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Common Core: High School - Number and Quantity : High School: Number and Quantity

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

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All Common Core: High School - Number and Quantity Resources

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-2,-2> , and w=<-1,-4> , what is v-w ?

Possible Answers:

<-1,2>

<-2,-1>

<2,1>

<1,-2>

<-6,-1>

Correct answer:

<-1,2>

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-2$

$(x\:\mbox{component in}\: w)=-1$

$(y\: \mbox{component in}\: v)=-2$

$(y\: \mbox{component in}\: w)=-4$

x=-2-(-1)=-2+1=-1

y=-2-(-4)=-2+4=2

So our final answer is <-1,2> .

Below is a visual representation.

Screen shot 2016 03 10 at 12.55.41 pm

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Example Question #3 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-10,-1> , and w=<-9,-7> , what is v-w ?

Possible Answers:

<-1,-6>

<-1,6>

<1,6>

<6, -1>

<1,-6>

Correct answer:

<-1,6>

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-10$

$(x\:\mbox{component in}\: w)=-9$

$(y\: \mbox{component in}\: v)=-1$

$(y\: \mbox{component in}\: w)=-7$

x=-10-(-9)=-10+9=-1

y=-1-(-7)=-1+7=6

So our final answer is <-1,6> .

Below is a visual representation.

Screen shot 2016 03 10 at 1.03.06 pm

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Example Question #4 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-9,-9> , and w=<-4,11> , what is v-w ?

Possible Answers:

<-5,-20>

<-13,-20>

<5,-20>

<13,20>

<13,-20>

Correct answer:

<-5,-20>

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-9$

$(x\:\mbox{component in}\: w)=-4$

$(y\: \mbox{component in}\: v)=-9$

$(y\: \mbox{component in}\: w)=11$

x=-9-(-4)=-9+4=-5

y=-9-11=-20

So our final answer is <-5,-20> .

Below is a visual representation.

Screen shot 2016 03 10 at 1.09.46 pm

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Example Question #5 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-8,-10> , and w=<4,14> , what is v-w ?

Possible Answers:

<-12,-24>

<24,-12>

<-12,24>

<-24,-12>

<-24,12>

Correct answer:

<-12,-24>

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-8$

$(x\:\mbox{component in}\: w)=4$

$(y\: \mbox{component in}\: v)=-10$

$(y\: \mbox{component in}\: w)=14$

x=-8-4=-12

y=-10-14=-24

So our final answer is <-12,-24> .

Below is a visual representation.

Screen shot 2016 03 10 at 1.16.09 pm

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Example Question #4 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<-15,1> , and w=<-2,3> , what is v-w ?

Possible Answers:

<-17,3>

<-13,3>

<13,-2>

<-1,-2>

<-13,-2>

Correct answer:

<-13,-2>

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=-15$

$(x\:\mbox{component in}\: w)=-2$

$(y\: \mbox{component in}\: v)=1$

$(y\: \mbox{component in}\: w)=3$

x=-15-(-2)=-15+2=-13

y=1-3=-2

So our final answer is <-13,-2> .

Below is a visual representation.

Screen shot 2016 03 10 at 1.25.04 pm

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Example Question #6 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

If v=<3,4> , and w=<-3,-12> , what is v-w ?

Possible Answers:

<6,-16>

<6,16>

<16,6>

<0,8>

<0,-8>

Correct answer:

<6,16>

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=3$

$(x\:\mbox{component in}\: w)=-3$

$(y\: \mbox{component in}\: v)=4$

$(y\: \mbox{component in}\: w)=-12$

x=3-(-3)=3+3=6

y=4-(-12)=4+12=16

So our final answer is <6,16> .

Below is a visual representation.

Screen shot 2016 03 10 at 1.38.47 pm

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Example Question #71 : Vector & Matrix Quantities

If v=<10,-10> , and w=<4,-14> , what is v-w ?

Possible Answers:

<-14,-24>

<6,4>

<14,-24>

<14,24>

<4,6>

Correct answer:

<6,4>

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=10$

$(x\:\mbox{component in}\: w)=4$

$(y\: \mbox{component in}\: v)=-10$

$(y\: \mbox{component in}\: w)=-14$

x=10-4=6

y=-10-(-14)=-10+14=4

So our final answer is <6,4> .

Below is a visual representation.

Screen shot 2016 03 10 at 2.06.50 pm

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Example Question #72 : Vector & Matrix Quantities

If v=<2,0> , and w=<5,-1> , what is v-w ?

Possible Answers:

<1,-3>

<-3,1>

<3,-1>

<-3,-1>

<3,1>

Correct answer:

<-3,1>

Explanation:

In order to solve this problem, we need to know how to subtract vectors. It is simply subtracting the x components and the y components.

$x=(x\: \mbox{component in}\: v) -(x\:\mbox{component in}\: w )$

$y=(y\: \mbox{component in}\: v) -(y\:\mbox{component in}\: w )$

$(x\: \mbox{component in}\: v)=2$

$(x\:\mbox{component in}\: w)=5$

$(y\: \mbox{component in}\: v)=0$

$(y\: \mbox{component in}\: w)=-1$

x=2-5=-3

y=0-(-1)=0+1=1

So our final answer is <-3,1> .

Below is a visual representation.

Screen shot 2016 03 10 at 2.13.54 pm

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Example Question #1 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

If v=<-3,7> , what is ?

Possible Answers:

6v=<-3,13>

6v=<-18,42>

6v=<-18,-42>

6v=<18,-42>

6v=<18,42>

Correct answer:

6v=<-18,42>

Explanation:

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

$x=k\cdot(x\: \mbox{component})$

$y=k\cdot(y\: \mbox{component})$

where is the scalar.

In this case it is

$x=6\cdot-3=-18$

$y=6\cdot7=42$

The final answer is then <-18,42> .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is .

Multscalar

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Example Question #1 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

If v=<-8,0> , what is ?

Possible Answers:

4v=<32,0>

4v=<0,32>

4v=<0,-32>

4v=<-32,0>

4v=<0,3>

Correct answer:

4v=<-32,0>

Explanation:

Multiplying a vector by a scalar is as simple as multiplying the scalar by each vector component. In equation form it looks like this.

$x=k\cdot(x\: \mbox{component})$

$y=k\cdot(y\: \mbox{component})$

where is the scalar.

In this case it is

$x=-8\cdot4=-32$

$y=0\cdot4=0$

The final answer is then <-32,0> .

There is a visual representation below.

The solid red arrow is , and the dashed blue line is .

Screen shot 2016 03 07 at 1.19.53 pm

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All Common Core: High School - Number and Quantity Resources

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Common Core: High School - Number and Quantity : High School: Number and Quantity

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #2 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #3 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #4 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #5 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #4 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #6 : Vector Subtraction As The Additive Inverse: Ccss.Math.Content.Hsn Vm.B.4c

Example Question #71 : Vector & Matrix Quantities

Example Question #72 : Vector & Matrix Quantities

Example Question #1 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

Example Question #1 : Represent Scalar Multiplication Graphically: Ccss.Math.Content.Hsn Vm.B.5a

All Common Core: High School - Number and Quantity Resources

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