IB- GRADE 9 QUARTERLY REVIEW QUESTIONS
1. Which of the following describes the figure below?
Answer: B
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), (๐๐) ⃗ 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
(๐๐) ⃗ 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
The midpoint formula for one-dimensional coordinates is:
M = (๐+๐)/2
2 = (−5+๐)/2
4 = −5+๐
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
[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" ๐)/("Change in" ๐)
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 - ๐/2 = 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 - ๐/2 = 6 Y = ๐/2 + 6 M = 1/2 [B] 2y-x=4 Y = ๐/2 +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= ๐ /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, (๐ต๐ถ) ̅||(๐ท๐ธ) ̅, 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.
๐จ๐ฉ/๐จ๐ซ = ๐ฉ๐ช/๐ซ๐ฌ
๐จ๐ฉ/(๐จ๐ฉ+๐ฉ๐ซ) = ๐ฉ๐ช/๐ซ๐ฌ
๐/(๐+๐ฉ๐ซ) = ๐/๐๐
๐+๐ฉ๐ซ = 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
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] (๐ด๐ถ) ̅ [B] (๐ต๐ถ) ̅ [C] (๐ด๐ต) ̅ [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 (๐ต๐ถ) ̅
ANSWER: B
25. Find m∠1 in the figure below. (๐๐) ⃡ and (๐ ๐) ⃡ 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]
(๐๐) ̅ = (๐๐) ̅ (Given)
(๐๐) ̅ = (๐๐) ̅(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
๐๐/๐๐ = ๐ฟ/๐๐ = ๐๐/๐
๐/๐๐ = ๐๐/๐ฟ๐
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
๐จ๐ฉ/๐ฟ๐ = ๐จ๐ช/๐ฟ๐
๐/๐๐ = ๐๐/๐ฟ๐
8*XZ = 11 X 15
XZ = 165/8
XZ = 20.625
ANSWER: D
29. Solve for x : (๐+๐)/๐ = ๐/๐ [A] -21 [B] (−๐)/๐ [C] (−๐)/๐ [D] ๐๐/๐
(๐+๐)/๐ = ๐/๐
9(x+7) = 7 x6
9x+63=42
9x= 42-63
9x=-21
X = (−๐)/๐
ANSWER: B
Find the geometric mean of 18 and 2 A 6 B 9 C 10 D 4
Geometric Mean of 2 and 18
If a and b are 2 numbers The geometric mean of a and b is √๐๐
Applying the formula
GM of 2 and 18 is
√(2 x 18) =√36 =6
The answer : A
THANK YOU
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