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Answers Math 9
NOTE: The correct answer is indicated by "x". Wherever the choices are not given, the answer
is printed in italics fonts.
*1* Which is the set of all factors of 36?
1

[12, 24, 36]


2

[2,3,4,6,9,12,18]


3

[1,2,3,4,6,9,12,18,36]

x

4

[36,72,108,144,180,…….]


*2* Prime factorization of 100
1

1x100


2

10x10


3

1x2x5x10x20x50x100


4

2x2x5x5

x

*3* Which expression does not name an integer?
*4* Which expression is not equivalent to 42/50?
1

0.42

x

2

0.84


3

84%


4

21/25


*5* Point out the irrational number
1

0.237176095……..

x

2

156.623565656……..


3

sq root of 0.64


4

14/3


*6* Which number is not greater than 5?
1

 5½

x

2

 5/2


3

0


4

5½


*7* Which expression is between 1.2986 and 2.9
1

sq root of 2

x

2

 2.0


3

0.986


4

 0.986


*8* 2.5 x 10 ^{2} ……. 2.5 x 10 ^{3}
*9* Which expression is not equivalent to:
 2m + 8v – 6vm
1

m + 8v – 6mv –m


2

2(m + 3mv) + 8v


3

2v(3m  4) – 2m

x

4

6vm + 8v – 2m


*10* If a+121 is an even integer, which is the next even integer:
1

a + 123

x

2

2a + 121


3

a + 122


4

2a


*11* For which value of z is the following true:
z < Öz + 1 < 1
*12* 2M  7 £ 8
1

M £ 2


2

M £ ½

X

3

M £ 2


4

M £  ½


*13* Which set contains only solutions to x >7?
1

{1,2,3,4,5,6,7,8,9}


2

{16,17,18,19,20,21,22,23}

x

3

{3,2,1,0,1,2,3,}


4

Any real number between 6 and 8


*14* Which statement is wrong for p £ q
1

P is less than or equal to q


2

P is no more than q


3

P is at most q


4

P and q is never be equal

x

*15* Which set is true for “Twice a number is less than 10”
1

1, 2, 3, 4, 5, 6, 7, 8, 9, 10


2

1, 4, 9, 16 …………


3

x < 10


4

1, 2, 3, 4

x

*16* “It is raining today” make negation
1

It is probably raining today


2

It is not raining today

x

3

Partially it is raining today


4

I don’t know raining or not raining today


*17* “I am not going to the mall today” make negation
1

Might be I am going to the mall today


2

Am I going to the mall today?


3

Am I not going to the mall today?


4

I am going to the mall today

x

*18* Write the prime factorization of 120
2x2x2x3x5
*19* Find the G.C.F. of 6, 8, 12 2
*20* Zero is a natural number. False/Trur F
*21* 8.3080080008….. is irrational F/T T
*22* Absolute value of a number is its distance from …… on a number line. zero
From 23 to 32: Write the phrase with algebraic variable
*23* eight more than a number t t + 8
*24* A number is decreased by eleven x  11
*25* the quotient when the square root of a number is divided by two. Öx ÷ 2
*26* Three times a number increased by 6 3x+6
*27* Seven times the sum of a number t and 9
7(9 + t)
*28* Square of a number is divided by 10
x^{2} / 10
*29* the quotient when the sum of two numbers is divided by their product. (a+b) ÷ ab
*30* Sona bought nineteen chairs. Each chair costs $ d. How much he paid. 19d
*31* A real number increased by six is more than four times that number. a+6 > 4a
*32* Tan = …… / ……. Perp / Base
*33* Suppose 2n – 4 represents an odd integer, write the next odd integer. 2n  2
*34* Is the equation a+8 = 7+a soluable? why
*35* Boiling point in Fahrenheit thermometer is ….. degree and in Celsius is ……. Degree.
212, 100
*36* Freezing point in Fahrenheit thermometer is ….. degree and in Celsius is ……. Degree.
32, 0
*37* Production in a factory was 1200 pencils per week, now it goes 1500 pencils per week. What percent increased?
25%
*38* If 3x – 1 is an even integer, write the even integer just before it. 3x  3
*39* Solve the equation: 50b  2.38 = 20.5b + 23.8
0.9
*40* Solve b2 1 = 7
b2 = 8, b2 = 8, 10, 6 Ans
*41* 12% students are bald in a School. If 66 students are bald. Find the total number of students in the school.
550 students
*42* I bought a TV on sale for $336. The regular price was $420. What was the percent of decrease in the price?
20%
*43* Identify the figure by the given points on the Coordinate Plane: P(1,3) Q(5,3) R(5,2) and S(1,2)
Rectangle
*44* A line with slope 1/3 contains R(3,n) and S(2,2). n=…… 11/3
*45* If a statement is true, its negation is ….. If a statement is false, its negation is …… false, true
*46* Subtract 23abc + 22 bcd + 20 abd from  15bcd + 18abc  25abd
5abc  37bcd  45 abd
*47* Square of a number is divided by the double of that number equals to 4. Find the number
8
*48* There were 75 members of the Drama Club last year but there are only 65 members this year. What is the percent of decrease?
13.3%
*49* David has a number of dimes and quarters worth $ 2.60 both together. Total coins are 14. How many dimes & quarters does he have?
8 quarters and 6 dimes
*50* Joe has 14 coins. Some are quarters and some are nickels. The total value of the coins is $1.70. How many quarters does Joe have?
Let q represent the number of quarters, then 14q is the number of nickels.
Value of quarters in cents = 25q
Value of nickels in cents = 5(14q)
Total amount in cents = 170 cents
25q + 5(14q) = 170, q = 5
*51* Catharine has invested $500 in an account that earns simple interest at an annual rate of 4%. How long will it take for this ney to earn $50 in interest?
I(interest amount) = $ 50
p(principal investment) = $500
r(rate of interest annually) = .04
t(time in years) = ?
applying formula ptv = I, t=2.5 years
*52* Ali works at an electronic store. He earns a 4% commission on all his sales. What amount must he sell for his commission to be $200?
$5000
*53* Carlos went to dinner. The price of the dinner was $45.60 and he left a 15% tip. What was the total cost of the dinner
including tip?
$52.44
*54* Write ratio in fraction
40 inches to 6 feet 5/9
*55* R : 8.5 = 3 : 4, find R 6.37
*56* The scale of a map is 1 inch = 24 miles. What map distance represents 75 miles?
Inches = 1 = n
Miles 24 75 3.125 inches
*57* Solve the equation: 7a + 8 = 7a
No solution
*58* 2a + b = c, make the equation expressing the value of a.
a = ½ (c – b)
*59* Find four consecutive numbers whose sum is 34.
7, 8 , 9, 10
*60* Which inequality represents the following statement “5 less than a number Y is at most 20”
1

Y – 5 < 20


2

Y – 5 = or < 20

x

3

5 – Y < 20


4

5 < Y < 20


*61* Which sign for “Is at least”
*62* Ahmed invested $1200 for a period of six years and earned $396 simple interest. What was the annual rate of interest?
Prt = I
1

5 ½ %

x

2

10 %


3

6 %


4

8 ¼ %


*63* Which sign represents “is at most 15”
1

£ 15

x

2

z 15


3

< 15


4

> 15


*64* Find two consecutive numbers whose product is 210.
14 & 15
*65* Total cost of cinema tickets for two adults and four students is $29. A student ticket costs four dollars less than an adult ticket. Find the cost of an adult ticket.
$7.50
*66* Perimeter of a rectangular garden is 64 feet. Its width is 12 feet less than the length. What is the length?
22 ft
*67* Allan plans to save 15% of his salary each week. His weekly salary is $700. What amount does he plan to save each week?
$105
*68* The price of a CD is $12.75 and the sales tax is 4% of the price. What is the total cost of the CD with tax?
$13.26
*69* A team’s win:loss:tie is 12:5:1. The team played 144 games. How many were lossess?
40
*70* A copy machine can print 125 pages in 3 minutes. How many minutes will it take for printing the 800 pages?
19 min 12 sec
*71* A real number c increased by 6 is more than four times c:
1

6c > 4c


2

c < 6 + 4c


3

c + 6 < 4c


4

c + 6 > 4c

x

*72* 12% of the students in a school belong to the Drama Club. There are 66 students in the Drama Club. How many students are in the school altogether?
1

600


2

500


3

550

x

4

650


*73* Slope (m) is zero
1

Points: (1, 1) and (5, 1)


2

Points: (4, 4) and (0, 3)


3

Points: (2, 3) and (5, 3)

x

4

Points: (4, 5) and (6, 7)


*74* If x is a real number, then x^{2} is always:
1

Negative


2

≥ 0

X

3

The perfect square


4

divisible by 2


75* Which point lies along the line containing P(3, 1) and Q(5, 6) First we have to make the equation; slope is
7/8; y6 = 7/8 (x5) or = 7/8 (x5) + 6, choice No.3 (x=21, y=20) can satisfy the equation
1

A(3,0)


2

B(21,19)


3

C(21.20)

X

4

D(3,2)


*76* Which line is parallel to the graph of 5x – 6y = 27 Given equation can be written as Y = 5/6 x – 1/3, a parallel line must have slope 5/6
1

Line with slope 5/6 & yintercept 1/3


2

Line with slope 5/6 & yintercept 3

x

3

Line with slope 6/5 & yintercept 1/3


4

Line with slope 6/5 & yintercept 3


*77* Which phrase best describes
–z^{3} + 3z^{2} – 2z – 3z^{2}
1

Cubic trinomial


2

Cubic monomial


3

Quadratic trinomial


4

Cubic binomial

x

*78* Write the additive inverse of 6a^{3} + a^{2}  a
1

6a^{3}  a^{2} + a

x

2

6a^{3} + a^{2} – a


3

6a^{3} + a^{2} + a


4

 a  6a^{3} + a^{2}


*79* Which is equivalent to 3^{5}. 9^{4}
1

3^{11}


2

3^{13}

x 
3

27^{9}


4

27^{20}


*80* The equal value of (6 x 10^{4})^{2}
1

3.6 x 10^{9}

x

2

3.6 x 10^{8}


3

6 x 10^{8}


4

36 x 10^{2}


*81* Suppose a, b and c are odd integers, which of the following must be even:
I. ab+c
II. c(ab+3)
III. 2a + bc
I and II
*82* G.C.F. of 12x^{3}, 30x^{2}, 42x
1

8x


2

8x^{2}


3

6x

x

4

6x^{2}


*83* Geri required to make fifty sales every month. So far this month she has made 42 sales. What percent of herrequirement has she achieved? 82%
*84* Point P(x,y) has coordinates x=3, y=4. Give the coordinates of A(x, 3y)
(3, 12)
*85* A function is a relationship between the members of …… sets in which every member of the first set has a common relationship with the member of the second set. Members of the first set are called the …… and the members of the second set called …….
two, domain, range
*86* Find the domain(x) and range(y) of each function:
{(1,5), (2,10), (3,15),(4,20), (5,25), (6,30)}
Domain:{1,2,3,4,5,6} Range:{5,10,15,20,25,30}
*87* {(0,0),(0,7),(6,6),(6,6)} is not a function, why? Because the domain values 0 and 6 are assigned two different range values.
*88* xintercept of a graph is the point where the graph crosses the ……. xaxis
*89* Write an equation in slopeintercept form if the line with slope ¾ contains P(2, 3)
y – (3) = ¾(x – 2)
y = ¾ x – 9/2
*90* Perpendicular is 7", base is 8", find Hypotenuse.
10.6"
*91* Write an equation with slope zero and containing P(2, 3) y = 3
*92* Standing pole is an example of vertical image or horizontal?
Vertical
*93* Write an equation for the line containing A(5, 6) and B(3,8)
Slope(m) = 7/4, then y – 8 = 7x/4 (x – 3)
y = 7x/4 + 11/4
*94* Write the equation of the line containing A(5,6) and B(3, 6) y = 6
*95* The above line is horizontal or vertical?
Horizontal(because y are equal)
*96* Write an equation of the line with the points (4.2, 6) and (4.2, 9) x = 4.2
*97* slopeintercept form is y = mx + b where b is a ……… yintercept point
*98* As you know the xmembers are domain and ymembers are range. Characterize the domain and range in y = x^{2} + 2
Domain(x): all real numbers
Range(y): 2, 3, 6, 11, 18, ……
99* Write an equation for line AB, if A(2,3) and B(8,11)
slope is 4/3, then y3 = 4/3 (x2) or y11 = 4/3 (x8)
in both cases the answer: 4x + 3y = 1
*100* The equation y = 2x + 5 makes a line with the point P(3,w). Find the value of w.
Value of x is given as 3, put it in the equation, we get y = 11, so y=w=11
*101* Find an equation in slopeintercept form for the line z containing P(4, 3) and parallel to the graph of y = ½ x + 3
Since line z is parallel to the graph of y = ½ x + 3, the slope of z is ½. Also line z
contains P(4, 3) so, y – (3) – ½ (x – 4)
y = ½ x  5
*102* Write 5x – 3y = 15 in slopeintercept form:
y = 5/3x  5
*103* The sum of two numbers is 26. Twice one number less the other number equals 16. Which equations do not represent the situation?
1

x + y = 26, 2x – y = 16


2

2x – y = 16, x + y = 26


3

26 = x + y, 16 = 2x – y


4

x + y = 16, 2x – y = 26

X

*104* 15 people attended a party. The cook prepared 2 pounds of food for each adult and 1.25 pounds of food for each child. The cook prepared a total of 24 pounds of food. How many children and how many adults attended the party?
1

10 children and 5 adults


2

8 children and 7 adults

x

3

7 children and 8 adults


4

5 children and 10 adults


*105* A line segment 15 inches long is separated into two parts. The length y of the longer segment is 3 inches more than twice the length of x of the shorter segment. Which equations do not represent this situation?
1

y+x=15 3+2x=y


2

x+y=15 y2x=3


3

x=15y y=2x+3


4

X+y=15 32y=y

x

*106* Which best represents the coordinates of the point of intersection of two blue lines?
1

x is between 2 & 3 and y between 1 & 2

2

x is between 2 & 3 and y between 0 & 1 x

3

x is between 2 & 3 and y between 1 & 2

4

x is between 2 & 3 and y between 0 & 1

*107* Which system of equations has the same solution as: 5x3y=24, 2x7y11=0
1

10x6y=48, 2x7y=11


2

2(5x3y)+48=0 2x7y11=0


3

10x35y=11, 30y+50x=240

x

4

½ (5x3y)=12 7y+2x=11


*108* Which equation has no solution?
1

b^{2} = 36

2

b^{2} = 0

3

b^{2} = 36

4

b^{2} = 36 x

*109* Four years from now, Ray will be twice as old as his sister will be then. If Ray is now r years old, how many
years old is his sister now?
After 4 yrs sister will be half of the Ray’s age.
After 4 yrs Ray’s age = R+4
After 4 yrs sister’s age = ½ (R+4)
Sister’s current age = ½ (R+4) – 4 (4 yrs less)
1

½ (R  4)

X

2

R – 4


3

½ (R + 4)


4

2R – 4


*110* If the slope is zero, the line is ………, if there is no slope, the line is ………
Horizontal, vertical
*111* Find an equation in slopeintercept form for the line n containing Q(2, 5) and perpendicular to the graph of y =  ½ x + 5.
Since line n is perpendicular to the said graph, the slope is 2. Also line n contains P(2, 5))
y – 5 = 2[x – (2)], y = 2x + 9
*112* Bibi has 30 nickels and dimes altogether. Their total value is $2.40. How many of each has she?
In all she has 30 coins n+d = 30
Total worth is 240 cents 5n+10d = 240
12 nickels and 18 dimes
*113* A quadratic is written in the form of ax^{2}+bx+c=0, where a,b,c are ……… and a is not ……….. real numbers, equal to zero
*114* Which equation does not have the same solutions as 3x^{2} = 6x – 9?
1

3x^{2}  6x + 9 = 0


2

3x^{2} – 6x = 9


3

3x^{2} – 6x – 9 = 0

x

4

x^{2} – 2x + 3 = 0


*115* Which is equivalent to n^{2} + n = 30?
1

0 = (n+6)(n5)

x

2

0 = (n6)(n+5)


3

0 = (n6)(n6)


4

0 = (n+5)(n+6)


*116* How many solutions does n^{2}2n+1=0 have
1

One

x

2

Two


3

None


4

Infinite


*117* Which does not represent a rectangle with its sides m+2 and m+4 inches and area 63 inches^{2}
1

(m+2)(m+4) = 63


2

(m+2)(m+4) – 63 = 0


3

m^{2} + 6m + 71 = 0

X

4

m^{2} + 6m + 8 = 63


*118* b ÷ 2a = …….
*119* Which is true of the graph of
y = 2x^{2} – 4x + 5
1

Graph opens down, x=1


2

Graph opens up, x=4


3

Graph opens up, x=1

x

4

Graph opens down, x=5


*120* Perpendicular of a Rt triangle is onefourth of its base and its area is 162 sq units. Find perpendicular and base in sq units.
9, 36
*121* Solve the quadratic equation by perfect square method: x^{2} – 8x – 33 = 0
11, 3
*122* The highest or lowest point of parabola is called ………
vertex
*123* Write the Equation of a Circle
x^{2}+ y^{2}=r^{2}
*124* Do the points (3,4) and (4,3) lie on the circle with equation x^{2} + y^{2} = 25
yes because 3^{2 }+4^{2} = 5^{2} and (4)^{ 2 }+3^{2} = 5^{2}
*125* Can you solve the equation n^{2} + 5n – 7 = 0 by factoring method?
No
*126* If the equation is 1^{2} = x^{2} + y^{2}, which points do not lie on the circle?
1

(1, 0), (0,1)


2

(0, 1), (0, 1)


3

(0, 1), (0, 1)


4

(2, 1), (2, 1)

x

*127* 35/0 is:
1

Defined


2

Undefined

x

3

Irrational


4

Odd


*128* Which statement is mutually exclusive?
1

Selecting a baseball card showing a Yankee too


2

Scoring above 80 on a test and scoring above 90 on the same test


3

Rolling a multiple of 2 that is also a 17

x

4

Rolling a prime number that is also an even number


*129* If a/b = 0.06 What is the value of b/a?
1

50/3

x

2

60.0


3

6.0


4

10/6


*130* Solve the quadratic equation by perfect sq method and by quadratic formula. 10, 5
*131* Sketch a circle from the equation
x^{2} + y^{2} = 4 The equation represents a circle with radius 2 and center at the origin, so first suppose x=0 then y=2 & 2,
graph (0,2) and (0,2). Afterward suppose y=0 then x=2 & 2, graph (2,0) and (2,0)
*132* Solve y=x^{2} and y=2x
(0, 0), (2, 4)
*133* Solve y = x – 3, y = x^{2} + 1
Unsolvable
*134* Solve y + 3x = 4, x^{2} – 2x – 87
(3, 5) and (4, 16)
*135* Solve y4=x3 and x^{2}+y^{2}=25
(4,3) and (3,4)
*136* Simplify P/Q ÷ R, if P = 5p25, Q = p+3,
R = p^{2}+2p15 5/(3+p)^{ 2}
*137* Simplify A/5 ÷ B/2, when A = z6 and
B = 6z  2/5
*138* 1 1 8
+ =
m – 4 m + 4 m.m – 16 [+,=]
4
*139* One copy machine can complete a job in 25 minutes. This machine and a newer machine working together can
complete the same job in 10 minutes. How long would it take the newer machine to complete the job working by itself.
Suppose the newer machine does the job in m minutes by itself.
part of job done part of job done part of job don
by old machine by old machine by old machine
In one minute In one minute In one minute
1/25 1/m 1/10
1/25 + 1/m = 1/10, m = 50/3 minutes
*140* When twothird is subtracted from the quotient of a number 7 divided by 3, the result equals the ratio of 1 to n. What is n?
n/3 – 2/3 = 1/n, n=3, 1
*141* If there are no outcomes common in two sets or two statements. These sets or statements are said to be ………… to each other. Mutually exclusive
*142* We can say 0.56 as 56% the same thing. Does 0.07 be the same thing as 7%? yes
*143* Simplify 1/P + 1/Q, when P=t^{2} and
Q=t+1 t^{2}+t+1 / t^{2} (t+1)
*144* 16% = 0.16, Is 8% = 0.8? no
*145* A triangle having its sides 7, 5 and Ö74. Is it a right triangle? Why? Ans: yes
*146* Sides of a right triangle are 12.4, 12 and 3. What is the value of sin of the smaller acute angle? 15/62
*147* Sides of a right triangle are 12.4, 12 and 3. What is the value of sin of the larger acute angle? 31/31
*148* In right triangle ABC, if mÐB is 90 degree and cos B = 3/5, what is the value of sin A? 3/5
R
*149* Sin R = …… 5/13
13 12
P 5 M
*150* Sin R = …… 5/13
*151* Cosec P = ……. 13/12
*152* Sec R = ……. 13/12
*153* Cos P = …… 5/13
Find the angle:
*154* Sin x = 2.7/4.5 30 degree
*155* Tan x = 1.00 45 degree
*156* Cot x = 1.00 45 degree
*157* Tan x = 1.732 Tan 60
*158* Cos x = 0.766 Cos 40
*159* In isosceles triangle ABC, AC=BC=20, mÐA = 68^{0} and CD is the altitude to side AB. What is the length of CD to the nearest tenth?
1

9.5


2

12.0


3

18.4

x

4

25.75


*160* If tan x = 4/8, what is the measure of the angle x?
1

60^{0}


2

30^{0}


3

7923^{0}


4

27^{0}


*161* Median? 5.3, 6, 5.5, 6, 5.7, 5, 4, 5, 6
*162* In right triangle ABC, hypotenuse AB = 10 and angle B is 53 degree. Find AC approx.
Sin 53^{0} = P/10 = .800, P = 8 Ans
*163* Tan B = 3.08, find the angle B (nearest)
72 degree
*164* The diagonal of a rectangle is 15 and its shorter side is 7. What is the size of the angle formed by the diagonal and the longer side (nearest)?
Tan x = 7/15 = 0.47, x = 26^{0}
*165* In rectangle ABCD, AD=10, CD=8 and diagonal AC is drawn, Find the mÐCAD?
Tan x = 8/10 = 0.80, x = 39^{0}
*166* A 10 ft long ladder is placed against the side of a wall. The base of the ladder is making an angle of 72 with the ground. How far the base of the ladder should be from the side of the building and how far up the side of the wall the ladder will reach?
Cos72 = B/10 = 0.39, B = 3.09 ft
Sin 72 = P/10 = 0.95, P = 9.5 ft
*167* Find the area & B 9 C
Perimeter of the
Trapezoid.
35^{0}
A 15 D
Make a line BE on point B parallel to CD, length of BC is 4.2. Measure AB which is 7.3.Measure the area of triangle and rectangle separately and add them i.e. Area is 50.5 and perimeter is
9+4.2+15+7.3 = 35.5
*168* If cot A^{0 }= 1⅞, what is the value of tan A^{0}
8/15
*169* In an oblique triangle ABC, A = 30°, B = 45°, and the perpendicular from C to AB is 12 inches long. Find the length of AB
12 + 12 Ö 3 or 32.7
