AMEN ACADEMY
ACADEMIC YEAR OF 2016E.C ,FIRST SEMESTER MATHEMATICS FINAL EXAMINATION FOR GRADE 9
NAME__________________________________GRADE/SECTION_______NO___________
PART – I : SAY “TRUE” IF THE STATEMENT IS CORRECT AND “FALSE” IF IT IS NOT CORRECT
_______1. There is no even prime number.
2 2
_______2. 2 ×3 ×5 is the prime factorization of 180.
_______3. 351 is divisible by 3.
_______4. Every quadratic equation has two distinct real roots.
_______5. The square root of all positive integers is irrational
PART – II : CHOOSE THE CORRECT ANSWER FROM THE GIVEN FOUR ALTERNATIVES AND PUT
THE LETTER OF YOUR ANSWER ON THE ANSWER SHEET.
_______1. Which one of the following is true ?
A. Any integer is a rational number
35 9
B. The simplest form of is
45 7
a
C. For a , b ∈ Z , is a rational number
b
2 11
D. The simplest form of 5 is
4 4
_______2. Real numbers between – 3 and 8 including – 3 and excluding 8 can be represented
using interval notation as_________
A . (−3 , 8 ) B . (−3 , 8 ] C . [ −3 , 8 ) D . [ −3 , 8 ]
_______3. Which one of the following is prime number?
A. 144 B. 243 C. 173 D. 169
_______4. The number of significant digits of the number 0.1800 is
A. 2 B. 4 C. 3 D. 1
_______5. Which one of the following is true about the numbers 48 and 120 ?
A. Their GCF is 48 C. The product of their GCF and LCM equals to 1200
B. Their LCM is 140 D. Their LCM is 240
_______6. Which one of the following is a rational number ?
A. √ 121 B . √ 2 C . 1.21212112111211112 … D . √ 5
_______7. Which one of the following is true ?
A. Every whole number is a natural number
B. Every rational number is an integer
C. Every integer is a rational number
D. Every integer is a whole number
_______8. Out of the following, the irrational number is
1
A . 0.5 B .1.4 77 C .−4.277 D . 0.121121112 …
p
_______9. 0.2222 …∈ form is
q
6 2 3 1
A. B. C . D.
99 9 5 66
_______10. The value of 2161 /3 is
A. 8 B. 4 C. 6 D. 32
_______11. According to the division algorithm, what should be the value of q and r respectively
so that 7 36=12 q+r ?
A . 60∧−4 B .54∧8 C .60∧4 D . 61∧4
_______12. The value of 95 / 2is
A. 243 B. 27 C. – 18 D. 1/27
2 /5 1/4 −3
_______13. 243 ×81 × 9 =¿ ¿
1 1 1
A. B.3C. D.
3 9 27
_______14. A small town has 530 flower pots. The gardener wants to arrange them in rows such
that each row contains 21 flower pots. What are the number of completed rows that a
gardener can make ?
A. 20 B. 19 C. 28 D. 25
_______15. The value of x for which √ x be a rational number is
A. 10 B. 8 C. 3 D. 49
_______16. The value of ( 2+ √ 2 ) ( 2−√ 2 ) is
A. 0 B. 3 C. 2 D. 4
1
_______17. On rationalizing the denominator of , we get
√3
A.
√ 3 B . 3C .− √ 3 D . √3
7 3
1
_______18. On rationalizing the denominator of , we get
√6−√ 5
A . √ √ B . √ √ C . √ 6+ √ 5 D . √ 6−√ 5
6+ 5 6− 5
6−√ 5 √6 + √5
_______19. For positive real numbers a and b, which is not true ?
A.
B.
√ ab=√ a √ b
( a+ √ b ) ( a−√ b )=a −b
2
C.
√ a √a
=
b √b
D. ( √ a+ √ b )( √ a−√ b )=a+ b
_______20. 0.005078 in scientific notation equals to
−4 −2 −3 3
A . 5.078× 10 B .5.078 × 10 C . 5.078× 10 D. 5.078 ×10
_______21. The solution set of √3 2 x −5=5 is
2
A. { 40 } B. {15} C. { 70 } D. { 65 }
2x 4 x−6
_______22. The truth set of 27 =3 is
A . { 3 } B . {−3 } C . {−2 } D . {30 }
_______23. The solution set of the equation x−2 y=4 is
A . ( 0 , 2 ) B . (2 , 0 ) C . ( 1 ,1 ) D . ( 4 , 0 )
_______24. If 12 ( x−2 )−52=−4 ,then the value of x is equal ¿
A. 7 B. – 10 C. 6 D. 8
_______25. The linear equation x−2 y=6 has
A. A unique solution C. Two solutions
B. Infinitely many solutions D. No solutions
_______26. If (−1 , 2 )is a solution of the linear equation x +4 y=k , then the value of k Is
A . 7 B . 6 C . 9 D .2
_______27. The graph of the linear equation 6 x +9 y=18 cuts the Y - axis at the point
A . ( 2 ,0 ) B . ( 0 ,3 ) C . ( 3 , 0 ) D .(0 , 2)
_______28. Which one of the following is not a linear equation in two variables ?
2
A . ax +by=c B .ax +by =c C .2 x+ 3 y=5 D .3 x +2 y=6
_______29. Which one of the following is the solution set of the system of the underneath
equations ? { 6 x−4 y=−6
4 x+ 2 y =8
{ 57 187 } { 125 163 }
A . ( , ) B . ( , ) C . { ( 4 , 9 ) } D . {( 5 , 18 ) }
_______30. Which one of the following systems of linear equations has infinitely many solution
{ { {
A . 9 x +3 y=−3 B . 2 x +6 y =4 C . 4 x +4 y=24 D . x−2 y=5
−3 x− y =1 6 x−12 y=3 x− y=0 {
−3 x+ 6 y=1
_______31. For the equation {
ax− y=2
6 x−2 y=3
to have infinite solutions , the value of a = ______
A. 3 B. – 3 C. – 12 D. no value
_______32. |6 x +10|=16 . Find the values of x which make this equation true
{
A . 1 ,−
13
3 } { 1
3
1
3 } { 1
B . 4 ,−4 C . 4 ,−1 D . { 1 ,−1 }
3 }
_______33. Which one of the following is equivalent to 3 x 2−14 x−5
A . ( x−1 ) ( x −5 ) B . ( 3 x + 11 )( x−5 ) C . ( x−1 )( 2 x−5 ) D. (x+1)(x +5)
_______34. The roots of quadratic equation 4 x 2+2 x +8=0 are
A. Both positive C. Positive and negative
B. Bothe negative D. No real roots.
2
_______35. A quadratic equation ax +bx +c=0 has two distinct real roots, if
2 2
A. b −4 ac> 0 B. b −4 ac=0 C. b 2−4 ac< 0 D. b 2−ac <0
_______36. The roots of the quadratic equation 12 x2 −2 x−4=0 is
3
A. {23 , 12 }B . {23 ,− 12 }C . {−23 , 12 } D .{−23 ,− 12 }
_______37. The sum of the roots of the quadratic equation 6 x 2−18 x+ 10=0
A . 3 B . 6 C .−3 D . 2
_______38. What is the solution set of the equation √ 15−2 x=x
A . { 3 ,−5 } B . {−3 , 5 } C . {−2 ,1 } D . {3 }
_______39. If one of the root of the quadratic equation 2 x 2+ kx−6=0 is 2, the value of k is
A . 1 B .−1 C .−2 D . 2
PART – IV : WORK OUT
Show all the necessary steps and answer the following questions
40. Write the number 0.1 24 in fraction form
1+ √ 3
41. If =a+b √ 3 , then find the values of a∧b
2+ √ 3
42. The area of a rectangle is 21 cm2. If one side exceeds the other by 4cm, find the
dimensions of the rectangle.
43. Find the solution set to the system of linear equations { −3 x+2 y=−6
x− y =4
44. If r 1∧r 2 are the two roots of quadratic equation 3 x 2+ 8 x −12=0, then
a. r 1 +r 2 =¿ ¿
b . r 1 .r 2=¿ ¿
45. Solve 2 x 2+8 x−8=0
