Download Semester 2: Algebra Geometry Study Guide

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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
Polynomials and 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. Name the polynomial and state the degree then,
solve by factoring
d. Name the polynomial and state the degree then,
solve by factoring
2x 2 + 22x + 48 = 0
0 = x 2 -10x + 21
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 : USE YOUR CALCULATOR
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:
x z  2y
y2
b) Solve the equation:
2
c)Solve the equation:
e)Simplify:
10 x  5
2x 1
5 x  1 3x  6

2
3
3x
 2x  7
5
d)Solve and graph the inequality:
f)Simplify:
x3
x2

2x
x3
7 x  2  3(6  x)
g)Simplify:
h)Simplify: (no negative exponents)
 4m3 n 
x2
x

x2  4
x2  2x
2
8m 3 n5
i)Solve for x:
j)Simplify:
2 x  3  11
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”
C  4, 1 and D  2, 5
A  4,3 and B  2, 5
j)
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?
Statistics:
Given the set of data find the Mean, Median, Mode and Range.
56, 65, 59, 57, 72, 43, 59, 43
Calculate the Mean, Variance and Standard Deviation of these values:
6.8, 8.7, 7.6, 4.8, 9.0
Create a Box and Whisker plot for the following data, state the Interquartile Range:
12, 11, 15, 12, 19, 20, 19, 14, 18, 15, 16