Quantitative Foundations for International Business Quiz Answers

Get All Weeks Quantitative Foundations for International Business Quiz Answers

This course provides the essential mathematics required to succeed in the finance and economics-related modules of the Global MBA, including equations, functions, derivatives, and matrices. You can test your understanding with quizzes and worksheets, while more advanced content will be available if you want to push yourself.

This course forms part of a specialization from the University of London designed to help you develop and build the essential business, academic, and cultural skills necessary to succeed in international business, or in further study.

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Quantitative Foundations for International Business Quiz Answers

Week 1 Quiz Answers

Quiz 1: Equations: Practice Exercises

Q1. If 4x=74x=7, what is xx?

Please give your answer as a fraction, not as a decimal (i.e. 1/2, not 0.5)

Preview will appear here…

Enter math expression here

Q2. If x-5=16x−5=16, what is xx?

Preview will appear here…

Enter math expression here

Q3. If 3x+5=73x+5=7 , what is xx?

Please give your answer as a fraction, not as a decimal (i.e. 1/2, not 0.5)

Preview will appear here…

Enter math expression here

Quiz 2: Equations: Summative Exercises

Q1. If \frac32x+1=4
2
3

x+1=4, what is xx?

Preview will appear here…

Enter math expression here

Q2. If \frac{y}{4}=16
4
y

=16, what is yy?

Preview will appear here…

Enter math expression here

Q3. If 16y–6y+2y=2416y–6y+2y=24, what is yy?

Preview will appear here…

Enter math expression here
Q4. If 4y+5=2-8y4y+5=2−8y, what is yy?

Please give your answer as a fraction, not as a decimal (i.e. 1/2, not 0.5)

Preview will appear here…

Enter math expression here

Q5. Given I=PRTI=PRT, how would you calculate PP?

P=RTIP=RTI

P=\frac{RT}{I}P=
I
RT

P=\frac{I}{RT}P=
RT
I

P=\frac{TI}{R}P=
R
TI

Q6. Solve for R in the formula M=P(1+TR)M=P(1+TR)

R=\frac{M-P}{PT}R=
PT
M−P

R=PTMR=PTM

R=\frac{M-T}{PT}R=
PT
M−T

R=\frac{P}{M-T}R=
M−T
P

Q7. Which of the following proportions are true? Use the method of cross products to find the answer, and select all that apply to

\frac{6}{5}=\frac{12}{10}
5
6

=
10
12

\frac{2}{3}=\frac{9}{16}
3
2

=
16
9

\frac{2}{3}=\frac{7}{18}
3
2

=
18
7

\frac{2}{4}=\frac{5}{10}
4
2

=
10
5

Q8. Find xx to solve the proportion \frac{3}{2}=\frac{x}{20}
2
3

=
20
x

Enter answer here

Quiz 3: Week 1: End of Week Quiz

Q1. A variable is an entity whose value can change, since it can take on different values.

  • True
  • False

Q2. When we try to find the solution of a system from the variables contained into the model, then these variables are endogenous variables.

  • True
  • False

Q3. The term constant indicates an entity which only sometime changes.

  • True
  • False

Q4. The set of the real number does not contain the negative fractions.

  • True
  • False

Q5. The constant which is along with a variable, indicates that sometime a variable can take a fixed value.

  • True
  • False

Week 2

Quiz 1: Summative Questions

Q1. What is the domain of g(x)=1-\sqrt{x+2}g(x)=1−
x+2

  • D: {𝑥∈𝑅 𝑥≥+2}D:{x∈Rx≥+2}
  • D: {𝑥∈𝑅 𝑥≥−2}D:{x∈Rx≥−2}
  • D: {𝑥∈𝑅 𝑥≥+1}D:{x∈Rx≥+1}
  • D: {𝑥∈𝑅 𝑥≥−1}D:{x∈Rx≥−1}

Q2. What is the range of g(x)=1-\sqrt{x+2}g(x)=1−
x+2

  • {∀y∈{R\,such\,that}\,{y\ge 1} }{∀y∈Rsuchthaty≥1}
  • {∀y∈R\,such\,that\,{y≤ -1} }{∀y∈Rsuchthaty≤−1}
  • {∀y∈Rsuchthaty≤1}
  • {∀y∈\,R\, such\, that\, {y\ge 2} }{∀y∈Rsuchthaty≥2}

Q3. Find the domain of the function ff defined by the formula f(x)=\frac{3x+6}{x-2}f(x)=
x−2
3x+6

  • D= {𝑥∈𝑅/𝑥≠3}D=x∈R/x
  • D= {𝑥∈𝑅/𝑥≠-2}D=x∈R/x
  • D= {𝑥∈𝑅/𝑥≠6}D=x∈R/x
  • D= {𝑥∈𝑅/𝑥≠2}D=x∈R/x

Q4. Find xx to show that the number 5 is in the range of ff in this equation: \frac{3x+6}{x-2}=5

What is xx?

Preview will appear here…

Enter math expression here

Q5. Which line in the graph below shows the graph of y=x-1y=x−1?

  • A
  • B
  • C
  • D

Q6. Which line in the graph below shows the graph of y=x-\frac{1}{3}y=x−

  • A
  • B
  • C
  • D

Q7. Given the equation y=3-5xy=3−5x, if x=1x=1, Calculate Y?

Preview will appear here…

Enter math expression here

Q8. Sketch or imagine the graph that satisfies the equation y=2+4xy=2+4x. What qualities would it have?

  • A straight line that slants upwards to the right
  • A U shaped curved line crossing the xx axis
  • A U shaped curved line crossing the yy axis
  • A straight line that slants upwards to the left

Quiz 2: End of Week Quiz

Q1. A function is a correspondence between two sets of elements such that to each element in the first set there corresponds one or more elements in the second set.

  • True
  • False

Q2. The domain of a function 𝑓(𝑥)=√(𝑥^2+1)f(x)=√(x
2
+1) is: D={𝑥|𝑥≤−1∨ 𝑥≥1}D={x∣x≤−1∨x≥1}

  • True
  • False

Q3. The range of a function 𝑓(𝑥)=𝑥^2−1f(x)=x
2
−1 is: R={𝑦|𝑦 ≥−1}R=y∣y≥−1

  • True
  • False

Q4. 𝑓(𝑥)=𝑥^3+2𝑥^2−4𝑥f(x)=x
3
+2x
2
−4x; If 𝑥=2x=2, then 𝑓(2)=8f(2)=8

  • True
  • False

Q5. By sketching the graph of the function f(𝑥) =𝑥^2+1f(x)=x
2
+1, we obtain a straight line.

  • True
  • False

Week 3

Quiz 1: Summative Questions

Q1. Which of the following is correct if you differentiate f(x)=5f(x)=5?

  • f'(x)=5^{-1}f′(x)=5−1
  • f'(x)=0f′(x)=0
  • f'(x)=\sqrt5f′(x)=5​

Q2. If you differentiate y=x^3+4x^2+3x^3+7x+4y=x3+4x2+3x3+7x+4, which of the following is correct?

  • y’=3x^2+8x+9x^2+7+4=16x^2+8x+11y′=3x2+8x+9x2+7+4=16x2+8x+11
  • y’3x^2+4x^2+9x^2+7=16x^2+7y′3x2+4x2+9x2+7=16x2+7
  • y’=3x^2+8x+9x^2+7=12x^2+8x+7y′=3x2+8x+9x2+7=12x2+8x+7

Q3. Given y=-3+3x-\frac{4}{2}x^4-x^3y=−3+3x−24​x4−x3, find the derivative.

  • y’=3-8x^3-3x^2y′=3−8x3−3x2
  • y’=3-\frac{16}{8}x^3-3x^2y′=3−816​x3−3x2
  • y’=3-2x^3-3x^2y′=3−2x3−3x2

Q4. Differentiate h(x)=f(x)\times{g(x)}h(x)=f(xg(x), where f(x)=(3x^4+x^2)f(x)=(3x4+x2) and g(x)=(6x^5-x^2)g(x)=(6x5−x2)

  • (12x^3+2x)\times(6x^5-x^2)+(3x^4+x^2)\times(30x^4-2x)(12x3+2x)×(6x5−x2)+(3x4+x2)×(30x4−2x)
  • (12x^3+2x)\times(30x^4-2x)+(3x^4+x^2)\times(6x^5-x^2)(12x3+2x)×(30x4−2x)+(3x4+x2)×(6x5−x2)
  • (12x^3+2x)\times6x^5-x^2)+(3x^4+x^2)\times(30x^4-2x)(12x3+2x)×6x5−x2)+(3x4+x2)×(30x4−2x)

Q5. Differentiate the following product of three factors:

  • y=(x+2)(x+4)(x+5)y=(x+2)(x+4)(x+5)
  • y’=\frac{d}{dx}(x+2)(x+4)\times(x+5)-(x+2)\times\frac{d}{dx}(x+4)(x+5)+(x+2)(x+4)y′=dxd​(x+2)(x+4)×(x+5)−(x+2)×dxd​(x+4)(x+5)+(x+2)(x+4)
  • y’=\frac{d}{dx}(x+2)(x+4)\times(x+5)-(x+2)\times\frac{d}{dx}(x+4)(x+5)+(x+2)(x+4)\times\frac{d}{dx}(x+5)y′=dxd​(x+2)(x+4)×(x+5)−(x+2)×dxd​(x+4)(x+5)+(x+2)(x+4)×dxd​(x+5)
  • y’=\frac{d}{dx}(x+2)(x+4)\times(x+5)+(x+2)\times\frac{d}{dx}(x+4)(x+5)+(x+2)(x+4)\times\frac{d}{dx}(x+5)y′=dxd​(x+2)(x+4)×(x+5)+(x+2)×dxd​(x+4)(x+5)+(x+2)(x+4)×dxd​(x+5)

Q6. Find the derivative of \frac{f(x)}{g(x)}=\frac{4x-5}{x+2}g(x)f(x)​=x+24x−5​

  • \frac{4x+8-4x+5}{(x+2)}=\frac{13}{x+2}(x+2)4x+8−4x+5​=x+213​
  • \frac{4x+8-4x+5}{(x+2)^2}=\frac{13}{(x+2)^2}(x+2)24x+8−4x+5​=(x+2)213​
  • \frac{4x+8-4}{(x+2)^2}=\frac{4x+4}{(x+2)^2}(x+2)24x+8−4​=(x+2)24x+4​

Q7. Given f(x)=\sqrt6f(x)=6​, differentiate the function

  • f'(x)=0f′(x)=0
  • f'(x)=2\times\sqrt6f′(x)=2×6​
  • f'(x)=6f′(x)=6

Quiz 2: End of Week Quiz

Q1. The product rule is ℎ’(𝑥) = 𝑓’(𝑥) × 𝑔(𝑥) + 𝑓(𝑥) × 𝑔’(𝑥)h’(x)=f’(x)×g(x)+f(x)×g’(x)

  • True
  • False

Q2. Multiplicative
constants are preserved; additive
constants disappear

  • True
  • False

Q3. The second derivative of the function 𝑓^′ (𝑥)=𝑥^2+3𝑥f

(x)=x
2
+3x is 5.

  • True
  • False

Q4. The function 𝑓(𝑥)=𝑥^2+3f(x)=x
2
+3 is increasing per x<0x<0

  • True
  • False

Q5. If f(x2 ) ≥ f(x1)f(x2)≥f(x1) whenever x2> x1x2>x1, then ff is increasing in A

  • True
  • False

Week 4

Quiz 1: Summative Questions

Q1. A transpose matrix is denoted by A^{-1}A
−1

  • True
  • False

Q2. 𝑘(𝐴+𝐵)=𝑘𝐴+𝑘𝐵k(A+B)=kA+kB

  • True
  • False

Q3. A is a matrix 3 X 2, B is a matrix 3 X 2, the the matrix product AB is defined.

  • True
  • False

Q4. A is a matrix 3 X 2, B is a matrix 2 X 3. Then AB is a matrix 2 X 2

  • True
  • False

Q5. A+(B+C)= (A+B)+C

  • True
  • False

Quiz 2: End of Course Quiz

Q1. Given two matrices, A^{m,n}A
m,n
and {\;}B^{p,r}B
p,r
:

  • The sum A+BA+B is always defined
  • The sum A+BA+B is never defined
  • The sum A+BA+B is defined only is m=pm=p and n=rn=r

Q2. Given y=2x^3+x^2-4x+10y=2x

  • f′′(1)=−4
  • increases for x>-1x>−1 v x>\frac{2}{3}x>32​
  • f'(x)=3x^2+2x-4f′(x)=3x2+2x−4

Q3. If 15x-3x=-10-515x−3x=−10−5

  • x=125​
  • x=-\frac{5}{4}x=−45​
  • x=\frac{5}{4}x=45​

Q4. Given y=x^3+2x^2+10x+1y=x

  • The function always increases
  • The function always increases {\forall}x ∈R∀xR
  • f'(x)=3x^2+4x+11f′(x)=3x2+4x+11

Q5. If 2-2x=4x+142−2x=4x+14, then what is xx?

  • x=-2x=−2
  • x=6x=6
  • x=2x=2

Q6. Given the function y=x2-3x+1y=x2−3x+1…

  • Increases for x<\frac{3}{2}x<23​
  • f'(x)=2x+3f′(x)=2x+3
  • The range is \{y ∈R|y {\le}-\frac{5}{4}{yRy≤−45​

Q7. If 12x+8=4-20x12x+8=4−20x…

  • Increases for x<\frac{3}{2}x<23​
  • f'(x)=2x+3f′(x)=2x+3
  • The range is \{y

Q8. Given the function y=3x^3+2xy=3x

  • It always increases
  • f'(-1)=-7f′(−1)=−7
  • f”(x)=9xf′′(x)=9x

Q9. If 6x+3-18x=396x+3−18x=39…

  • x=\frac{3}{2}x=23​
  • x=6x=6
  • x=-3x=−3

Q10. Given the function y=5x+1y=5x+1, then…

  • D=R
  • f(-2)-9f(−2)−9
  • f”(x)=5f′′(x)=5

Q11. If 10x+2-12+20=1610x+2−12+20=16, then…

  • D=RD=R
  • f(-2)-9f(−2)−9
  • f”(x)=5f′′(x)=5

Q12. Given the function y=2x^2-1y=2x

  • x=\frac{3}{5}x=53​
  • x=-\frac{3}{5}x=−53​
  • x-4x−4

Q13. If 3x+2=2x+13x+2=2x+1, what is xx?

  • x=53​
  • x=1x=1
  • x=-1x=−1

Q14. Given the function f(x)=3x^5-12x^4+3x^2f(x)=3x

  • f'(x)=15x^4-48x^3+6xf′(x)=15x4−48x3+6x
  • f'(x)=13x^4+12x^3=3xf′(x)=13x4+12x3=3x
  • f'(x)=5x^4-4x^3+2xf′(x)=5x4−4x3+2x

Q15. If 2x-2+8=3x-22x−2+8=3x−2, then…

  • x=−8
  • x=\frac{8}{5}x=58​
  • x=8x=8

Q16. Given the function y=\frac{x+2}{x+1}y=

f'(x)=1f′(x)=1

f'(x)=(x+1)-(x+2)f′(x)=(x+1)−(x+2)

f'(x)=\frac{(x+1)-(x+2)}{(x+1)^2}f′(x)=(x+1)2(x+1)−(x+2)​

Q17. If -6x+6=3x+9-10x-7−6x+6=3x+9−10x−7,then…

  • f′(x)=3⋅1=3
  • f'(x)=(3x-1)+(x+5)f′(x)=(3x−1)+(x+5)
  • f'(x)=(3x-1)+3(x+5)f′(x)=(3x−1)+3(x+5)

Q18. Given the function y=(x+5)(3x-1)y=(x+5)(3x−1)…

  • f′(x)=3⋅1=3
  • f'(x)=(3x-1)+(x+5)f′(x)=(3x−1)+(x+5)
  • f'(x)=(3x-1)+3(x+5)f′(x)=(3x−1)+3(x+5)

Q19. If 8+2x-10=1-3x-48+2x−10=1−3x−4, then…

  • x=-\frac{1}{5}x=−51​
  • x=-6x=−6
  • x=6x=6

Q20. Given the function x^2-xx

  • It always increases
  • It always decreases

Q21. Which of the following inequalities is correct?

  • D[f(x)+g(x)]=f′(x)+g(x)+g′(x)+f(x)
  • D[kf(x)]=0D[kf(x)]=0
  • D[f(x)\cdot{g(x)}]=f'(x)\cdot{g(x)}+g'(x)\cdot{f(x)}D[f(x)⋅g(x)]=f′(x)⋅g(x)+g′(x)⋅f(x)

Q22. Given the function y=x^3+x^2+2x+3y=x

  • It is always increasing
  • It is always decreasing
  • It has a maximum but it does not have a minimum

Q23. Given the linear function y=3x-1y=3x−1, then…

D=\{x ∈ R/x \neq \frac{1}{3}\}D={xR/x​=31​}

f”(x)=2f′′(x)=2

\frac{\Delta y}{\Delta x}=3ΔxΔy​=3

Q24. Given the matrices A [n \times m]A[n×m] and K[p \times r]K[p×r]…

  • the product is defined only if m=pm=p
  • the product is always defined
  • the product is never defined

Q25. Given the function f(x)=x^2+5x+6f(x)=x

  • f(x)f(x) decreases per x>-\frac{5}{2}x>−25​
  • D=RD=R
  • f(x)f(x) increases per x<2x<2 or x>3x>3

Q26. Given the function f(x)=x^3-2x+1f(x)=x

  • f”(x)=3x-2f′′(x)=3x−2
  • f(x)=3x^2-2xf(x)=3x2−2x
  • f(1)=0f(1)=0

Q27. In order to take the transpose of a matrix…

  • The rows of a matrix becomes the columns of the new matrix
  • We change the order of the rows
  • We change the order of the columns

Q28. Given the function f(x)=5x^2-3x+1f(x)=5x

  • It increases for x>\frac{3}{10}x>103​
  • It always increases
  • It always decreases

Q29. Given the function f(x)=(x+1)(2x+3)f(x)=(x+1)(2x+3)

  • f'(x)=4x+5f′(x)=4x+5
  • f'(x)=2f′(x)=2
  • f'(x)=2x+3(2x+2)f′(x)=2x+3(2x+2)

Q30. Given the following two matrices

What will their matrix product be?

  • (3 x 1) vector
  • (2 x 2) matrix
  • The product is not defined
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