#### Quiz 1: Equations: Practice Exercises

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

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Enter math expression here

Q2. If x-5=16x−5=16, what is xx?

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Enter math expression here

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

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Enter math expression here

#### Quiz 2: Equations: Summative Exercises

Q1. If \frac32x+1=4
2
3

x+1=4, what is xx?

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Enter math expression here

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

=16, what is yy?

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Enter math expression here

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

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

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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?

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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?

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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 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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