Download 8 Honors Midterm Review

Name________________________________________ Period ___ Date____________________
Algebra Midterm Topics (Jan. 2017)

Exponents: positive, negative, laws of exponents

Properties: commutative, associative, distributive, additive/multiplicative inverse,
additive/multiplicative identity, flow diagrams/lists

Scientific Notation: basic, all operations with

Solving Equations: multi-step, including literal equations (all variables), no solution/infinite
solutions

Operations with Polynomials: add, subtract, multiply, and divide, use of diagrams to multiply

Factoring: GCF, DOTS, Trinomials (grouping if leading coefficient is >1), factor completely

Graphing Linear Equations: y= mx + b form- identify m and b, slope (rate of change)-interpret
from graph/table/equation, find x and y-intercepts

Systems of Linear Equations: solve graphically and algebraically (substitution/elimination), word
problems

Inequalities: solving basic and compound, solution set in interval/set notation/# line/words,
translating inequalities, graphing linear inequalities, systems of linear inequalities (including word
problems)

Functions: notation, evaluating given function/graph, relation vs. function, domain/range, vertical
line test

Exponential Functions: Growth/Decay formulas, graphing, real-life examples

Sequences: arithmetic and geometric (given formulas), find terms, find common
difference/ratio, find formula for nth term, graphing sequences
Name
Date
MATH 8H MIDTERM REVIEW
1) Does the following equation
represent growth or decay, and what is the percent of
change per unit of time?
1) growth, 85%
2) decay, 85%
2) If one root is the equation
1) -8
3) growth, 8.5%
4) decay, 8.5%
is 5, what is the other root?
2) -3
3) 17
4) 3
3) 0.000081324 x 10n is written in scientific notation. What is the value for n?
1) -6
2) -5
3) 5
4) -4
2) 7
3) -2
4)
2) x = c + b – a
3)
4)
4) Simplify the following:
1)
5) Solve for x: ax – bx = c
1) x = c – a – b
6) Represent the area of a rectangle that has a length represented as
1)
2)
3)
4)
7) The expression
1)
and a width represented as
is equivalent to:
2)
3)
4)
2) x = -36
3) x = 12
4) x = -12
2)
3)
4)
8) Solve the following for x:
1) x = 36
9) Simplify the following:
1)
10)
11) Represent the product of (8x2 + 6x – 3) and (4x + 9) in simplest form.
12) Factor completely: x4 -5x2 - 36
13) If given
and d = 5:
A) Write a rule for the nth term of the arithmetic sequence.
B) Graph the first five terms of the sequence.
C) Using your answer from A, find the 15th term in the sequence
14) Simplify the expression: (abc4)(a3b)2
a. a7b3c4
c. a4b2c4
b. a6b3c4
d. a4b2c5
15) What is the eleventh term of the sequence? an = 7(-3)n-1
c. -1,240,029
c. 413,343
d. -413,343
d. 1,240,029
16) The rate of change for the data on the following table can be described as:
x
y
-1
8
-3
5
e. positive
c. negative
f. zero
d. undefined
17) Which equation is an example of the distributive property?
g. a + 0 = 0
c. 3(x + y ) = 3x + y
h. 3(x + y) = 3x + 3y
d. (3 + x) + y = 3 + (x + y)
18) Which relation is not a function?
1)
2)
3)
4)
19) The accompanying graph shows the elevation of a certain region in
New York State as a hiker travels along a trail. What is the domain of this
function?
1)
2)
3)
4)
-5
2
-7
-1
20)
What is
divided by
?
1)
2)
3)
4)
21) What is the common difference of the arithmetic sequence 6, 2, -2, -6…?
1
a. 4
c. 3
b. -4
d. -3
22) The solution set for the equation
is
1)
2)
3)
4)
Part II. Show all work.
23) For the following inequality, a) describe the solution set in words. b) write the solution in
set-builder notation. c) write the solution in interval notation.
24) Solve for y.
y 1 y  6

5
4
25) Factor Completely:
26) Michele found a bank account that offered an interest rate that was compounded yearly.
She decides to put money into the account. The formula below represents her account balance
over the time, t.
f(t) = 100(1.037)t
A) What does the 100 represent?
B) What is the interest rate for the account?
C) How much money will Michele have in the account after 10 years?
27) The cost of operating Jelly’s Doughnuts is $1600 per week plus $.10 to make each donut.
A) Write a function, C(d), to model the company’s weekly costs for producing d donuts.
B) What is the total weekly cost if the company produces 4,000 donuts?
C) Jelly’s Donuts makes a gross profit of $.60 for each donut they sell. If they sold all
4000 donuts they made, would they make money or lose money for the week?
28) Albany begins the day with 5 inches of snow on the ground and Buffalo begins the same day with
2 inches of snow on the ground. Two snowstorms begin at the same time in Albany and Buffalo,
snowing at a rate of 0.8 inches per hour in Albany and 1.4 inches per hour in Buffalo. The number of
inches of snow on the ground in Albany and Buffalo during the course of these snowstorms are
modeled by f(x) and g(x), respectively.
a) In function notation, write f(x) and g(x) to represent the number of inches of snow on the
ground in Albany and Buffalo during the course of these snowstorms.
b) Determine the number of hours (x) that would pass before Albany and Buffalo have the
same amount of snow on the ground. [The use of the grid below is optional.]
c) A researcher records the total amount of snow three and half hours into the snowstorms.
Determine if Albany or Buffalo has more snow on the ground at this time. Justify your
answer.
29)
30) Jason is a college student who makes extra money tutoring high school and middle school students.
He charges $25.50 an hour for high school, and $23.00 for middle school. On Saturday, Jason made
$222.00 tutoring. Write an equation to represent the possible number of high school and middle school
students that Jason may have tutored on Saturday. Is it possible that Jason tutored 5 high school
students and 5 middle school students on Saturday? Justify your answer by using your equation. Jason
actually tutored at total of 9 students on Saturday. How many of those students were high school
students?
31) An arithmetic sequence has a fourth term of 15 and a sixth term of 21. If the first term is a1,
write an explicit formula for the nth term of the sequence.
32) MaryAnn is on the party planning committee at work and has been put in charge of snacks for the
next party. She wants to buy an assortment of fruits and cookies. One package of cookies costs $3.00,
and assorted fruits cost $5.00 per pound. She has only $50 in total for the snacks so she must spent
less than that amount. From buying snacks before, MaryAnn knows that she will buy at least 4 pounds
of assorted fruit to serve her colleagues.
A) If x = cookies and y = fruit; write a system of inequalities representing the information above.
B) Using the graph below, represent the possible amounts of snacks she can purchase.
C) Find 2 possible amounts of snacks that she can purchase
33) What is the slope of the line whose equation is 2y – 4x = 12?
a) 6
b) 2
c) -4
d) -2
c) 12
d) -12
34) What is the value of h(-2) if h(x) = 2x2 – 4?
a) 4
b) 0
35) Factor: x2 – 121
a) (x – 11)(x – 11)
b) x(x – 121)
c) (x + 11)(x – 11)
d) (x – 121)(x + 121)
36) Which expression is not equivalent to
a) 3-2
b)
1
?
9
32
34
1
3
2
c)  
1

9
0
d) 
37) Which interval notation represents x > 3?
a) (3, ∞)
b) [3, ∞)
c) (0, 3)
d) (3, ∞]
38) What is the solution for the following system of equations?
2x – y = 3
5x + y = 4
a) (1, -1)
b) (1, 1)
c) (2, 1)
d) (0 , 4)
39) Which inequality is represented in the graph below?
a) y  
1
x 4
2
b) y  
1
x 4
2
c) y  
1
x 2
2
40) Which value of y is not in the solution set of the inequality 
a) -2
41) If
b) -18
, what is the value of
a) -8
c) 18
2
y  12 ?
3
d) 0
?
b) 7
42) What is the average rate of change for the
table from 0 to 4?
d) y  0.5x  4
c) -2
d) 16