convert the following numbers to Mayan numerals.
a) 12
b) 255
c) 1011
2. Match the sequence with its rule.
a) 2n + 1 5, 12, 19, 26…
b) 3n - 1 5, 10, 15, 20…
c) 5n-2 3, 8, 13, 18…
d) 5n + 0 3, 5, 7, 9…
e) 7n - 2 2, 5, 8, 11…
Draw the line of symmetry for each pair of figures.
Find the area and perimeter of each figure.
1. 3.
36yd.
8 ft.
Area: 200.96 squared feet Area: 4069.44 squared yard
Perimeter: 50.24 ft. Perimeter: 226.08 yd.
2. 4.
7 ft. 6 ft.
10 ft.
Area: 70 squared feet Area: 36 squared feet
Perimeter: 34 ft. Perimeter: 24 ft.
Calculate the interest. (I=PRT)
Sarah has $$480 in her saving account earning 4.25% interest. How much interest
will she earn in 2.5 years? $51.00
3. Bianca borrowed $120 for 9 months at 3.5% interest. How much interest will she
pay? What is the total amount she will pay back?
Interest: $3.15
Total amount: $123.15
A store allows customers 1 year to pay for their purchases, but it charges 14%
interest. How much interest would be charged on a purchase of $620? What is the
total amount the customer would pay?
Interest: $86.80
Total amount: $706.80
Write each as an algebraic expression.
The difference of 10 and 5 x increased by 6
10 - 5 x+6
The sum of q and 8 Twice q
q+8 2q
Evaluate the expression.
The product of 10 and 8. The quotient of 96 and 8 Twice 6
80 12 12
m +p ÷5, when m=1 and y + 9 – x, when x=1 y÷2 + x, when x=1 and
p=5 and y=3 y=2
2 11 2
a – 5 – b, when a=10 and z(x+y), when x=6, y=8 z – (y÷3-1), when y=3 and
b=4. z=7
and z=6
1 84 7
4. Evaluate.
3(6+7) 72 ÷ 9 + 7 48 ÷ (4+4)
39 15 6
20 ÷ [4 - (10-8) ] 9+8-7 40 ÷ 4 - (5 – 3)
10 10 8
Complete the following line segments. Write the missing numbers.