IBC Final-term Jeopardy Board

Algebra

100

Solve for x: 3x+5=20

x=5

200

Solve the quadratic equation: x²+4x-12=0

x=2 or -6

300

If a+b=6, a²+b²=52, determine the value of ab.

ab=-8

500

For real numbers a and b with a>0 and b>0, the operation * is defined by a*b=(a+4b)^1/2. Determine the value of (9*18)*10.

7

Geometry

100

Find the midpoint of (2,-1) and (8,5)

(5,2)

200

Find the distance between (1,2) and (4,6)

5

300

Given a sector with a radius of 5 cm and a central angle of 60°, find the arc length of this sector.

5pi/6 cm²

500

Points A, B, C. and D lie along a line, in that order. If AB : AC = 1 : 5, and BC: CD = 2: 1, 

then the ratio AB : CD is equal to ( )

(A) 1: 1 

(B) 1: 2

(C) 1:3 

(D) 2:5 

(E) 3:5

(B) 1: 2

Functions & Graphs

100

Identify the type of graph represented by y=x²+4x+1.

Parabola

200

Determine the vertex of the graph of y=2|x-1|+1.

(1,1)

300

Trapezoid ABCD has vertices A(0,0), B(12,0), C(11,5), D(2,5). The sides AD and BC are extended to intersect at the point F. Determine the coordinates of F.

F(8,20)

500

A function f is such that f(x)-f(X-1)=4x-9 and f(5)=18. If f(x)=2x²+px+1, determine the values of p and q.

p=7, q=67

Calculus

100

Differentiate y=3x⁴

12x³

200

∫ x²+2x dx

1/3 x³+x²+c

300

y=x³−4x²+5x, find the normal at point P whose x coordinate is 1.

x=1

500

If x approaches 0, what will (x+2)⁴-16/x approach?

32