Factorization
Factorize:
6x + 12
6(x+2)
Solve: x2−9=0
x=3 or x=−3
Define a relation in mathematics.
A set of ordered pairs that shows the relationship between elements of two sets.
What is the general form of a quadratic function?
y=ax2+bx+c
Define a composite function.
A function formed by applying one function to the result of another.
Q1. What is the DOMAIN of the relation {(2, 5), (4, 7), (6, 9)}?
Domain = {2, 4, 6}
Factorize using the distributive law: 8x−16
8(x−2)
Solve: x2+7x+12=0
x=−3 or x=−4
Name the type of relation: Each student has exactly one school ID.
One-to-one relation
What is the shape of a quadratic graph called?
A parabola
Given f(x)=x+1, find f(3).
4
Q2. State the RANGE of the relation {(1, 3), (2, 3), (5, 8)}.
Range = {3, 8}
Factorize by grouping: ax+ay+bx+by
(a+b)(x+y)
Solve:
x2−16=0
x=4 or x=−4
State the difference between a relation and a function.
A function is a relation where each input has exactly one output.
Identify the vertex of the function: y=(x−3)2+2
(3,2)
Given f(x)=x+2 and g(x)=3x, Find f(g(2)).
g(2)=6
f(6)=8
Q3. Given the domain {−2, −1, 0, 1, 2} and the rule y = x + 3, list ALL ordered pairs.
{(−2, 1), (−1, 2), (0, 3), (1, 4), (2, 5)}
Factorize the quadratic expression: x2+7x+10
(x+5)(x+2)
Solve:
2x2−8x=0
x=0 or x=4
Evaluate the function if: f(x)=2x+3 , Find f(4)
11
State the axis of symmetry of the function:
y=(x−4)2+1
x=4
Find the inverse of
f(x)=x+6
f−1(x)= x - 6
Q4. An arrow diagram shows: 1→1, 2→4, 3→9, 4→16. Write the algebraic rule and identify the type of mapping (one-to-one, many-to-one, one-to-many).
Rule: y = x² Type: One-to-one mapping (each input maps to a unique output)
Factorize as a perfect square: x2+10x+25
(x+5)2
Solve:
x2−x−12=0
x=4 or x=−3
Evaluate f(x)=x2+1, for when x= 3
10
Find the y-intercept of the function
y=x2+4x+3
(0,3)
Find the inverse of
f(x)=2x
f−1(x)=x/2
Q5. The relation R = {(x, y) : y = |x| − 1, x ∈ {−3, −1, 0, 1, 3}}. List all ordered pairs and state the range.
Pairs: {(−3, 2), (−1, 0), (0, −1), (1, 0), (3, 2)} Range = {−1, 0, 2}