Free Printable DIAGNOSTIC TEST GENERAL MATHEMATICS

1.

Examine the following sets of ordered pairs. Which one represents a one-to-one relation?

a)

$\left(1,-1\right),\ \left(1,1\right),\ \left(2,4\right),\ \left(2,\ 6\right)$

b)

$\left(2,0\right),\ \left(3,1\right),\ \left(2,1\right),\ \left(4,-3\right)$

c)

$\left(-2,\ 3\right),\ \left(-1,1\right),\ \left(0,0\right),\ \left(2,1\right)$

d)

$\left(-1,-1\right),\ \left(1,1\right),\left(2,3\right),\left(4,5\right)$

2.

Which of the following equation is not a function?

a)

$f\left(x\right)\ =\ 2x\ -3$

b)

$f\left(x\right)\ =\ \sqrt{x}$

c)

$y^2=2x$

d)

$y\ =\ \frac{x\ -\ 3}{x\ +\ 1}$

3.

Using $f\left(x\right)\ =\ x\ -2\$ and $g\left(x\right)\ =\ 5x\ +\ 3,$ find $f\left(g\left(2\right)\right)?$

a)

3

b)

9

c)

11

d)

13

4.

$f\left(x\right)\ =\ -3x-6$ and $g\left(x\right)\ =\ 5x\ +2.$ Find $f\left(x\right)\ +\ g\left(x\right).$

Let

a)

$2x-4$

b)

$-8x-8$

c)

$-8x-4$

d)

$2x-8$

5.

Let

f\left(x\right)\ =3x\ +\ 2\

and

g\left(x\right)\ =\ x-3.

Find

f\left(x\right)\ -g\left(x\right).

a)

$2x-5$

b)

$2x+5$

c)

$4x-1$

d)

$2x-1$

6.

$Let\ f\left(x\right)\ =x^2\ +2x-1$ and $g\left(x\right)=2x-4$

Find $2\left(f\left(x\right)\right)-3\left(g\left(x\right)\right)$

a)

$2x^2-2x-14$

b)

$2x^2-2x+10$

c)

$-3x^2-2x-1$

d)

$-3x^2-2x-7$

7.

$f\left(x\right)=5x^2-7x+3\ and\ g\left(x\right)=\ 4x\ +\ 9.\$

Given the following functions. Evaluate $\left(f\circ\ g\right)\left(x\right)?$

a)

$-8x-15$

b)

$30x^2+332x+345$

c)

$80x^2+332x+345$

d)

$80x^2+152x+345$

8.

$If\ f\left(x\right)\ =\ 5x^2-7x+3\ and\ g\left(x\right)\ =4x\ +9$

Evaluate $\left(f+g\right)\left(x\right)?$

a)

$5x^2-11x+12$

b)

$5x^2+3x+12$

c)

$5x^2-3x+12$

d)

$5x^2-2x+12$

9.

$Let\ f\left(x\right)\ =3x+2\ and\ g\left(x\right)=7x+6$

Find $f\left(x\right)\ \cdot\ g\left(x\right)$ and its domain.

a)

$6x^2+4x+42;\$ all real numbers except $x=-\frac{2}{3}$

b)

$6x^2+4x+42;$ all real numbers

c)

$21x^2+32x+12;$ all real numbers

d)

$21x^2+32x+12;$ all real numbers except $x=-\frac{6}{7}$

10.

$Let\ f\left(x\right)=3x-6\ and\ g\left(x\right)=x-2.\ Find\ \frac{f\left(x\right)}{g\left(x\right)}$ and its domain.

a)

3; all real numbers

b)

3; all real numbers except x=2

c)

1; all real numbers

d)

-3; all real numbers except x = 3

11.

$Let\ f\left(x\right)\ =-2x-7\ and\ g\left(x\right)=-4x+3$ Find $\left(f\circ\ g\right)\left(-5\right)$

a)

23

b)

-53

c)

-9

d)

3

12.

$Let\ f\left(x\right)\ =\ x^2+6\ and\ g\left(x\right)\ =\ \frac{x+8}{x}$ Find $\left(g\ \circ\ f\right)\left(-7\right).$

a)

$-\frac{55}{7}$

b)

$\frac{384}{7}$

c)

$\frac{295}{49}$

d)

$\frac{63}{55}$

13.

$Let\ f\left(x\right)=\ 4+5x\ and\ g\left(x\right)\ =\ 2x-1$ Find $f\left(g\left(x\right)\right)\ and\ g\left(f\left(x\right)\right).$

a)

$f\left(g\left(x\right)\right)=10x-1;\ g\left(f\left(x\right)\right)=10x+7$

b)

$f\left(g\left(x\right)\right)=7x+3;\ g\left(f\left(x\right)\right)=10x+7$

c)

$f\left(g\left(x\right)\right)=-7x-3;\ g\left(f\left(x\right)\right)=-10x+7$

d)

$f\left(g\left(x\right)\right)=-10x-7;\ g\left(f\left(x\right)\right)=7x+3$

14.

Which of the following is the inverse of $f\left(x\right)=\ 5x^3-1$

a)

$f^{-1}\left(x\right)\ =\ ^3\sqrt{x+1}$

b)

$f^{-1}\left(x\right)=\ ^{3\sqrt{\frac{x\ -1}{5}}}$

c)

$f^{-1}\left(x\right)=\ ^3\sqrt{\frac{x+1}{5}}$

d)

$f^{-1}\left(x\right)=\ ^{3\sqrt{\ 5x+1}}$

15.

$\ Find\ the\ inverse\ of\ f\left(x\right)=x+1$

a)

$f^{-1}\left(x\right)\ =\ x\ -1\$

b)

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

c)

$f^{-1}\left(x\right)=-x-1$

d)

$f^{-1}\left(x\right)=2x+2$

16.

Which of the following functions is not one-to-one?

a)

$f\left(x\right)=x^3+2x+1$

b)

$f\left(x\right)\ =\ \sqrt{x}$

c)

$f\left(x\right)=\ 1-9x$

d)

$f\left(x\right)=\frac{1}{x^2}$

17.

Solve

\frac{x^2+6x+8}{x-2}\le\ 0.

Express your answer using interval notation.

a)

$\left\{\left(-\infty,-4\right)\cup\left(-2,2\right)\right\}$

b)

$\left\{\left(-\infty,-4\right],\ \left[-2,2\right)\right\}$

c)

$\left\{\left(-\infty,-4\right),\left(-2,2\right)\right\}$

d)

$\left\{\left(-\infty,-4\right]\ \cup\left[-2,2\right)\right\}$

18.

Which of the following has a horizontal asymptote at y=0?

a)

$f\left(x\right)=\ \frac{x^3\ +\ 2}{2x\ +\ 3}$

b)

$f\left(x\right)\ =\ \frac{x\ +\ 5}{2x\ -3}$

c)

$f\left(x\right)\ =\ \frac{3x\ +\ 2}{x^3\ -8}$

d)

$f\left(x\right)\ =\ \frac{x^2\ +\ 2x\ -1}{x^2\ -4}$

19.

Which has a vertical asymptotes at x = -3 and x = -1/2?

a)

$f\left(x\right)\ =\ \frac{2}{2x^2\ +\ x\ -1}$

b)

$f\left(x\right)\ =\ \frac{1}{2x^2+5x\ -3}$

c)

$f\left(x\right)\ =\ -\frac{1}{2x^2+5x\ -3}$

d)

All of the above

20.

What is the equation of the horizontal asymptote of the graph of the function shown?

a)

x = 2

b)

x = 4

c)

y = 2

d)

y = 4

21.

What is the x-intercept of the graph of

f\left(x\right)\ =\ \frac{x^2+4x\ -21}{x^2-x-20}?

a)

$\left(-4,0\right)\ and\ \left(5,0\right)$

b)

$\left(-7,0\right)\ and\ \left(3,0\right)$

c)

$\left(4,0\right)\ and\ \left(-5,0\right)$

d)

$\left(7,0\right)\ and\ \left(-3,0\right)$

22.

Which of the following function has a hole at x = 5?

a)

$f\left(x\right)\ =\ \frac{x^2-25}{x+5}$

b)

$f\left(x\right)\ =\ \frac{x-5}{x^2-25}$

c)

$f\left(x\right)\ =\ \frac{x^2-25}{x-5}$

d)

B and C

23.

What is the simplest form of

5\log_7x\ +\ \frac{1}{3}\log_7\ y\ -\log_7z^2?

a)

$\log_7\ \frac{5xy}{3z^2}$

b)

$\log_7\ \frac{x^5y^3}{z^2}$

c)

$\log_7\ \frac{x^5y^{\frac{1}{3}}}{z^2}$

d)

$\log_7\ x^5y^{\frac{1}{3}}z^2$

24.

Evaluate the logarithmic equation.

\log\sqrt{x}\ =\ \left(\log x\right)^2

a)

$x=0\ or\ x\ =1$

b)

$x=0\ or\ x\ =\ \sqrt{10}$

c)

$x=1\ or\ x=\ 100$

d)

$x=\sqrt{10}\ or\ x\ =\ 100$

25.

What is the solution set of

8^{\left(2x-1\right)}\le\ 16^x\ ?

a)

$x\le\ \frac{2}{3}$

b)

$x\le\frac{3}{2}$

c)

$x<\frac{3}{2}$

d)

$x<\frac{2}{3}$

26.

Given the function

f\left(x\right)\ =\ \frac{x+2}{x-1}.

What is the domain of the function?

a)

All real numbers except x =1.

b)

$x\ge0$

c)

$x\ge1$

d)

All real numbers except x = -1

27.

Which of the following does not define an exponential function?

a)

$f\left(x\right)\ =\ 2^x-3$

b)

$f\left(x\right)\ =\ 12\ +\ 8x-x^2$

c)

$f\left(x\right)\ =\ -\left(5^x\right)$

d)

$f\left(x\right)\ =\ 3\left(7^x\right)$

28.

Which one has a graph same as that of

y\ =\ 3^x

but all points of which are moved 4 units above the given graph?

a)

$y\ =\ 3^x\ +\ 4$

b)

$y\ =\ 3^{-x}\ +\ 4$

c)

$y\ =\ 3^{\left(x+4\right)}$

d)

$y\ =\ 3^{\left(-x+4\right)}$

29.

Solve for x:

5^{\left(x-1\right)}=125

a)

-4

b)

-2

c)

2

d)

4

30.

Solve for x:

\left(\frac{1}{7}\right)^{\left(x+3\right)}=49^{\left(x-3\right)}

a)

-2

b)

1

c)

5

d)

9

31.

A culture of microorganism doubles every hour. How many microorganisms will there be in the culture after 4 hours if there were 250 of them at the beginning?

a)

500

b)

2000

c)

1000

d)

4000

32.

A colony of bacteria doubles every 3 hours. At present there are 10,000 bacteria. How many bacteria were there 6 hours ago?

a)

2,500

b)

5,000

c)

20,000

d)

40,000

33.

Mrs. Ramos invested Php 25,000 in a mutual fund for his children's college education at 0.2% compounded semi-annually. Which of the following gives the amount of his investment after 10 years?

a)

$y\ =\ 25000\left(1.02\right)^{10}$

b)

$y=25000\left(1.02\right)^{20}$

c)

$y=\ 25000\left(1.001\right)^{20}$

d)

$y=25000\left(1.0001\right)^{20}$

34.

How much would Php 15,000 amount to in 5 years at 4% compounded annually?

a)

17, 500.00

b)

18, 249.79

c)

20,120.50

d)

18, 349.15

35.

What is the principal amount, if the amount of interest at the end of 4 years is Php 500 for a simple interest of 10% per annum?

a)

Php 12.50

b)

Php 125.00

c)

Php 1,250.00

d)

Php 12, 500.00

36.

How much interest is earned when an amount of Php 20,000 is invested with annual interest rate of 8% for 3 years?

a)

Php 480.00

b)

Php 4,800.00

c)

Php 48,000.00

d)

Php 480, 000.00

37.

p: Rafael is a singer
q: Janrick plays a piano
Which of the following is the translation of

\sim p\ \vee\ \sim q?

a)

Rafael is not a singer and Janrick plays the piano.

b)

Rafael is not a singer or Janrick can’t play the piano.

c)

Either Rafael is not a singer or Janrick plays the piano.

d)

Either Rafael is not a singer or Janrick plays the piano.

38.

“It is not true that Rafael is a singer or Janrick plays the piano”. Which of the following is the correct proposition?

a)

$\sim p\vee\sim q$

b)

$\sim p\vee q$

c)

$\sim\left(p\vee\sim q\right)$

d)

$\sim\left(p\vee q\right)$

39.

What is the negation statement of “All scientists are mathematicians”

a)

No scientists are mathematicians

b)

No mathematicians are scientists.

c)

Some scientists are mathematicians.

d)

A. Some scientists are not mathematicians.

40.

What are the truth values of the given statements

\left(p\wedge q\right)\vee p?

a)

b)

c)

d)

DIAGNOSTIC TEST GENERAL MATHEMATICS

Total questions: 40

Worksheet time: 20mins

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