Free Printable 1st Quarterly Exam in General Mathematics

1.

Which of the following is a rational equation?

a)

$\frac{5X}{6}-\frac{1}{2}=\frac{1}{3}$

b)

$\frac{5}{X-2}=F\left(X\right)$

c)

$X-9\le\frac{X}{X+1}$

d)

$f\left(x\right)=x+2$

2.

Which of the following is a rational inequality?

a)

$\frac{5X}{6}-\frac{1}{2}=\frac{1}{3}$

b)

$\frac{5}{X-2}=F\left(X\right)$

c)

$X-9\le\frac{X}{X+1}$

d)

$f\left(x\right)=x+2$

3.

$\frac{x+3}{x-4}=\frac{x-5}{x+4}$ Solve for x:

a)

$x=-\frac{32}{41}$

b)

$x=0\ or\ x=\ 14$

c)

$x=\frac{1}{2}$

d)

$\left(-2,0\right)$

e)

[1,4)

4.

What is the graph of the function.

$f\left(x\right)=\frac{-x+1}{x-4}$

a)

b)

c)

d)

5.

Simplify the rational function

a)

1/(x + 5)

b)

1/(x - 5)

c)

(x - 5)(x + 5)

d)

(x - 5)/[(x - 5)(x + 5)]

6.

What is the LCD? $\frac{7}{\left(x+1\right)}+\frac{2x}{\left(x-1\right)}$

a)

(x-1)

b)

(x-2)(x+2)

c)

(x+1)(x-1)

d)

(x+1)

7.

What is the LCD? $\frac{x^2}{\left(x+3\right)}+\frac{\left(x-3\right)}{2x}$

a)

$\left(x+3\right)$

b)

$x^2\left(x+3\right)$

c)

$2x\left(x+3\right)$

d)

$\left(x+3\right)\left(x-3\right)$

8.

What is the LCD? $\frac{x}{x^2-9}-\frac{1}{x+3}+\frac{2x}{x-3}$

a)

$x\left(x+3\right)\left(x-3\right)$

b)

$\left(x+3\right)\left(x^2-9\right)\left(x-3\right)$

c)

$\left(x-3\right)\left(x^2-9\right)$

d)

$\left(x+3\right)\left(x-3\right)$

9.

What is the LCD? $\frac{\left(x-5\right)}{x^2-7x+12}+\frac{\left(x+3\right)}{x^2+2x-15}$

a)

$\left(x-3\right)\left(x-4\right)$

b)

$\left(x-3\right)\left(x-4\right)\left(x+5\right)$

c)

$\left(x+5\right)\left(x-3\right)$

d)

$\left(x-3\right)\left(x-4\right)\left(x-5\right)$

10.

What is the LCD? $-\frac{3\left(x+4\right)}{3x^2}+\frac{\left(x-4\right)}{\left(x+4\right)}$

a)

$\left(x+4\right)\left(x-4\right)$

b)

$3\left(x-4\right)$

c)

$3x^2$

d)

$3x^2\left(x+4\right)$

11.

Solve!

a)

x = 2

b)

x = 6

c)

x = 5

d)

x = 4

12.

Solve the equation for x.

a)

6

b)

12

c)

0

d)

3

13.

Finally, using a test point, what is the solution to the rational inequality

\frac{-x+8}{𝑥+2}≤0

?

a)

$\left(-\infty,\ -2\right)\cup\left[8,\ \infty\right)$

b)

$\left(-\infty,\ -2\right)$

c)

$\left[8,\ \infty\right)$

d)

$\left(-2,\ 8\right]$

14.

These numbers are the zeros of the numerator and denominator of a rational inequality.

a)

zeroes

b)

critical values

c)

undefined

d)

solution set

15.

When solving rational inequality, we need to move all the terms in one side, combine like terms and write as a single fraction

a)

TRUE

b)

FALSE

16.

It is a root obtained in the process of solving an equation which looks correct but after analyzing it turns incorrect

a)

rational expression

b)

extraneous solution

c)

least common denominator

d)

quotient

17.

The usual technique to eliminate denominator in solving a rational equation is to multiply both sides of the equation by

a)

inverse factor

b)

GCF

c)

LCD

d)

GCD

18.

Solve the rational inequality and state your solution in interval notation.

$\frac{-x}{x-3}\ge0$

a)

$\left(0,\ +\infty\right)$

b)

$\left[0,\ 3\right)$

c)

$\left(-\infty,\ 0\right)\cup\left(3,\ +\infty\right)$

d)

$\left(-\infty,\ 0\right]\cup\left[3,\ +\infty\right)$

19.

Find the Critical Value of the given Rational Inequlity,

\frac{-x+8}{𝑥+2}≤0

a)

8 and -2

b)

-8 and -2

c)

8 and 2

d)

-8 and 2

20.

What sign will satisfy the given Rational Inequality,

\frac{-x+8}{𝑥+2}≤0

a)

all real numbers

b)

Negative

c)

Positive

d)

Infinity

21.

What critical value will mark as included in Rational Inequality,

\frac{-x+8}{𝑥+2}≤0

a)

-8

b)

-2

c)

8

d)

2

22.

What critical value will mark as not included in Rational Inequality,

\frac{-x+8}{𝑥+2}≤0

a)

-8

b)

-2

c)

8

d)

2

23.

What symbol is used if the critical value is included?

a)

( ) and hallow circle

b)

( ) and Closed dot

c)

[ ] and hallow circle

d)

[ ] and Closed dot

24.

What symbol we are using if the critical value is included included?

a)

( ) and hallow circle

b)

( ) and Closed dot

c)

[ ] and hallow circle

d)

[ ] and Closed dot

25.

What is the step number 4 in Solving rational inequalities?

a)

Make a number line

b)

Perform the sign analysis

c)

Write the Interval Notation

d)

Mark the Critical Values

e)

Identify what sign will satisfy the inequality

26.

What is the step number 6 in Solving rational inequalities?

a)

Make a number line

b)

Perform the sign analysis

c)

Write the Interval Notation

d)

Mark the Critical Values

e)

Identify what sign will satisfy the inequality

27.

Substituting the critical value of the denominator will always result as ________________.

a)

included

b)

not included

c)

true

d)

false

28.

1. What is the interval notation of the given?

a)

[-3, 4)

b)

[-3, 4]

c)

(-3, 4]

d)

(-3, 4)

29.

1. What is the interval notation of the given?

a)

( -∞, - 6] U (1, 4]

b)

( -∞, - 6] U [1, 4)

c)

( -∞, - 6] U (1, 4)

d)

( -∞, - 6] U [1, 4]

30.

The horizontal asymptote equals zero when:

a)

the exponents in the numerator and denominator are equal

b)

the exponents in the numerator are less than the denominator

c)

the exponents in the numerator are greater than the denominator

d)

the numerator equals zero

31.

What are the asymptotes?

a)

x=-2 and y=-1

b)

x=-2 and y=1

c)

x=2 and y=1

d)

x=2 and y = -1

32.

Find the horizontal asymptote.

a)

y = -2

b)

none

c)

y = 0

d)

y = 1/2

33.

What are the asymptotes of the given graph

a)

x=1, x= 2, y =1, y= 2

b)

x= 2, x= -2, y = 1

c)

x=2 and y= -1

d)

x=1, y =2, y = -2

34.

What is the hole?

a)

x= 4

b)

x= -4

c)

x= 5

d)

x= -5

35.

What is the Domain of the function $f\left(x\right)\ =\ \frac{x+1}{\left(x-1\right)\left(x+8\right)}$ ?

a)

$All\ Real\ Numbers$

b)

$x=1\ and\ x=-8$

c)

$x\ne1\ and\ x\ne-8$

d)

$∀R|\ x\ ≠\ 1,\ x\ ≠-8$

36.

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

a)

b)

c)

d)

37.

How do you find the y-intercept?

a)

replace all x-values with 0

b)

replace all y-values with 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

38.

How do you find the x-intercept?

a)

replace all x-values with 0

b)

replace the y-value with 0 or make the numerator equal 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

39.

$f\left(x\right)=\frac{3x-6}{x^2-4}$ has a y-intercept at:

a)

$\left(0,3\right)$

b)

$\left(0,\frac{3}{2}\right)$

c)

$\left(2,0\right)$

d)

There are no y-intercepts.

e)

$\left(0,0\right)$

40.

Solve :

a)

x = 6

b)

x = -6

c)

x = 6/7

d)

x = -6/7

1st Quarterly Exam in General Mathematics

Total questions: 40

Worksheet time: 54mins

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