[PRE-TEST GEN MATH]

1. It is an equation in two variables x and y, where the variable y may be expressed as f(x) if every value of x corresponds to a single value of y.

• A. function

• B. equation

• C. variable

• D. notation

Answer explanation

In an equation in two variables x and y, the variable y may be expressed as f(x) if every value of x corresponds to a single value of y. This is known as a function.

2. This denotes equality between two expressions.

• A. variable

• B. notation

• C. function

• D. equation

Answer explanation

Equations denote equality between two expressions.

3. What type of function is defined on a sequence of intervals?

• A. independent function

• B. dependent function

• C. piecewise function

• D. candidate function

Answer explanation

A function which is defined on a sequence of intervals is known as a piecewise function.

4. Which of the following is not a correct form of expressing a function?

Answer explanation

The notation d(x)=y+5 is an incorrect way of expressing a function because the variable used is y instead of x.

5. How will you read x→2x+5?

• A.

  x approaches 2x+5

• B.

  from x to 2x+5

• C.

  x can be written as 2x+5

• D.

  x is mapped to 2x+5

Answer explanation

In function notations, the arrow is read as “is mapped to”. Thus, x→2x+5 is read as "x is mapped to 2x+5".

6. Which of the following is not a function?

Answer explanation

A function denotes relationship between two variables. It always involves a set of inputs and a set of outputs. Thus, 5x+2 is not a function.

7. Elaine bought a cake-making kit. She sells one-pound cakes for ₱75 each. Write a function C that shows how much she earns selling p pounds of cake.

• A.

  C(p)=75p

• B.

  C(p)=75+p

• C.

  C(p)=75p+150

• D.

  C(p)=75p+150+p

Answer explanation

The cost of the cake is ₱75 per pound, so if Elaine sells p pounds of cake, her earnings will be 75 multiplied by p, or 75p.

8. A rectangular garden has a perimeter of 120 m. Express its area A as a function of the width w.

Answer explanation

If the length of the rectangle is l and the width is w, then the perimeter P can be expressed as

P=2l+2w

120=2l+2w

Express the length in terms of the width.

120−2w=2l

l=60−w

Solve for the area.

A(w)=w(60−w)

A(w)=60w−w2

9. A photocopy shop charges ₱0.60 per page for orders of less than 30 pages, ₱0.50 per page for orders of 30 to 60 pages, and ₱0.40 per page for orders of more than 60 pages. Which function best represents the cost C for x pages of photocopies?

• 
• 
• 
• 

Answer explanation

The rate per page changes depending on the number of pages: ₱0.60 per page for 1 to 29 pages, ₱0.50 per page for 30 to 60 pages, and ₱0.40 for 61 pages or more.

Thus, the function that best represents the cost C for x pages of photocopies is

10. It is a set of numbers grouped with each other that may or may not represent a pattern.

• A. correspondence

• B. function

• C. relation

• D. ordered pairs

Answer explanation

A relation is a set of numbers grouped with each other that may or may not represent a pattern. It is simply a set of ordered pairs of numbers such as (x,y) that are arranged in an orderly manner.