B.I.S.E. Mathematics Papers 2017-2023

Flashcards generated from B.I.S.E. Mathematics papers from 2017-2023.

What is the integral of [1,dx/(x+2)]?

ln(x+2)+c

What conic section is represented by x= a seco, y=b tan?

Hyperbola

What is the value of [21,jx2k]?

2

What is the limit of (sin 20)/0 as 0 approaches 0?

2

What is the integral of dx/(x²+1)²?

x/[2(x²+1)] + 1/2 tan⁻¹x + c

What is the value of [1,1+x] dx from -1 to 1?

2

What is the derivative of -cot² 2x with respect to x?

4 cot 2x csc² 2x

Is (1,0) a solution of the inequality 9x+2y<8?

Yes

What is the measure of an angle in a semicircle?

Right angle

What is the length of each latus rectum of an ellipse?

2b²/a

What is the distance between the points (0,0) and (1,2)?

√5

If f(x) = cos x, then what is f'(x)?

-sin x

What is the integral of sec x dx?

ln|sec x + tan x| + c

What is the definition of sinh x?

(e^x - e^-x) / 2

What is the integral of eˣ(ln x + 1/x) dx?

eˣ ln x + c

If m1 and m2 are slopes of two perpendicular lines, what is the relationship between them?

m1m2 + 1 = 0

What is the derivative of 2x/(1+x^2)?

2(1-x^2)/(1+x^2)^2

At how many points do two non-parallel lines intersect each other?

1 point

What is the derivative of e^(ln x) with respect to x?

1

What condition must be met for two lines represented by ax²+2hxy+by² =0 to be parallel?

h² - ab = 0

What is the solution to the differential equation dy/dx = y?

y = ce^x

What is the inclination of the line x=y?

45°

What is the equation of the directrix of the parabola x²=-8y?

y-2=0

If the line (3x-y+5)+k(2x-3y-4)=0 is parallel to the y-axis, then what is the value of k?

-3/2

What is the integral of tan x dx?

ln|sec x| + c

What type of expression is ax+b<c?

Linear inequality

If y = cos x * sin x, then what is dy/dx?

-tan x

What is the limit of (5^(n+1))/(5^n) as n approaches infinity?

5

What is the equation of a horizontal line through (a,b)?

y=b

If the two lines 4x+by=q1 and ax+by=q2 are parallel, what condition must be met?

ab-4b = 0

What is the integral of e^x(x + tan x + tan²x) dx?

e^x tan x + c

If f(x)=cosh x, then what is f(x)²-f'(x)²?

1

What type of series is f(0) + xf'(0) + (x^2/2!)f''(0) + …?

Maclaurin's series

What is the derivative of 2x/(1+x^2)?

2(1-x^2) / (1+x^2)^2

If the vectors 2i+j+k and i-4j+ak are perpendicular, then what is the value of a?

2

If the ends of the diameter of the circle are (0,1) and (2,3), then what is its area?

2π

What is [a b a] equal to?

0

What is the derivative of (ln x)⁴?

4(ln x)³/x

What is the integral of sin 3x cos x dx?

1/8 (cos 2x - cos 4x) + c

What conic section is described by the parametric equations x=at², y=2at?

Parabola

If f(x)=sinx+cosx, then what is f(x)+f(-x) equal to?

2cosx

What is lim(e^x - 1)/x as x→0?

1

What is the derivative of (x²+1)⁹ with respect to x³?

3x²(x²+1)⁸

What is lim (f(x)-f(a))/(x-a) as x→a?

f'(a)

What is integral of sec x dx?

ln |sec x + tan x| + C

What is d/dx (1/√x)?

-1/(2x√x)

What is d/dx (a^x)?

a^x ln a

What is ∫ sec²x dx?

2√tan x + c

What is ∫ a^(2x)dx?

a^(2x) / (2 ln a) + c

What is ∫ (-sin x)dx?

cos x + c

What is ∫ tan x dx?

-ln |cos x| + c

What is slope of line parallel to x-axis?

0

In what ratio does the mid-point divide a line segment?

1:1

What is the condition for lines a1x+b1y+c1=0 and a2x+b2y+c2=0 to be perpendicular?

a1a2+b1b2=0

What is the point of intersection of altitudes of a triangle

orthocenter

What is the feasible solution that maximizes or minimizes the objective function called?

Optimal solution

What are the end points of minor axes of an ellipse?

vertices

What is equation of x=y²+1?

parabola

If projection of a and b have same direction, then what is a.b equal to?

|a||b|

What is the value of a.b if vectors a and b have the same direction?

|a||b|

What is the feasible solution which maximizes or minimizes the objective function called?

Optimal solution

If alpha is inclincation of the line, then what is (x-xr)/(cos(aplha))+(y-yr)/(sin(alpha))

symmetric from

What is the length of the vector 2i-j-2k?

3

What is the perpendicular distance of the line 3x+4y-10=0 from the origin?

2

The direction cosines of y-axis are

(0,1,0)

The centroid of a triangle divides each median in the ratio

2:1

When is straight line y=mx+c tangent to ellipse

c² = a²m² +b²

What is centre of equaiton x²+y²+2gx+2fy+c=0?

(-g,-f)

If a is the inclination of a line L then?

0 ≤ α <pi

Axis of prabola y²=4ay is?

y = 0

what is derivative sin⁻¹(x)

1/√1-x²

what is cosh² x – sinh² x

1

What's the order of the differential equation dy/dx(d²y/dx²)+2x=0?

2

where are we given y=√1-x²,0<x<1, the dy/dx=?

-x/√(1-x²)

what is ∫cos xdx=

sin x

If f(x) has second derivative at "c" such that f'(c)=0 and f''(c)0 then "c" is a point of

Maxima

∫(f'(x)/f(x))dx=?

ln|f(x)|+c

If f(x)=x²+cosx then f(x) is

Even Function

∫√3^x=?

(3^x)/ln3 +c

If y=e^(cosx), then dy/dx=?

-e^(cosx)sinx

∫log base a xdx =?

x(lnx-x)/xlna

The value of ∫(sinxe^cosxdx)

-e^cos2x

Formula for ∫√(x)/(x²-1)dx?

sec⁻¹x

If x = (0), y = g(0) then dy/dx = ?

dy / dx = (dy/de) / (dx/de)

Derivative for sech x= ?

-sech x tanh x

Define When at least one vertical line meets the curve at more than two points then curve is?

Not a function

∫sec²xdx=?

tan x

Solution of dy/y=dx/x is?

xy=c

Domain Of f(x)=x²/x²-1: is ?

R- { -1,1}

Equation of line bisecting li and Iv quadrant is:

y=x

what is Set of all points equidistant from a fixed point form?

Circle

Joint equation of two lines is ax²+2hxy+by =0, if is angle between them,

2√(h² + ab)/a+b

Which of following is called Focal chord perpendicular to axis of parabloal

Latus Rectum

Horizontal line through (7,-9)=?

y=-9

Projection of vector u on vector v is

(U.V)/|v|

What's formula to get shortest distance of (x,y) from line ax+by+c=0 is

|ax₁+by₁+c |/√a²+b²

for ellipse what formula for eccentricity? a and b are given

√(a² -b²)/a

If is any vector then vector of magnitude 5 opposite to v is

-5v/|v|

What is System of linear inequalities involve in the problem called

Problem constraints

fe^af(x)+ f'(x)dx=?

e^af(x)