Name______________________________
Semester 2: Algebra Geometry Study Guide
Radicals:
a. Simplify:
18
d. Simplify fully:
28
7
g. Simplify fully:
5 6
10 3
j. Simplify:
6 2 6
b. Simplify fully:
c. Simplify fully:
2  10
3 12
e. Simplify fully:

5 2

f. Simplify:
5 2

h. Rationalize the denominator:
1
6
k. Simplify fully:
3
3 2
2 20  3 45
i. Rationalize the denominator and simplify:
2
5 2
l. Solve and check for extraneous solutions:
3x  1  5
Quadratics:
a. Complete the table of values for the function:
y
x
b. Make a labeled graph of
2
x
4
4
x2
y  4
4
y
-4
-2
0
2
4
c. Find the vertex of
d. Name the vertex and the axis of symmetry of
f ( x)  ( x  2)2  3
y  x 2  4 x  10
e. Solve by factoring:
f.
Solve by factoring:
3x2 – 5x – 2 = 0
y  x 2  7 x  12
g)The height h (in meters) of a ball after t seconds is given by the function
h   x 2  12 x  3
a. Graph the function on your calculator to
make a neat sketch of the path of the ball
in the box at the right.
b. Determine the height of the ball
after 2 seconds.
c. Determine the maximum height
reached by the ball (to 1 decimal place).
d. Calculate the time it takes for the ball to hit the ground (to 1 decimal place).
Algebra:
a) If x  3 , y  2 and z  4 , evaluate:
b) Solve the equation:
x z  2y
y2
2
c)Solve the equation:
e)Simplify:
10 x  5
2x 1
g)Simplify:
x2
x
 2
2
x 4
x  2x
i)Solve for x:
2 x  3  11
5 x  1 3x  6

2
3
3x
 2x  7
5
d)Solve and graph the inequality:
7 x  2  3(6  x)
f)Simplify:
x3
x2

2x
x3
h)Simplify: (no negative exponents)
 4m n 
3
2
8m 3 n5
j)Simplify:
22  23  (3  5)
10  8
Geometry: (know ALL definitions from Geo Vocab sheet)
a)Write in mathematical
notation:
b)Determine the distance between
the points
c)Find the midpoint of a segment joining
d)Find the value of x, to
determine that the lines are
parallel. State the reason why
e) State the reason(s) why.
f)Find the value of x.
g) In this kite, find the values of
the angles marked 1 and 2.
h)
i)
“The segment joining point A to
point B is perpendicular to the
segment joining point C to point D”
j)
C  4, 1 and D  2, 5
A  4,3 and B  2, 5
k)
3D shapes Area and Volume:
Find the total surface area of these solids. You may need to make use of Pythagoras’ theorem.
2) Find the total surface area of this cylinder. Leave your answer in terms of π.
3) Find the total surface area of this square based
pyramid
4) Find the surface area of this solid. Round your
answer to one decimal place.
Probability:
a) In a room there are 7 girls and 11 boys. If child is
selected at random, then what is the probability of
selecting a girl?
b) A box contains 4 white, 6 black and 10 red balls. A
ball is chosen at random from the box. After
replacing it, a second ball is chosen. What is the
probability of choosing two white balls?
c) In a class of 21 students, 5 are wearing jeans. If 2
students are randomly selected, what is the
probability that both are wearing jeans?
(Obviously the students are not replaced after they
have been selected.)
d) A jar contains 8 pink, 5 green and 3 blue marbles.
Two marbles are chosen at random from the jar
without replacement. What is the probability of
choosing two pink marbles?
e) In a group of 40 students, 27 like basketball and 24 like pizza. 3 students like neither of these.
a. Draw and complete a labeled Venn diagram to represent this information.
b. If an student is chosen at random,
what is the probability that he or she:
1. likes both basketball and pizza?
2. likes pizza but not basketball?
3. likes basketball or pizza but not both?
4. likes basketball, given that he or she likes pizza?
Story Problems: there will be approximately 10 story problems on your final. Please refer to your daily story problem
notes. Read each question very carefully and be sure to answer the question being asked. There are many ways to solve a
multi-step story problem so be sure to show all work and use correct units in final answer.