QUADRATIC EQUATIONS MULTIPLE CHOICE TEST

This mathematics MCQs is made to help student learn mathematics by a certain topic. In this section, we'll get a test about quadratic equations. The target of this test is student can find the solution of quadratic equations by factoring, the square root property, and the quadratic formula.

Mathematics MCQs E1

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INSTRUCTION

Choose the one alternative answers Your choice can not be replaced Click "solutions" button to check your answer Answer all questions before you check the solutions Click "next" button to find another MCQs

1. By factoring, the solution of x² + 3x − 10 = 0 is ....
   
   A. -2 or 5
   B. -5 or 2
   C. 2 or 5
   D. -2 or 4
   E. -4 or 2
   

   Solution :
   ⇒ x² + 3x − 10 = 0
   ⇒ (x + 5)(x − 2) = 0
   ⇒ x = -5 or x = 2.
   

   Answer : B

   
   
2. The solution set of x²  − 2x − 8 = 0 is .....
   
   A. 270
   B. 280
   C. 290
   D. 300
   E. 320
   

   Solution :
   ⇒ x²  − 2x − 8  = 0
   ⇒ (x + 2)(x − 4) = 0
   ⇒ x = -2 or x = 4
   The soluiton set = {-2,4}
   

   Answer : A

   
   
3. By use the square root property, the solution of x²  − 4x = 0 is .....
   
   A. ±4
   B. 4
   C. -4 or 2
   D. -2 or 4
   E. -4
   

   Solution :
   ⇒ x²  − 4x = 0
   ⇒ x²  − 4x + 4 = 0 + 4
   ⇒ (x − 2)² = 4
   ⇒  x − 2 = ±2
   ⇒ x = 2 + 2 = 4
   

   Answer : B

   
   
4. The solution set of  x²  + 5x − 50 = 0 is....
   
   A. {-10,5}
   B. {-5,10}
   C. {-25,2}
   D. {-2,25}
   E. {-4,5}
   

   Solution :
   ⇒ x²  + 5x − 50  = 0
   ⇒ (x + 10)(x − 5) = 0
   ⇒ x = -10 or x = 5
   The soluiton set = {-10,5}
   

   Answer : A

   
   
5. By using the quadratic formula, the solution of x²  + 2x − 3 = 0 is ...
   A. {-3,1}
   B. {1,-3}
   C. {-2,3}
   D. {-3,2}
   E. {-3,3}
   

   Solutions :
   

   ⇒ x1,2 =	-b ± √b2 − 4.a.c
   	2a

   ⇒ x1,2 =	-2 ± √22 − 4.1.(-3)
   	2.1

   ⇒ x1,2 =	-2 ± √16
   	2

   ⇒ x1 =	-2 + 4
   	2

   ⇒ x₁ = 1
   

   ⇒ x2 =	-2 − 4
   	2

   ⇒ x₂ = -3
   

   Answer : A

   
   

 

FIND THE ANGLE BETWEEN TWO VECTORS

1. The vectors A and B are given by A = 3i + 5j − 4k and B = 8i − 4j + k. The angle between the two vectors is ......

   A. 90o	D. 37o
   B. 60o	E. 30o
   C. 45o

   
   
   Solution :
   To find the angle between two vectors, we can use the dot product formula. The dot product (the scalar product) of two vectors is defined by : 
   
   A.B = |A|.|B| cos θ
   
   With :
   |A| = the magnitude of vector A
   |B| = the magnitude of vector B
   θ = the angle between vectors A and B.
   
   According to the formula above :
   ⇒ A.B = |A|.|B| cos θ
   ⇒ A.B = |A|.|B| cos θ
   ⇒ (3i + 5j − 4k).(8i − 4j + k) = |A|.|B| cos θ
   ⇒ 3(8) + 5(-4) + (-4)(1) = |A|.|B| cos θ
   ⇒ 24 − 20 − 4 = |A|.|B| cos θ
   ⇒ 0 = |A|.|B| cos θ
   ⇒ cos θ = 0
   ⇒ θ = 90^o
   

   Answer : A

   
   
2. The angle between u = i + √2 j + √5 k and v = i − √2 j + √5  k is .....

   A. 90o	D. 30o
   B. 60o	E. 15o
   C. 45o

   
   
   Solution :
   According to the dot product formula :
   ⇒ u.v = |u|.|v| cos θ
   ⇒ u.v = |u|.|v| cos θ
   ⇒ (i + √2 j + √5 k).(i − √2 j + √5) = |u|.|v| cos θ
   ⇒ 1 − 2 + 5 = √1 + 2 + 5.√1 + 2 + 5 cos θ
   ⇒ 4 = 8 cos θ
   ⇒ cos θ = ½
   ⇒ θ = 60^o.
   

   Answer : B

   
   
3. The vectors A and B are given by A = 2i − j − 3k, and B = pi + j − k. If the two vectors are perpendicular to each other, the value of p is .....

   A. -2	D. 2
   B. -1	E. 3
   C. 1

   
   
   Solution :
   Since the two vectors are perpendicular to each other, so the angle between them is 90^o. According to scalar product formula :
   ⇒ a.b = |a|.|b| cos θ
   ⇒ a.b = |a|.|b| cos 90^o
   ⇒ (2i − j − 3k).(pi + j − k) = |a|.|b| (0)
   ⇒ 2(p) + (-1)(1) + (-3)(-1) = 0
   ⇒ 2p − 1 + 3 = 0
   ⇒ 2p + 2 = 0
   ⇒ 2p = -2
   ⇒ p = -1
   

   Answer : B

   
   

SOLVING SECTORS AND CIRCLES PROBLEMS

1. Look at the picture below! If the length of arc AB is equal to twice the length of radius r of the circle, the area of sector OAB in terms of the radius r will be equal to .....
   

   A. ½r2

   B. r2

   C. 2r2

   D. 4r2

   
   Solution :
   The area of sector AOB can be calculated by this formula :
   

   ⇒ Area AOB =	angle AOB	.Area of circle
   	360o

   ⇒ Area AOB =	angle AOB	.πr2
   	360o

   
   Now, we must find the angle AOB first.
   ⇒ Length of arc AB = radius x angle AOB
   ⇒ 2r = r. angle AOB
   ⇒ Angle AOB = 2 radians
   ⇒ Angle AOB = ²⁄_π.180^o
   
   Now, back to the formula above :
   

   ⇒ Area AOB =	2⁄π.180o	.πr2
   	360o

   ⇒ Area AOB =	2⁄π.1	.πr2
   	2

   ⇒ Area AOB =	1	.πr2
   	π

   ⇒ Area AOB = r²
   

   Answer : B

   
   
2. The angle of a sector in a given circle is 60 degrees and the area of the sector is equal to 18,84 cm². Calculate the arc length of the sector.

   A. 6,00 cm	D. 6,44 cm
   B. 6,02 cm	E. 6,82 cm
   C. 6,28 cm

   
   Solution :
   First, we can calculate the radius r by the formula below :
   

   ⇒ Area of sector =	60o	.πr2
   	360o

   ⇒ 18,84 =	1	.πr2
   	6

   ⇒ 113,04 = 3,14 r²
   ⇒  r² = 36
   ⇒ r = 6 cm.
   
   The arc length of the sector :
   ⇒ arc length of sector = radius x angle AOB
   ⇒ arc length of sector =  ⁶⁰⁄₁₈₀.π  x 6 cm 
   ⇒ arc length of sector = 6,28 cm.
   

   Answer : C

   
   
3. The angle of a sector in a given circle is 45 degrees and the radius is 8 cm. The area of sector is equal to .....

   A. 25,12 cm2	D. 26,22 cm2
   B. 25,42 cm2	E. 26,52 cm2
   C. 25,68 cm2

   
   Solution :
   

   ⇒ Area of sector =	angle of sector	.Area of circle
   	360o

   ⇒ Area of sector =	45o	.(3,14)(8)2
   	360o

   ⇒ Area of sector =	1	.(200,96)
   	8

   ⇒ Area of sector = 25,12 cm².
   

   Answer : A

AVAILABLE CHART TYPES IN MICROSOFT EXCEL

As we know, Microsoft Excel has many features that help us to process numbers. Among its many features, Microsoft Excel helps us to make charts. This feature provides a way to add visual appeal to our reports. In Excel 2013, there are ten types of chart. Each of chart types has different features so it will be better if we use the right type. Because each of chart types is better suited for specific tasks, then we must understand what is the different between them and what are their functions. To make the information easier to understand, we must pair a chart with its correct data style. Here the ten available chart types in microsoft excel.

DO WE REALLY NEED A CREDIT CARD?

Last year, I got a call from someone from a financial company (I never heard it before) who offer me a credit card. I wonder how they get my number and how they know my name? No privacy anymore in this world people! The girl just told me that they, her company, has special offer for me if I want to get a credit card from them. For a moment, I just thought Do I really need it? A rectangular piece of plastic, graphite, or metallic alloy that identifies a financial account. No, no, I didn't need it yet. 

WE CONTROL MONEY OR MONEY CONTROLS US

When we live in a society where money is not the medium for power, maybe we can actually control money. But the question is, is that society exist?  We need money everywhere and we work hard for it. The fact is all of us live in societies that deal with money and we try to control it. My father told me that money is something we can reach but we can't control. He said let money control us. 

I agree that maybe money is something we can't control but I think we can control ourselves. Money is just a paper. Yeah, a powerful paper. Some people will claim that they try to control money and money doesn't control them, but the truth is money controls us all. We work hard all day just to get money so we can fulfill our need. People can do bad thing just because they want to have much money. Sometimes, someone is killed in the name of money. We just need to realize it. Really??

HOW CAN MONEY CONTROL PEOPLE?

Hi people, this is my first cut in blog! I am so excited because I didn't know why I decided to make this blog. Believe me, I don't! My English is suck but I must try before I stop, right? When I was in senior high school, I saw my classmates had everything. Money, new arrival gadgets, super cool shoes, they had everything that I wanted. Sometimes, I just thought, how pity I am! But then, I found something in my book. Something really good that changed me. No, I mean changed my mind.