Given that \[\begin{array} { l } G = 50 \\ I = 40 \\ C = 0.75 Y _ { d } + 45 \\ T = 0.2 Y + 80 \end{array}\] calculate the equilibrium level of national income.

A) 175 B) 187.5 C) 125 D) 487.5 E) 75 A) 175 B) 187.5 C) 125 D) 487.5 E) 75

Exam 1: Linear Equations

If the line, $P = - \frac { 2 } { 3 } Q + 6$ is sketched with P on the horizontal axis, and Q on the vertical axis, which of the following gives the gradient, m, and vertical intercept, c?

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(Multiple Choice)

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Question 1

Correct Answer:

Verified

C

Multiply out the brackets and simplify 1) $( x - y ) ( x + y ) - ( x + 2 ) ( x - y + 3 )$

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(Multiple Choice)

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Question 2

Correct Answer:

Verified

A

How many of the following points lie on the line 3x - 5y = 25? $( 5 , - 2 ) , ( 10 , - 1 ) , ( - 5,0 ) , ( 5,10 ) , ( - 5,10 ) , ( 0,5 )$

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(Multiple Choice)

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Question 3

Correct Answer:

Verified

C

If x= - 3, y = 4 and z = - 2, evaluate 2x2 + 3y - 5z.

(Multiple Choice)

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Question 4

If the following system of linear equations has infinitely many solutions, find the value of k. 6x - 4y = 2 - 3x + 2y = k

(Multiple Choice)

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Question 5

Given that G=50 I=40 C=0.75+45 T=0.2Y+80 calculate the equilibrium level of national income.

(Multiple Choice)

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Question 6

Simplify $\frac { 2 x + 5 } { 4 } \frac { x - 1 } { 2 }$

(Multiple Choice)

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Question 7

Transpose the formula $Y=\frac{b+I}{1-a}$ $\text { to express } a \text { in terms of } Y, b \text { and } I$

(Multiple Choice)

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Question 8

If the line, $P = - \frac { 2 } { 3 } Q + 6$ is sketched with P on the horizontal axis, and Q on the vertical axis, which of the following gives the gradient, m, and vertical intercept, c?

Multiply out the brackets and simplify 1) $( x - y ) ( x + y ) - ( x + 2 ) ( x - y + 3 )$

How many of the following points lie on the line 3x - 5y = 25? $( 5 , - 2 ) , ( 10 , - 1 ) , ( - 5,0 ) , ( 5,10 ) , ( - 5,10 ) , ( 0,5 )$

If x= - 3, y = 4 and z = - 2, evaluate 2x2 + 3y - 5z.

If the following system of linear equations has infinitely many solutions, find the value of k. 6x - 4y = 2 - 3x + 2y = k

Given that G=50 I=40 C=0.75+45 T=0.2Y+80 calculate the equilibrium level of national income.

Simplify $\frac { 2 x + 5 } { 4 } \frac { x - 1 } { 2 }$

Transpose the formula $Y=\frac{b+I}{1-a}$ $\text { to express } a \text { in terms of } Y, b \text { and } I$

Non-Linear Equations

Mathematics of Finance

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Exam 1: Linear Equations

If the line, P=−23Q+6P = - \frac { 2 } { 3 } Q + 6P=−32​Q+6 is sketched with P on the horizontal axis, and Q on the vertical axis, which of the following gives the gradient, m, and vertical intercept, c?

Multiply out the brackets and simplify 1) (x−y)(x+y)−(x+2)(x−y+3)( x - y ) ( x + y ) - ( x + 2 ) ( x - y + 3 )(x−y)(x+y)−(x+2)(x−y+3)

How many of the following points lie on the line 3x - 5y = 25? (5,−2),(10,−1),(−5,0),(5,10),(−5,10),(0,5)( 5 , - 2 ) , ( 10 , - 1 ) , ( - 5,0 ) , ( 5,10 ) , ( - 5,10 ) , ( 0,5 )(5,−2),(10,−1),(−5,0),(5,10),(−5,10),(0,5)

If x= - 3, y = 4 and z = - 2, evaluate 2x2 + 3y - 5z.

If the following system of linear equations has infinitely many solutions, find the value of k. 6x - 4y = 2 - 3x + 2y = k

Given that G=50 I=40 C=0.75+45 T=0.2Y+80 calculate the equilibrium level of national income.

Simplify 2x+54x−12\frac { 2 x + 5 } { 4 } \frac { x - 1 } { 2 }42x+5​2x−1​

Transpose the formula Y=b+I1−aY=\frac{b+I}{1-a}Y=1−ab+I​ to express a in terms of Y,b and I\text { to express } a \text { in terms of } Y, b \text { and } I to express a in terms of Y,b and I

Non-Linear Equations

Mathematics of Finance

Differentiation

Partial Differentiation

Integration

Matrices

Linear Prgamming

Dynamics

Filters

If the line, $P = - \frac { 2 } { 3 } Q + 6$ is sketched with P on the horizontal axis, and Q on the vertical axis, which of the following gives the gradient, m, and vertical intercept, c?

Multiply out the brackets and simplify 1) $( x - y ) ( x + y ) - ( x + 2 ) ( x - y + 3 )$

How many of the following points lie on the line 3x - 5y = 25? $( 5 , - 2 ) , ( 10 , - 1 ) , ( - 5,0 ) , ( 5,10 ) , ( - 5,10 ) , ( 0,5 )$

Simplify $\frac { 2 x + 5 } { 4 } \frac { x - 1 } { 2 }$

Transpose the formula $Y=\frac{b+I}{1-a}$ $\text { to express } a \text { in terms of } Y, b \text { and } I$