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1st Year Mathematics 1st Quarter Book Paper1st Year · Mathematics · Punjab (PTB)
Q1. Multiple choice questions (Attempt all · 12 × 1 = 12)
If f:
is a function such that rang
, then f is called a/an ...... function:
To solve absolute value quadratic function we must illuminate roots which are:
The (0,0) solution of the system a1x+b1y=0 and a2x+b2y=0 is called ......:
Multiplicative inverse of (1,0) is:
Point of intersection f(x)=2x+5 and g(x)= -x+5 is a point which satisfies:
Inverse of a quadratic function should be:
For homogeneous linear equations, system AX=0 non-trivial solution is possible if IAI = ......:
If
A bijective function is ......:
Name the type of equation
.
The inverse of a square matrix exists if A is:
If Z is complex number, then
is:
Q2. Short questions (Attempt any 8 of 12 · 8 × 2 = 16)
Without expansion show that:
=0
Find the domain and range of
.
Solve the following:
If
then find: z1+z2
If
them compute A2B.
Given f(x)=x3-2x2+4x-1 find: f(-2)
Solve the following:
If
then find the following and express the result into x+
y form: z1+z2
Without expansion show that:
Given f(x)=x3-2x2+4x-1 find: f(0)
Find the inverse of
. Also find its domain and range.
Find the product of
.
Q3. Long questions (Attempt any 3 of 4 · 3 × 4 = 12)
A building's height over time is modeled by H(t)=100+20t which is in metres and t is the time in months. The height of a growing tree nearby is given by T(t)=50+10t+t2. (i) At what time will the building and tree have the same height? (ii) What will be the height be?. Sketch the graph of both functions and determine the time when the tree will overtake the height of the building.
Solve the following system of linear equation by matrix inversion method:
Find the maximum and minimum point by sketching the following quadratic function. Also find their domain and range:
Evaluate: