### All ACT Math Resources

## Example Questions

### Example Question #56 : Algebraic Functions

Two consecutive negative odd numbers have a product of 15. What is the sum of the two numbers?

**Possible Answers:**

–8

–12

–6

–4

–10

**Correct answer:**

–8

Define the variables x = first number and x + 2 = second number

The product is x(x + 2) = 15, so we need to solve the quadratic equation x^{2} + 2x – 15 = 0. Factoring we get (x + 5)(x – 3) = 0, so x = –5 or x = 3. The problem calls for negative numbers, so the answers are –5 and –3 and the sum is –8

### Example Question #57 : Algebraic Functions

What is the difference of the values of *x* that satisfy

4*x*^{2}+ 3*x *– 1 = 0?

**Possible Answers:**

3

0

5/4

4/5

**Correct answer:**

5/4

Factor the equation (4*x* – 1) (*x* + 1)

The solutions are *x* = –1 and *x* = 1/4.

The difference is (1/4) – (–1) = 5/4

### Example Question #1 : How To Use The Quadratic Function

2*x* + *y* = 1

What is the slope and the *y*-intercept of the given equation, respectively?

**Possible Answers:**

–2, 1

1, 1

1, 2

2, –2

2, 1

**Correct answer:**

–2, 1

You put the equation into slope-intercept form (*y* = *mx *+ *b*)

The new equation is *y*= –2*x* + 1

*m *= –2 and *b *= 1

### Example Question #2 : How To Use The Quadratic Function

How many solutions are there to: x^{2 }– 9 = 0

**Possible Answers:**

Infinitely many

0

2

1

**Correct answer:**

2

There are two solutions that make the solution true: 3 and **–**3.