Download Practice Test Questions

1. What is scientific notation?
_A number is written as the product of two factors in the form a*10^n, where n is an
integer and 1  a<10
2. Write 1,123,000 in scientific notation:
_1,123,000=1.123*10^6
3. Write 0.85*10^6 in standard notation:
_0.85*10^6=850,000
4. Simplify 7n^4*4n^2
_7n^4*4n^2=(7*4)(n^4*n^2)
=28(n^4+2)
=28n^6
5. Simplify
_
a ^6
a ^14
a ^6
= a^6-14
a ^14
=a^-8
1
=
a ^8
Problem:
a -1.2b= -3
0.2b+0.6a= 12
Solution:
a=1.2b-3
Solve for b:
0.2b+0.6 (1.2b-3) = 12
0.2b+0.72b-1.8=12
0.92b-1.8=12
0.92b=13.8
b= 15
Solve for a:
a-1.2(15) = -3
a- 18= -3
a=15
CHAP 5
1. Find the third, tenth, thirty- fifth terms of the sequence.
A(n) = -5 + (n-1)19
Answer:
n= 3
A(3) = -5 + (3-1)19
= -5 + 2(19)
= -5 + 38
= 33
n= 15
A(15) = -5 + (15-1)19
= -5 + 14(19)
= -5 + 266
= 261
n= 35
A(35) = -5 + (35-1)19
= -5 + 34 (19)
= -5 + 466
= 461
2. Write a function rule for each table of values
X
2
3
4
y
x
Y
18
27
36
1

1
18
9
2
y
x
2

2
27
9
3
The numbers are the same so the function is: y= 9x
3. This table represent a direct variation or an inverse variation?
X
Y
3
27
7
63
12
108
y
x
1
1

27
9
3
y
x
1
1

63
9
7
y
x
1
1

108
9
12
The ratio is the same for all pairs of data. So this is a direct variation,
and k=9
4. This table represent a direct variation or an inverse variation?
y
x
1
1

X
Y
2
30
8
120
12
132
30
 15
2
y
x
1
1

120
 15
8
y
x
1
1

132
 11
12
One of the ratios is not the same for all other pairs of data. No solution.
5. Write a function rule for the table
X
Y
-1
-3.4
-2
-3.2
0
-3
1
-2.8
2
-2.6
Answer:y=1/5x-3
Chapter 7 – System equations
1)The total cost of the tickets to a show for 2 adults and 3 children is $16 while the
cost of 3 adults and 2 children is $19. Find the cost of an adult’s ticket and a
child’s ticket.
Solution
Let the cost of an adult’s ticket be $a and a child’s $b.
2a+3b=16
(1)
2a+2b=19
(2)
(1)*2
(2)*3
4a+6b=32
9a+6b=57
(1)’
(2)’
(2)’-(1)’ 5a=25
a=5
Substitute a=5 into (1),
2(5)+3b=16
10+3b=16
3b=6
b=2
Adult’s ticket = $5
A child’s ticket = $2
2)In a farm, there are some cows and some chickens. If the animals have a total of
35 heads and 96 legs, how many cows and chickens are there?
Solution
Let the number of cows be x and chickens be y.
Since cows have 4 legs and chickens have 2 legs, and each of them has 1 head,
(2)*2
(1)-(2)’
4x+2y=96
x+y =35
(1)
(2)
2x+2y=70
(2)’
2x=26
x=13
Substitute x=13 into (1)
4(13)+2y=96
52+2y=96
2y=44
y=22
Cows = 13
Chickens = 22
1)
a)
b)
c)
Use these sequences -40, 20,-10, 5…
Find the common ratio
What are the next three terms?
Find the 11th term of the sequence
Answer:
a) -2
b) -2.5,1.25,-0.625
c) a(11)  40  (2) 11-1
a(11)  40 * (2) 10
a(11)  40 * (1024)
a(11)  40960
Question 1: In 2006, AIS 6th grades tuition was $5,950. It has been
increasing 85% every year. Find how much tuition will be in 2011?
Answer:
y = abx
y = 5,950 (100% + 85%)
y = 5,950 (1.85) 2011-2006
y = 5,950 (1.85)5
y = $128,936.46
Question 2: -5, -2.5, -1.25, -0.625 What is the common ratio? Find the 7th
term.
Answer:
Common Ratio = 1/2
A(n) = a x rn-1
A(7) = -5 (1/2)7-1
A(7) = -0.078125
Question 3: (2c-2 x 3c)/ (6y2)2 + c-4/ (12g4)-1. Simplified
6c-1/6y4 + c-4/ 12g-4
c-1/y4 + c-4/12g-4
1/y4 + g4/12c4
Question 4:
6.3 x 10-7, 75 x 102, 0.07 x 10-3, 72 x 10-2
Answer: 72 x 10-2, 75 x 102, 0.07 x 10-3, 6.3 x 10-7
Question 5: Which equation is exponential growth, which is decay.
Y = a – bx
y= abx
When a>0; b>0
When a>0; 0>b>1
Answer: growth: When a>0; b>0
decay: When a>0; 0>1
1. Solve by completing the square
2x^2  7 x  6
1
Ans: -2,  1
2
2. Solve using the quadratic formula
 x^ 2  8x  4  5
Ans: 0.13, 7.87
3. Write in standard form, then solve by factoring
3x^ 2  5 x  3x^ 2  6
Ans: 3,
1
2
Find the number of solutions of 5x2 + 8 = 2x
5x2 + 8 = 2x
5x2 - 2x + 8 = 0
b2 – 4ac = (-2)2 – (4)(5)(8)
= 4 – 160
= -156  -156< 0  No real solutions
Tell whether it models quadratic, exponential or linear. Write an equation for each set of
points.
a. (-4, 18), (-2, 6), (-1, 3), (3, 11), (4, 18)
b. (-2,-7 1/3), (-1, -7 2/3), (0, -8), (2, -8 2/3), (5, -9 2/3), (6, -10)
c. (-3, 0.2936), (2, 2.25), (3, 3.375), (4, 5.0625), (5, 7.5938), (6, 11.391)
a. Quadratic function x2 + 2
b. Linear function –(1/3)x – 8
c. Exponential function 1.5x
Chapter 9 Math Questions
Multiplying Special Cases:
_ (9j-2) ^2
(9j-2)^2 = (9j-2) (9j-2)
= 81j^2 -18j -18j +4
= 81j^2 -36j +4
Multiplying Trinomials:
_ (9x+10) (11x-2)
(9x+10) (11x-2) = 99x^2+110x+-18x-20
=99x^2+98x-20
_ (3x+9) (8x+10)
(3x+9) (8x+10)= 24x^2+72x+30x+90
=24^2+102x+90
Factoring Trinomials of the Type ax^2 +bx +c:
_15p^2 -26p +11
15p^2
-26p
FOIL: 15*1 [15*(-1)] + [1*(-11)] =-26
+11
(-11)*-1
15p^2 -26p +11= [15p*(-11)] [1p*(-1)]
Factoring Special Cases:
_3m^2 -12
3m^2 -12= 3(m^2 -4)
= 3(m^2 - 2^2)
= 3(m-2) (m+2)
Factoring by Grouping:
_26t^2 +24t +9
26t^2 +24t +9
= 4t (4t +3) +4t (4t+3)
= (4t+3) (4t+3)
Answer
16*9= 144
12*12=144
->12+12=24
Chapter 2
9.8  7
5
8.5
0.98
6.4
8.9
 8 4.5 0.21
-
9
9
0 .4
8 .5
8 =
0.21 0.7
7 .4
8.82  7.4
 2.1
4
1. 1
16.9
1
4.29
 0.49
X= -2 Y= 3, evaluate the expression
20-xy= 20- -2(3)
=20+6
=26
What is the property of the following expression?
5(1/5) =1Inverse Property of Multiplication
There are 13 marbles in a bag. 5 are blue, 4 are red and 4 are yellow. What is the
probability of picking a blue marble then a red, without replacing?
5/13 * 4/12= 20/156 = 10/78 = 5/39
Solve each system of inequality by graphing
6 x  5 y  15
 5 y  6 x  15
6
x3
5
x  2y  7
y
2 y  x  7
1
y   x  3.5
2
Answer:
You change it into slope-intercept form to graph. y < or  , shade below the boundary
line.
y > or  , shade above the boundary line.
Be careful to see it’s a solid or dashed line.
The region where both equation shaded, those number are satisfied for both equation.
Chapter 10, Algebra
1) Question: Compare the graph of -3x2+ 2x-3 and the parent function graph (y=x2)
- Shift down 3 units (c = -3), narrower (a = further from 0), shift up- side down (a =
negative)
2) Graph these equations: y ≤ ½x2 +2x + 1 & y ≥ ½x2 + 2x -3
3) Question: Solve by complete the square : 12354x2+98832x-14823 = 0
12354x2+98832x-148238 = 0
- X2 + 8x -12 = 0
- X2 + 8x = 12
-
X2 + 8x + ( )2 = 12 + ( )2
√(x+4)2 = √(28)
X+4 = ± 5.29
X= -9.29 or 1.29
4) Question: Solve 18x2-360 = 0 quadratic equation
-
1. Derive the quadratic formula
- ax2 + bx + c = 0
-
ax2 +
-
= -c
+
=
-
x2 +
x=
-
x2 +
x+(
-
(x+
=
Take the square Root
-
x+
=
+(
2. How do you make the graph open downward?
- Make A negative.
3. Factoring to solve quadratic equations
a. x^2 + 14x – 240 = 0
x*x
24*(-10)
= (x+24)(x-10) = 0
=
x+24 = 0
x = -24
OR
OR
= x – 10 = 0
x = 10
b. x^2 + 8x = -15
= x^2 + 8x + 15 = 0
x*x
5*3
= ( x + 5)( x + 3) = 0
= x+5=0
=
x = -5
OR
OR
= x+3=0
=
x = -3
4. Completing the square
a. x^2 + 10x +17 = 0
=
=
=
x^2 + 10x = -17
x^2 + 10x + (10/2)^2 = -17 + (10/2)^2
( x + 5) ^2 + = 8
= (x + 5) = +or = x + 5 = +or – 2.8
= x + 5 = 2.8
=
x = -2.2
8
OR
OR
= x + 5 = -2.8
=
x = -7.8
(Time vs acceleration)
Describe the graph above
Answer:
Constant speed
Drive faster
Slow down
Stop for the light
Start driving
Is this direct or constant variation:
X
Y
2
4
3
4
5
2
6
7
8
1
Answer:
Inverse variation, because X times Y equals 8 and so K= 8
In inverse variation
so k= x*y
X
2
3
Y
4
K
8
8
4
5
2
8
8
6
8
7
8
8
1
8
CHAPTER 3
1/ Solve
x
30
A
B
2/
39
26
Triangle A and B are similar. Find x.
3/ A bus and a car leave the same place and traveled in opposite directions. If the bus is
traveling at 50mph, and the car is traveling at 55mph, in how many hours will they be
210 miles apart?
50t + 55t = 210
105t = 210
t=2
4/
Find x.
52 + x2 = 132
x2 = 132 – 52
5 – 25
x2 = 169
2
x = 144
x = 12
13
x
1. What is slope?
Rise/run
2. What is linear parent function?
F(x) =x
What is slope-intercept form?
Y= mx+b
Write an equation of a line with the given slope and y-intercept?
m=-3
b=1/3
Find the x and y intercept of 7x-3y=7
7x-3 . 0=7
7 . 0 -3y=7
7x=7
-3y=7
X=1
y=-7/3
Write 3x+2y=l in slope- intercept form
Y=-3/2x+3
What is perpendicular line of y=-1/4x-1
Y=4x+2
Change (-2;1) and slope is -3 to point slope form
(y-1)=-3(x+2)
1. Simplify this expression
2. Is there a negative, positive, or no correlation?
3. Write an equation to model the relationship
#
Cost
1
$2.30
2
$4.60
3
$6.90
4. What is the mean, median and mode of 15, 15, 9, 9, 20, 23, 7, 17, and
6?
1. What is the slope of this line?
 Slope =
( y 2  y1)
(9  13)
4


( x2  x1) (5  (4))
9
2. Given 2 points (8,7), (-1,-1), write the slope equation
a) Find Slope
b) Substitute the slope and 1 point to find the y-intercept y=mx+b
(7  (1) 8

(8  (1) 9
 a)
Substitute (1,-1) in:
8
( 1)  b
9
1
b
9
-1=
Substitute the slope and y-intercept in the equation y=mx+b
8
1
x
9
9
3. What is the standard form of a linear equation? Point-slope form?
 Standard form Ax+by=C
Point-Slope form: (y-y1) = m(x-x1)
4. What is the slope of the parallel line with another line contains the slope 3? Slope of
the perpendicular line
 Parallel: 3
Perpendicular: -1/3
5. Make a scatter plot of the data below and draw a trend line and write its equation.
Find the correlation coefficient.
Yearly Box Office gross for movies
(Billions)
1995
1996
1997
1998
1999
2000
2001
2002
2003
5.5
6
6.4
7
7.4
8.0
8.3
9.9
9.9

Two points on the trend line (95,5) and (100,8).
The Equation :
( y  5) 
(8  5)
3
 Use point slope form substitute (95,5) and slope:
(100  95) 5
3
( x  95)
5
Correlation coefficient = 0.983399
1. Find the degree of this monomial
12x10y70
Answer: 80
2. Simplify the product
3x3 (4x5 + (-9) x7 + 10x9 + (-11) x11)
12x8 + (-27) x10 + 30x12- 33x14
12x8 – 27x10 + 30x12 – 33x14
Answer: 12x8 – 27x10 + 30x12 – 33x14
3. Factor
50k3- 40k2 + 75- 60
(50k3+ 75) (-40k2 -60)
25k (2k2 +3) -20 (2k2 +3)
(25k-20) (2k3 +3)
(5k● 5- 4) (2K3+3)
Answer: (5k● 5- 4) (2K3+3)
4. Expand
(-10x -8) (-10x +8)
-10x -8
 10 x  8
 80 x  64
Answer:
100 x 2  80 x
100 x 2  64
100 x 2  80 x
100 x 2  64
1)
2)
3)
4)
1. List the three special cases of factoring trinomial?
a2 + 2ab + b2 = (a+b)(a+b)= (a+b )2
a2 - 2ab + b2 = (a-b)(a-b)= (a-b )2
a2-b2 = (a-b)(a+b)
2. What is FOIL? Solve the equation using FOIL?
First Outer Inner Last
(4x + 5) * (2x + 3)
(4x + 5) * (2x + 3)= 4x * 2x + 4x * 5 + 5 * 2x + 5 * 3 = 8x 2 + 20x + 10x + 15 = 8x2 + 30x + 15
3. Factor this equation by grouping
15m3 + 11m2 - 45m - 33
=(15m3 - 45m) + ( 11m2 - 33)
= 15m (m2 - 3) + 11 (m2 - 3)
= (m2 - 3) (15m + 11)
4. Solve this question by using special case.
4x2 – 9
4x2 – 9 = (2x + 3)(2x – 3) = 2x * 2x + 2x * (-3) + 3 * 2x + 3* (-3) = 4x2 – 6x + 6x -9= 4x2 - 9
CHAPTER 11
Lesson 1:
Simplify
180a 37 b17
5a 21b15
Answer:
36a 16 6a 8
=
b
b2
Lesson 2:
Simplify
 10  7 12  10 
13

Answer:
10  130  7 120  7 13 = 10  130  14 30  14 39
Lesson 3:
Find x
(6 x  2)  (10 x  16)
Answer:
(6 x  2) 2  (10 x  16) 2
6x  2  10x  16
2  4x  16
4 x  18
x
18
 4.5
4
Lesson 4:
Graph the equation
y  x5 4
Answer:
The domain ->
x5  0
x  05
x5
X
Y
5
-4
6
-3
7
-2.59
8
-2.27
9
-2
10
-1.76
Lesson 5:
Find x
Answer:
opposite
x

hypotenuse 12
x  sin( 35) * 12  6.88
sin( 35) 
Lesson 6:
You are on the roof of a 100-feet tall building, looking down to
the parking lot of that building, which is a few feet away. The
angle of depression is 48 degree. Write an equation, that will
help you find the distance from the parking lot to the building,
then solve it.
Answer:
If we use the angle of depression:
tan( 48) 
x  90.04
opposite 100

adjacent
x
1. _____ is a shorthand way to write very large and very small numbers.
ANS: scientific notation
2. 27x^12 * 3x^-5
(27*3)(x^12*x^-5)
ANS: 81x^6
3. The property of division properties of exponent
ANS: for every nonzero number a and integers m and n, a^m/a^n = a^m-m
4. ____ can be modeled with the function y=a*b^x for a>0 and b>1.
ANS: exponential growth
Chapter 8:
Question:
1/ Solve this equation
8y22-36y27-23x38x3
392
3y2y2x22x
48y416x5
= 392
6y24x3 392
8y24x2
= 8y24x2 = 32y2x2
= 392
392
2/ A photo is being copied over and over again. The next picture is 150% bigger than the
previous.
a/ Write an equation model this situation
b/ Make a table
Answer:
a/ 150% =1.5
x = the number of the enlargements
Equation: f(x) = 1.5x
b/
x
1.5 to the x square
1
2
1.5
2.3
(x, f(x))
(1,1.5)
(2, 2.3)
3
4
5
3.4
5.1
7.6
(3, 3.4)
(4, 5.1)
(5, 7.6)
3/ The cost of land in 1996 was approximately $1000. Since then, the price goes up 10%
each year:
a/ Write an equation to model this question
b/ Use your equation to estimate the approximately cost for 2010.
Answer:
a/ y = The cost of land at various times
x = The number of years since 1996
a = The cost of land in 1996
b = The growth factor, which is 110% = 1.1
Equation: y = 1,000 x 1.1x
b/ y = 1,000 x 1.1 14 (2010-1996 = 14)
y = $ 3797. 5
4/ Solve this equation write the answer in scientific notation
(27  2) 2  32 120
(3 10)3
5/ 1.6 103 ;4 102 ;3.2 104 ;8 103 ;2 101
a) Write these expressions in standard form and order them from greatest to least.
b) Determine whether this sequence is arithmetic, or geometric.
c) Write the equation for this sequence and find the 7th term and write it in
scientific notation
Answer:
(27  2) 2  32 120
27 2  4 1
4/

(3 10)3
27 103  9
27  4
 3
10  9
3 4
 3
10
12

1000
 0.012
 1.2  10  2
5/
a) 0.2; 0.04; 0.0016, 0.00032
b) Geometric sequence
c) A(n)  a  r ( n1) a = first term r = common ratio
1
A(7)  0.2  ( ) ( 7 1)
5
=0.000013
= 1.3 10 5