IB - GRADE 9 QUARTERLY REVIEW QUESTIONS

IB- GRADE 9 QUARTERLY REVIEW QUESTIONS

1. Which of the following describes the figure below?

Answer: B

2. Which one of the following gives the distance between the numbers-1 and 7?[A] 8[B] 6[c] -8[D] -6

Distance=∣7−(−1)∣ 

Distance=∣7+1∣

Distance=∣7+1∣ 

Distance=∣8∣

So, the distance between -1 and 7 is 8 units.

ANSWER: A

3. If RS=38; and QS=86.4, find QR.[A] 38.4[B]124.4[C] 38[D] 48.4

QR=QS−RS 

QR=86.4−38

QR=86.4−38 

QR=48.4

ANSWER = D

4. Solve: In the figure (not drawn to scale), (𝑀𝑂) ⃗ bisects ∠LMN, m ∠LMO=18x-34 and M ∠NMO=x+136. Solve for x and find m ∠ LMN[A] 6,44[B]10,214[C] 6,74[D] 10, 292

(𝑀𝑂) ⃗ bisects ∠LMN, SO BY ANGLE BISECTOR THEOREM

m ∠LMO= M ∠NMO

18x-34 = x+136. 

18X-X = 136+34

17X=170

X=10

m ∠ LMO = 18X -34 = 18 X 10 -34 = 180 -34 = 146

M ∠NMO=x+136 = 10 + 136 =146

M ∠LMN= 146 + 146 = 292

ANSWER : D

5. If M is the midpoint of (𝑃𝑄) ̅ find the value of x.[A] 7[B] 9[C] 14[D]-3

The midpoint formula for one-dimensional coordinates is:

M = (𝑃+𝑄)/2

2 = (−5+𝑋)/2

4 = −5+𝑋

X = 9

ANSWER: B

6. If∠A and ∠ B are supplementary angles and m ∠A = 3m ∠B find m ∠A and m ∠ B.[A] 120,60[B] 67.5.22.5[C] 60, 30[D] 135,45

Given that m∠A=3m∠B, 

m∠A+m∠B=180°

3m∠B+m∠B=180 °

4m∠B=180 °

m∠B=180"°" /4

m∠B=45 °

m∠A=3m∠B 

m∠A=3×45 °

m∠A=135 °

ANSWER: D

7. In the figure shown, m ∠AED=108°. Which of the following statements is false?[A] ∠ BEC and and ∠ CED are adjacent angles. [B] ∠AEΒ= 72°[C] ∠ AEB & ∠ DEC are vertical angles.[D] m ∠ BEC=72°

[A] ∠BEC and ∠CED are adjacent angles.

Adjacent angles are angles that share a common side and a common vertex but do not overlap. In the figure, ∠BEC and ∠CED share the common side EC and the common vertex E, but they do not overlap. So, this statement is true.

[B] ∠AEB = 72°

Since ∠AED = 108°, and ∠AED and ∠AEB are supplementary angles (forming a straight line), then ∠AEB = 180° - 108° = 72°. So, this statement is true.

[C] ∠AEB and ∠DEC are vertical angles.

Vertical angles are formed by intersecting lines and are opposite each other. In the figure, ∠AEB and ∠DEC are opposite each other. So, this statement is TRUE.

[D] m∠BEC = 72°

Since ∠AED = 108°, and ∠AED and ∠BEC are Vertically opposite angles then ∠BEC = ∠AED = 108° So, this statement is false.

ANSWER: D  the false statement is m ∠ BEC=72°

8. IF ∠ A and ∠ B are complementary angles and m∠A=5m∠B find m ∠A and m ∠B.[A] none of these[B] 144°,36°[C] 150°,30°[D] 72°,18 °

m∠A=5m∠B

m∠A + m∠B = 90° (COMPLEMENTARY ANGLES)

m∠B+5m∠B = 90°

6m∠B = 90°

m∠B =90/6

m∠B = 15°

m∠A=5m∠B

m∠A=5 X 15° = 75°

ANSWER: A

9. Find the distance between points P(-4, 2) and Q(5,-3) .[A] 2√17[B] √106[C] 10[D] √2

The distance between points P(-4, 2) and Q(5,-3)

D = √(〖"(x2" −"x1" )〗^2+〖"(y2" −"y1" )〗^2 )

D = √(〖"(5" +4)〗^2+〖"(−" 3−2)〗^2 )

D = √(〖"(9" )〗^2+〖"(" −5)〗^2 )

D = √(81+25)

D = √106

ANSWER: B

10. Find the coordinates of the midpoint of the segment connecting       H(-2,-4) and K(-12,6)[A] (5,5)[B] (-7,1)(C) (10, 1)[D] (-14, 2)

H(-2,-4) and K(-12,6)

Mid point Formula

M = ("x2 + x1" /"2"  , ("y2 +y" 1)/"2"   )

M = (("−12 −" 2)/"2"  , "6−4" /"2"   )

M = ((−14)/"2"  , 2/"2"   )

M = (-7, 1)

ANSWER: B

11. Find the values of x, y, and z.[A] x=91 , y=89 z=66[B] x=91 y=89 z = 49[c] x=89 , y=91 z=66[ D]x=89,y=91,z=49

∠BAC + ∠ABC = ∠BCD=Y

65° +26° = 91° =Y

X+Y=180° (LINEAR PAIR)

X+91° = 180°

X=180-91=89°

23° + Z+Y=180° (ANGLE SUM PROPERTY OF TRIANGLE)

23° + Z+91° =180°

Z = 180° - 114° = 66°

ANSWER: C

12. Find a and b.[A] a=33,57  [C] a=33,b=78[B] a=45,b=57  [D] a=45, b = 33

∠C = 90° = 45 ° +45 °

b + 78 +45 = 180 ° (ANGLE SUM PROPERTY OF A TRIANGLE)

b = 180 ° - 123 °=57 °

LINEAR PAIR +78 = 180 °

LINEAR PAIR = 180 -78 ° = 102 °

102 °+a + 45 ° = 180 °

a = 180 – 147 = 33 °

ANSWER: A



13. In A ABC, m∠ A=64 ° and m ∠ C=52 °, Calculate m ∠ B.[A] 74 °[B] 26 °[C] 244 °[D] 64 °

Angle sum property of a triangle∠  B=180° −(64° +52°) 

∠  B=180° −116° 

∠  B=64°

ANSWER : D

14. Classify the triangle with sides of length 15, 15, and 15.[A] isosceles[B] scalene[C] straight[D] equilateral

A triangle with all three sides of equal length is called an equilateral triangle. So, a triangle with sides of length 15, 15, and 15 is an equilateral triangle.

ANSWER: D

15. Classify the triangle with angles measuring 84°, 65° and 31° [A] straight [B] obtuse[C] right [D] acute

this triangle is classified as an "acute triangle". An acute triangle is a triangle where all three angles are less than 90°.

ANSWER: D

16. Graph: y=5x+5

17. Find the slope of the line passing through the points A(-7,-3) and B(-4,5)[A] (−2)/11   [B]  13/8  [C]    3/( 8)   [D]    8/3

SLOPE = ("Change in"  𝑋)/("Change in"  𝑌) 

m = "y2 −y1" /"x2 −x1"   

m =  ("5+" 3)/(" −4+" 7) 

m= 8/3

ANSWER: D

18. Which of the lines is not perpendicular to 2x+y=8?[A] Y - 𝑋/2 = 6[B] 2y-x=4[C] X – 2Y =3[D] 2x-y=4

Two lines are perpendicular if and only if the product of their slopes is -1. 

[2x + y = 8] [y = -2x + 8] M= -2

[A] Y - 𝑋/2 = 6  Y = 𝑋/2 + 6 M = 1/2[B] 2y-x=4  Y =  𝑋/2 +2  M = 1/2

[C] X – 2Y =3  Y = 1/2X+ 3/2  M = 1/2[D] 2x-y=4  Y= 2X+4  M = 2

the line not perpendicular to (2x+y=8) is line [D] (2x-y=4).

ANSWER: D

19. In the figure shown, PQ-18 centimeters ST=6 centimeters and m∠QRP=60°. Find m∠S[A]30°[B] 90°[C] 60°[D] 120°

m∠QRP=60°= m∠TRS (Vertically opposite angles)

m∠RTS=90°

Angle sum property of a triangle

m∠TRS + m∠RTS + m∠RST=180°

60°+90°+ m∠S =180°m∠S =180°- 150°

m∠S =30°

ANSWER: A

20. Two pentagons are similar. The perimeter of one is 42 m and that of the other is 105 m. Find the ratio of the sides of the pentagons.[A] 1:2.5[B] 1:2[C] 1:6.25[D] 2:5

If two pentagons are similar, it means their corresponding sides are proportional. 

"Perimeter of smaller pentagon" /"Perimeter of LARGER pentagon"  ="Ratio of sides of smaller pentagon" /"Ratio of sides of LARGER pentagon" 

42/105=  𝑅/1

R = 2/5 = 1/2.5 

each side of the smaller pentagon is 2/5 times the length of the corresponding side of the larger pentagon.

RATIO = 1/2.5

ANSWER: A 1:2.5

21. In the figure shown, (𝐵𝐶) ̅||(𝐷𝐸) ̅, AB= 4 yards, BC=6 yards, AE=20 yards, and DE=24 yards. Find BD.[A] 15 yd[B] 12 yd[ C]5 yd[D]16yd

In similar triangles, corresponding sides are proportional.

𝑨𝑩/𝑨𝑫 = 𝑩𝑪/𝑫𝑬

𝑨𝑩/(𝑨𝑩+𝑩𝑫) = 𝑩𝑪/𝑫𝑬

𝟒/(𝟒+𝑩𝑫) = 𝟔/𝟐𝟒

𝟒+𝑩𝑫 = 16

BD = 16-4 = 12 YARDS

ANSWER: B



22. Find the values of x and y.[A] x=8 ° y=86 °[C] x =86°; y =94°[B]x=86 °;y=66 °[D] x=8 °; y=94 °

LINEAR PAIR OF ANGLES

94°+Z = 180°

Z = 180 ° -94 °= 86°

IN AN ISOSCELES TRIANGLE, THE ANGLES OPPOSITE TO EQUAL SIDES ARE EQUAL.

Y = 86°

ANGLE SUM PROPERTY OF A TRIANGLE

86 °+86 °+X = 180 °

X = 180 °-172 °

X = 8 °

ANSWER: A

23. Which of these lengths could be the sides of a triangle?[A] 24 cm, 15 cm, 8 cm[B] 6 cm, 19 cm, 13 cm[C] 19 cm, 6 cm, 14 cm[D]15cm,24cm,7cm

The triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

[A] 24 cm, 15 cm, 8 cm:

24 + 15 > 8 (True)

24 + 8 > 15 (True)

15 + 8 > 24 (True) All three conditions are true, so these lengths can form a triangle.

[B] 6 cm, 19 cm, 13 cm:

6 + 19 > 13 (True)

6 + 13 > 19 (True)

19 + 13 > 6 (True) All three conditions are true, so these lengths can form a triangle.

[C] 19 cm, 6 cm, 14 cm:

19 + 6 > 14 (True)

19 + 14 > 6 (True)

6 + 14 > 19 (True) All three conditions are true, so these lengths can form a triangle.

[D] 15 cm, 24 cm, 7 cm:

15 + 24 > 7 (True)

15 + 7 > 24 (False)

24 + 7 > 15 (True) The second condition is false, so these lengths cannot form a triangle.

So, the options [A], [B], and [C] are valid triangles, but option [D] is not.

24. Find the largest side of the triangle, (not drawn to scale)[A] (𝐴𝐶) ̅[B] (𝐵𝐶) ̅[C] (𝐴𝐵) ̅[D] not enough information

∠ BAC = 180°-82°=98°

SUM OF ALL THE ANGLES OF A TRIANGLE = 180°

∠ ABC = 180° – (98°+51°) = 180° – 149° = 31°

SIDE OPPOSITE TO LARGEST ANGLE IS LARGEST SIDE. 

SO SIDE OPPOSITE TO 98 ° IS  (𝐵𝐶) ̅

ANSWER: B

25. Find m∠1 in the figure below. (𝑃𝑄) ⃡ and (𝑅𝑆) ⃡  are parallel.[A] 61 °[B]109 °[C]29 °[D] 119 °

Corresponding angles are equal = 61° 

Linear pair of angles 

 m ∠ 1 + 61 ° = 180 °

m ∠1= 180 °-61 °

m ∠1 = 119 °

ANSWER: D

26. Refer to the figure shown. Which of the following statements is true?

ANSWER: [B]

(𝑇𝑉) ̅ = (𝑉𝑊) ̅ (Given)

(𝑈𝑉) ̅ = (𝑉𝑋) ̅(given)

  ∠UVT = ∠ WVX (vertically opposite angles)

THEN  ∆TUV ≅ ∆WXV BY SAS

ANSWER: D

27. The triangles below are similar. Find the length of x.[A] 70[B] 73.5[C] 5.7[D] 73

𝟒𝟗/𝟏𝟒 =  𝑿/𝟐𝟎 = 𝟐𝟖/𝟖 

 𝟖/𝟏𝟓 = 𝟏𝟏/𝑿𝒁 

14*X = 49 X 20

X = 980/14

X = 70

ANSWER: A

28. Triangles ABC and XYZ are similar with ∠A = ∠ X and ∠ B\= ∠ Y. IF AB, BC, and AC are 8 inches, 9 inches, and 11 inches long, respectively, and YY is 15 inches long, find XZ. (Answer to the nearest tenth.)[A] 4.8 in.[B] 5.9 in.[C] 16.9 in.[D] 20.6 in.

AC corresponds to XZ and XY corresponds to AB

𝑨𝑩/𝑿𝒀 = 𝑨𝑪/𝑿𝒁 

 𝟖/𝟏𝟓 = 𝟏𝟏/𝑿𝒁 

8*XZ = 11 X 15

XZ = 165/8

XZ = 20.625

ANSWER: D

29. Solve for x : (𝒙+𝟕)/𝟔 = 𝟕/𝟗[A] -21[B] (−𝟕)/𝟑 [C] (−𝟑)/𝟕[D] 𝟑𝟓/𝟑

(𝒙+𝟕)/𝟔 = 𝟕/𝟗

9(x+7) = 7 x6

9x+63=42

9x= 42-63

9x=-21

X = (−𝟕)/𝟑 

ANSWER: B

Find the geometric mean of 18 and 2A 6B 9C 10D 4

Geometric Mean of 2 and 18

If a and b are 2 numbers The geometric mean of a and b is √𝑎𝑏

Applying the formula

GM of 2 and 18 is

√(2 x 18) =√36 =6

The answer : A



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