MATH 105 PAST QUESTIONS AND ANSWER

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1: … is the amount by which a resource is under utilized.  

Answer: Slack

2: … is the point at which the curve is neither a maximum nor a minimum value.

Answer: Point of reflexion

3: At point of inflexion, the turning points are………

Answer: Equal

4: If the value of turning point in the second derivative is negative, then it is a …

Answer: Maximum point

05: If the value of turning point in the second derivative is positive, then it is a ……..

Answer: Minimum point

06: These are point on

the curve at which and the value of the function at this point is

called…………..

Answer:  stationary point

07: Stationary points are also called…………..

Answer: turning point

08: The coordinate of the point of interception of the lines, 2x + 3y = 5 and x + 2y = 3, is………..  

Answer: (1, 1)

011: The limn→∞⁡7-2x  is ….…  

Answer: 7

012: The limit of function fx=12x as x→0, is ……………

Answer: 1

013: The limit of function fx=12x as x→2, is ……………

Answer: ¼

015: The common ratio of the G.P 2, 6, 18, 54, 162, is …  

Answer: 3

016: A … is a sequence in which each successive terms of the sequence are in equal ratio.   

Answer: geometric progression

017: The 7th term of an A.P is 15 and the fourth term is 9. The first term and the common difference are … and  … respectively   

Answer: 3, 2

018: The 7th term of an A.P whose first term is 102 and common difference is -3 is

Answer: 84

019: The square of common difference of the sequence 3, 5, 7, 9, 11,… is  

Answer: 4

020: … is a sequence in which each term differs by a common difference

Answer: Arithmetic progression

021: An infinite sequence is one whose terms are…

Answer: Uncountable

022: …. is a succession of terms spanned by a rule or formula.

Answer: A sequence

023: … is the amount of goods requested for by customers at any point in time.

Answer: Demand

024: The demand curve is the relationship between quantity and ……. of goods

Answer: Price

025: A physical quantity having both magnitude and direction is called ____

Answer: vector

026: The necessary and sufficient conditions for two lines to intercept are that they must be consistent and ……………..

Answer: Independent

027: A good application of intercept of two lines is the……………

Answer: market equilibrium

028: ………..…will the equation of a line (-1, -4) whose gradient is 1?

Answer: y=x-3

029: The equation of a straight line is of the form ………..

Answer: y=mx+c 

030: The distance between the pairs of points A(0, 1) and B(6, 9) is ………….

Answer: 10

039: Calculate the distance between the points: A(0,1) and B(6,9)

Answer: 10

043: Two vectors are said to be ___ if they are in equal direction

Answer: parallel

046:  The 6th term of an A.P whose first term is 102 and common difference is -3 is ____

Answer: 87

048:  The 11th term of an A.P whose first term is 102 and common difference is -3 

Answer: 72

01: … is the study and analysis of a mathematical proposition as to ascertain the Truth Value of the proposition. 

Answer: Logic

02: Lagos is a cosmopolitan state. The Truth Value of this is …

Answer: true

022:  Given that A=123456 and B=123456, Find AB? 

Answer: 51215192631294051

023:  Find the determinant of the A=2-456?

Answer: 32

024:  Given that A =123321132, Find the determinant of  A

Answer: 3

025: A matrix is said to be singular if the determinant is equal to 

Answer: 0

029:  Given that x + 2y + 3z =1, 3x + 2y + z = 4, x + 3y + 2z = 0. What is x,y and z?

Answer: 74 , - 34,  14    

030:  Let A =123450214 , then the cofactor of matrix A is the matrix

Answer: 20-16-6-5-23-1512-3 

031: What is the common difference in the sequence 3, 5, 7, 9, 11… 

Answer: 2

038:  Obtain the equation of the line having points A(-2, 3) and B(4, -6)

039:   The equation of the line with points A(-3, -2) and B(-1, 0)

041: Two lines are said to be parallel if

Answer:  All the options

042: Find the coordinate of the point of interception of the lines: 2x + 3y = 5 ; x + 2y = 3043: Find the coordinate of the point of interception of the lines: x + 2y = 5 ; x + y = 3

Answer:

044: Find the coordinate of the point of interception of the lines: 2x + y = 5 ; x + y = 3045: Let the gradient of a line be 3, find the equation of the line at point (1,2)

Answer: y = 2x

046: Find the equation of the line which is parallel to 3x + 2y = 5 and passes through the point (2, -4)

Answer: 3x + 2y = -2

047: Find the equation of the line which is parallel to 3x - 2y = 5 and passes through the point    (-2, -4)

Answer: -3x + 2y = -2

048: Find the equation of line that passes through the points: A(2, 3) and B(4, 6)

Answer:  2y =3x

050: What is the gradient the line that passes through points A(-3, -2) and B(1, 0)? 

01: … is the study and analysis of a mathematical proposition as to ascertain the Truth Value of the proposition. 

Answer: Logic

02: Lagos is a cosmopolitan state. The Truth Value of this is …

Answer: true

03: There are two types of statements:

Answer: simple and composite

04: The connective "∧" in logic is a…

Answer: conjunction

05: The connective "⇒ " in logic is a…

Answer: conditional

06: The connective "∼" in logic is a…

Answer: negative

07:  The connective "⟺ " in logic is a…

Answer: bi – implication    

08: The negation of contradiction is a …

Answer: tautology

09: … is said to be formed when the conjunction of a set of simple mathematical statements gives rise to another mathematical statement.

Answer: argument

010: If ( p ∧ q) = p and  ( p ∨ q) = p implies an… 

Answer: Idempototent Laws   

011: If  (p ∨ q) ∨ r = p ∨ (q∨ r) and (p ∧ q) ∧ r = p ∧ (q∧ r) implies ..… 

Answer: Associate Laws    

012: If (p ∧ q) = (q∧ p) and  (p ∨ q) = (q∨ p) implies an… 

Answer: Commutative Laws    

013:  --- reads “the goods are standard and the goods are expensive

Answer: (p ∧ q)   

014: … reads “the goods are standard if and only if the goods are expensive”

Answer: (p ↔ q)

014: … reads “the goods are standard or they are made of expensive materials”

Answer: (p ( q)

014: … reads “Tom is tall not shot”

Answer: (p ͠ q)

015:  … is equivalent to (p ∨ q)

Answer: (p ↔ q)

016:  Which of the following statement is true

Answer: (p ∨ q) ∧ ( p∨ r) = p∨ (q ∧ r )    

017: Which of the following statement is true

Answer: (~ (p∨ ~ q)= ~ (p∧~ q)

018: …. is a rectangular array of numbers with reference to specific rules governing the; array

Answer: Matrix

019: A matrix that has elements only on its diagonal is called 

Answer: diagonal matrix   

020: The …  of a matrix is the inter- changing of its row with the column. 

Answer: transpose matrix     

021:  A matrix in which its transpose is equal to itself is called…

Answer: symmetric matrix

The __________ are the amount of time available for material purchases and construction.

Ans Constraints

_____________ is the first step in linear programming

Ans Define the constraints

________ is the inverse process of differentiation.

Ans Integration 

______ describe what happen to a function

Ans Limits

A circle is the _____ of a curve

Ans Locus

The _______  is the distance between the centre of the circle and the

circumference.

Ans: Radius

What is the formular for Distances in Complex Numbers

022:  Given that A=123456 and B=123456, Find AB? 

Answer: 51215192631294051

023:  Find the determinant of the A=2-456?

Answer: 32

024:  Given that A =123321132, Find the determinant of  A

Answer: 3

026:  Given that 13k4 is a singular matrix. Find the value of  k?

Answer: 43

027: Given that A =201k23214 , what is the value of k, if A is said be a singular matrix? 

Answer: -6

028:  Given that x + 2y = 3, 3x + 4y =1. What is x and y?

Answer: -5,  4     

029:  Given that x + 2y + 3z =1, 3x + 2y + z = 4, x + 3y + 2z = 0. What is x,y and z?

Answer: 74 , - 34,  14    

030:  Let A =123450214 , then the cofactor of matrix A is the matrix

Answer: 20-16-6-5-23-1512-3 

031: What is the common difference in the sequence 3, 5, 7, 9, 11… 

Answer: 2

035: The equation of a straight line at point and slope 5 is given by

Answer:

036: The equation of the straight line given one point and slope 3 is

Answer:  

037: The equation of a line given two points ,is given by

Answer:  

038:  Obtain the equation of the line having points A(-2, 3) and B(4, -6)

Answer:  

039:   The equation of the line with points A(-3, -2) and B(-1, 0)

Answer:    

040: The necessary and sufficient conditions for two lines to intercept are

Answer:  they must be consistent and independent

041: Two lines are said to be parallel if

Answer:  All the options

042: Find the coordinate of the point of interception of the lines: 2x + 3y = 5 ; x + 2y = 3

Answer:

043: Find the coordinate of the point of interception of the lines: x + 2y = 5 ; x + y = 3

Answer:

044: Find the coordinate of the point of interception of the lines: 2x + y = 5 ; x + y = 3

Answer:

045: Let the gradient of a line be 3, find the equation of the line at point (1,2)

Answer: y = 2x

046: Find the equation of the line which is parallel to 3x + 2y = 5 and passes through the point (2, -4)

Answer: 3x + 2y = -2

047: Find the equation of the line which is parallel to 3x - 2y = 5 and passes through the point    (-2, -4)

Answer: -3x + 2y = -2

048: Find the equation of line that passes through the points: A(2, 3) and B(4, 6)

Answer:  2y =3x

050: What is the gradient the line that passes through points A(-3, -2) and B(1, 0)? 

Answer: Magnitude of the vectors