# PAF Tests of Mathematics with Answers

PAF Past papers of Mathematics are available here for preparation of PAF initial tests including, PAF Aeronautical Engineering, PAF Met Branch, PAF Account branch, PAF Admin Branch, PAF Education Branch, Lecturer mathematics, Education Instructors, Aero trade Airman, and PAF Civilians tests. All past papers experiences are included here regarding tests of mathematics.

If you cover all these tests of mathematics then you can pass the tests of mathematics with 100% success. Learn all tests of mathematics which are given below for full PAF initial tests preparation.

**In matrix notation, the element in the 2nd row and 3rd column of matrix A is denoted by ______.**(A(2, 3))**The determinant of a 2×2 matrix [a b; c d] is given by _____. (**ad – bc**)****The transpose of a matrix is obtained by______**.**(**Interchanging its rows and columns**)****A matrix with only one column is called a**______.**(**Column Matrix**)**- The product of two matrices is defined if______
**.(**The number of columns in the first matrix is equal to the number of rows in the second matrix**)** **The inverse of a matrix A is denoted by _______.(**A^{(-1)}**)****The determinant of a square matrix is zero if _______.(**The matrix is singular**)****The trace of a square matrix is the sum of its ______. (**Diagonal elements**)****The rank of a matrix is defined as ______.(**The number of linearly independent rows or columns in the matrix**)****The adjoint of a matrix is obtained by ______. (**Finding the cofactor of each element and taking its transpose**)****0 can be write in the form of ______. (**p/q**)****The three rational numbers between 3 and 4 are ______. (**13/4, 14/4, 15/4)**In between any two numbers, there are _____. (**Infinite rational numbers)**Every rational number is _____. (**Real number)**√9 is __________ number _____.(**A rational)- √12
**is an number ______. (**irrational**)** **3√6 + 4√6 is equal to _____. (**7√6)**√6 x √27 is equal to ______. (**9√2)- x
^{6}/x^{3 }**is equal to ______. (x**^{3}) - √23
**is an number _______. (**irrational**)**

## PAF Tests of Mathematics For Initial Tests with Answers

List of PAF Tests of Mathematics are available here for initial tests in the following.

- 0.4014001400014……
**is an ______ number. (**Irrational) **2√3+√3 = ______. (**3√3)**The number obtained on rationalizing the denominator of 1/ (√7 – 2) is ______. (**(√7+2)/3)**0/4 is number ______. (rational)****The irrational number between 2 and 2.5 is ______. (**√5)**The value of √10 times √15 is equal to _____. (**5√6)**The decimal representation of the rational number is _____. (**Either terminating or repeating)**0 is a number ______. (rational)**- √7
**is an _______ number.**(irrational) **X**One Variable)^{2}-2x+1 is a polynomial in _______. (**The coefficient of x**^{2}in 3x^{3}+2x^{2}-x+1 is ______. (2)**A binomial of degree 20 in the following is _____. (**x^{20}+1)**The degree of 4x**^{3}-12x^{2}+3x+9 is _____. (3)**x**Quadratic)^{2}– x is ________ polynomial. (**x – x**Cubic)^{3}is a ________ polynomial. (**1+3x is a _________ polynomial. (**Linear)**The value of f(x) = 5x−4x²+3 when x = -1, is ________.**( -6)**The value of p(t) = 2+t+2t²−t³ when t = 0 is ________.**(2)**The zero of the polynomial f(x) = 2x+7 is ________.**(-7/2)**The degree of the polynomial √3 is ________.**(0)

## PAF Tests of Mathematics for Commissioned Officers and Airman

More important tests of mathematics are given here to get 100% result.

**The degree of the constant polynomial is ________.**(0)**One of the linear factors of 3x²+8x+5 is ________.**(x+1)**The coefficient of x in 7x²+6x-2 is ________.**(6)**2x²+x-1 is an example of a ____ ____polynomial.**(quadratic)**The value of 72-52 is ________.**(24)**If x²+kx+6 = (x+2)(x+3) for all k, the value of k is ________.**(5)**________ is the zero of the polynomial p(x) = cx+d.**(-d/c)**The zero of the polynomial p(x) = -5x+5 is ________.**(1)**3 is a ________ polynomial.**(constant)**If ax = n, then x = ________.**log_{a}n**The relation of y = log**( xz = y)_{z}x implies ________.**The logarithm of unity to any base is ________.**(0)**The logarithm of any number to itself as the base is ________.**(1)**Express 53 = 125 in logarithm form.**(log_{5}125 = 3)**Find the log of 32 to the base 4.**( log_{4}32 = 5/2)**The factors of x^3 − x^2y − xy^2 + y^3 are ________.**(x – y)^2(x + y)**The factors of x^3 − 1 + y^3 + 3xy are ________.**(x – 1 + y)(x^2 + 1 + y^2 + x + y – xy)**The factors of 8a^3 + b^3 − 6ab + 1 are ________.**(2a + b + 1)(4a^2 + b^2 + 1 – 2ab – b – 2a)**(x + y)^3 − (x − y)^3 can be factorized as ________.**( 2y(3x^2 + y^2))**The expression (a – b)**(3(a – b)(b – c)(c – a))^{3}+ (b – c)^{3}+ (c – a)^{3}can be factorized as ________.

## PAF Tests of Mathematics for 100% Free Pass Result

Very important and past experienced based tests of mathematics are available here.

**Simplify the expression 2(3x – 4) – 5(2x + 1).**(6x – 8)**Solve the equation 2(x + 3) = 4x – 6.**( x = 4)**The equation 2x + 5 = 17 can be solved by substituting x with _______.**(x = 8)**To solve the equation 3(2x – 4) = 12, we find that _______. (**x = 2)**By solving the equation 4x – 7 = 5x + 2, we get _______.**(x = -9)**The solution to the inequality 2x – 3 > 7 is _______.**(x > 8)**When solving the inequality 3 – 2x ≤ 5, we find that _______.**(x ≥ -1)**By solving the inequality 2(x + 4) > 3x – 1, we get _______.**(x < 7)**The solution to the equation 5x + 2 = 3(4x – 1) is _______.**(x = 1/2)**To find the solution to the equation 2(3x – 4) = 4 – x, we find that _______.**(x = 3/5)**By solving the inequality 2x + 3 < 5x – 1, we get _______.**(x > 4/3)**The solution to the inequality 4 – 3x ≥ 1 + 2x is _______.**( x ≤ 4/5)**Two triangles are congruent if they have _______.**(The same corresponding sides and angles)**If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent by _______. (**ASA (Angle-Side-Angle) Congruence)**If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent by _______. (**AAS (Angle-Angle-Side) Congruence)**If two sides and a non-included angle of one triangle are congruent to two sides and a non-included angle of another triangle, then the triangles are congruent by _______. (**SAS (Side-Angle-Side) Congruence)**If two triangles are congruent, then their corresponding angles are _______. (**Congruent)**If two triangles are congruent, then their corresponding angles are _______.**(Equal)**If two triangles are congruent, then their corresponding angles are _______.**(Congruent)**In a parallelogram, opposite sides are _______.**(Equal in length and parallel)

## Tests of Mathematics for PAF Initial Tests

Importance tests of mathematics which are past experiences of PAF initial tests are given below.

**The sum of the angles in a triangle is _______. (**180 degrees)**A triangle with all sides of equal length is called _______. (**Equilateral triangle)**The perimeter of a rectangle with length 10 units and width 6 units is _______.**(22 units)**The standard form of a quadratic equation is _______. (**ax^{2}+ bx + c = 0)**The solutions of a quadratic equation can be found using _______.(**Quadratic formula)**The discriminant of a quadratic equation ax**( b^{2}+ bx + c = 0 is given by _______.^{2}– 4ac)**If the discriminant of a quadratic equation is positive, then the equation has _______.**(Two real and distinct solutions)**If the discriminant of a quadratic equation is zero, then the equation has _______.**(One real solution)**If the discriminant of a quadratic equation is negative, then the equation has _______. (**Two complex solutions)**In set notation, the symbol “U” represents _______**. (Union)**The cardinality of a set A is denoted by _______.**( |A|)**The empty set is a subset of _______. (**Every set)**The set {1, 2, 3} is a subset of _______.**{1, 2, 3, 4}**A function is defined as a special type of relation that _______.**(Maps each element of the domain to a unique element of the co-domain)**The range of a function is _______.**(The set of all possible outputs of the function)**If f: A → B is a function, the domain of f is _______. (**A)**If f: A → B is a function, the codomain of f is _______.**(B)**The measure of central tendency that is most influenced by extreme values is the: ___________.**(Mean)**The range of a data set is calculated by: ___________.**(subtracting the highest value from the lowest value)**The interquartile range is a measure of: ___________.**(variability)**The standard deviation is a measure of: ___________.**(variability)**The z-score of a data point measures: ___________. (**How far the data point is from the mean in standard deviation units)**The coefficient of variation is a measure of: ___________. (**Relative variability**)****The p**p% of the data values lie)^{th}percentile of a data set is the value below which: ___________. (**The correlation coefficient ranges from: ___________. (0 to 1)**

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