Republic of the Philippines
Department of Education
Region X – Northern Mindanao
Division of Ozamiz City
OZAMIZ CITY SCHOOL OF ARTS AND TRADES
Maningcol, Ozamiz City
General Mathematics
First Grading Examination
First Semester
2018 – 2019
I. Multiple Choices: Read each question carefully. Choose the
answer on the blank provided before each number.
1) A function is always a relation.
A) Always true
B) sometimes true
C) never true
D) cannot be determined
2) Which of the following has a graph of a function?
A) x2 + y2 = 9
B) x2 - y2 = 1
2
C) y - x = 4
D) x - y2
3) Which of the following sets of ordered pairs does NOT
define a function?
A) {(4,1),(3,2),(2,3),(1,4)}
B) {(6,3),(8,-1),(7,0),(4,2)}
C) {(2,3),(6,4),(6,5),(8,9)}
D) {(10,4),(11,4),(12,2),(13,1)}
4) Which of the following is not a function?
A) The rule which assigns to each integer its factor
B) The rule which assigns to every person his/her
biological father
C) The rule which assigns to a person’s surname his/her
gender
D) The rule which assigns to each counting number it’s
reciprocal
5) Which function below best describes the following
statement?
The average daily level of carbon monoxide in the air
is denoted by c, where c is a function of the
population, p, c is measured in parts per million and p
is measured in thousands and c is equal to 0.5 times
the population plus one.
A) p(c)=0.5c+1
B) p(c)=0.5p+1
C) c(p)=0.5c+1
D) c(p)=0.5p+1
7) Which of the following best describes the diagram?
3
A) x is a factor of y.
3
2
6
8
B) x is a prime factor of y.
9
3
14
C) x is a multiple of y.
5
15
20
D) x is a composite factor of y.
8) Which of the following is NOT a piecewise function?
A) f(x) = x - 2
B) f(x) = x, x < 0
f(x) = x + 5, x = 0
f(x) = 2, x > 0
C) f(x) = 2 - x, x < -7
f(x) = x² + 1, x ≥ -7
D) f(x) = |x|
9) Evaluate the following piecewise function for x = 0 and
x = 5.
f(x) = 2x - 3, x < 0
f(x) = x² - 1, x = 0
f(x) = x + 3, x > 0
A) (0, -1) and (5, 8)
B) (0, -1) and (5, 24)
C) (0, 3) and (5, 8)
C) (0, -1) and (5, 7)
10) Let g(x) = 1 – x2. What is g (- √7)?
A) -6
B) 8
C) 48
D) 50
11) For what value of x will make {(3, 5) (7, 9) (x-3, 13)
(15, 17)} satisfy the relation y = x + 2?
A) 6
B) 10
C) 14
D) 18
letter of the correct answer. Write the letter of the correct
13) Let f(x) = 2x2. If (f – h) (x) = 2x2 – x – 1, what is
h(x)?
A) x + 1
B) x – 1
C) 1 – x
D) x – 1
14) Given f(x) = 5 – 2x, evaluate f(x + 1).
A) 7 – 2x B) – 2x + 3
C) 3 + 2x
D) 2x – 7
15) If f(x) = 2x + 1 and g(x) = 3x, find (f º g) (x).
A) 5x + 1 B) 6x + 3
C) x – 6
D) 6x + 1
16) If f(x) = x – 4 and g(x) = 2x + 3, what is (f + g) (x)?
A) x – 1
B) 3x – 1
C) 3x + 1
D) x + 7
17) If f(x) = x2 + 2 and g(x) = 2/x, find (g º f) (2).
A) 6
B) 1/3
C) 3
D) 1/6
18) Which graph represents a function?
A)
D)
B)
C)
_
19) Which of the following statements about the domain
and range of a relation is always true?
A) The domain must always have at least two values.
B) The range must always have at least two values.
C) If all the ordered pairs in the relation are of the
form ( x, y), then the domain is the set of all x's and
the range is the set of all y's.
4
20) Which family of functions does y = 2 belong to?
𝑥
A) Trigonometric
B) Exponential
C) Logarithmic
D) Rational
21) Which of the following functions is not rational?
A) f(x) =
C) f(x) =
1
√3𝑥
B) f(x) =
𝑥+5
3
𝑥 2 −1
D f(x) = 2
𝑥
𝑥−4
𝑥+8
𝑥 −2𝑥+1
22) Simplify the expression and state the excluded values:
p2 - 4p - 32
p+4
A) -p + 8; p ≠ -4
B) -p - 8; p ≠ 4
C) p - 8; p ≠ -4
D) p + 8; p ≠ 4
23) Simplify:
7
+
𝑎+8
7
.
𝑎2 −64
7a – 49 __
(a - 8)(a + 8)
C)
14____
a2 + a – 56
A)
24) Solve the equation for
A)
−13
B)
6
−8
B)
14____
(a - 8)(a + 8)
D)
7a + 63__
(a - 8)(a + 8)
A)
− 14
B)
A) f -1(x) =
𝑥+5
4
𝑥+3
C) −
3
25) Solve the equation for w:
3
−2
x: 𝑥+4 =
11
− 24
5
6𝑤
+
C)
1
D) -11
3
𝑤
11
6
.
11
= −4.
𝟑𝟏
D)
− 𝟐𝟒
26) If f(x) = x 2 , g(x) = 3x, what is the value of [ g ○
f] (-2)?
A) 12
B) 10
C) 8
D) 6
27) What is f -1(x) given that f(x) = 2x – 5 is one-to-one?
2
C) f -1(x) = 5x
2
B) f -1(x) =
𝑥+2
D) f -1(x) =
25
2x
5
28) Sketch the asymptotes and graph the function.
A)
B)
C)
D)
36) Given the function y=ax, which of the following is true?
I) a is any real number
II) a › 0
II). a ‹ 0
IV) a ≠ 0
A) I only
B) II and IV
C) III and IV
D) II only
37) Which function describes an exponential growth?
A) y = 400(1.208)t
B) y = 400(1.208)t
C) y= 400t(1.208)
D) y= 400(1.208)
38) Which of the following is not true about the graph of
f(x) = 5x?
A) The y-intercept is 1.
B) The graph is asymptotic to the x-axis.
C) As x increases, f(x) also increases.
D) F(x) crosses the x-axis.
39 – 43: Solve for the value of x.
39) 92x = 27
A) ⅛
B) ¼
C) ½
D) ¾
40) 9√2x-1 = 27
A) 8/13
B) 13/8
C) -8/13
D) -13/8
X+3
29) The graph of
A) intersects the
B) intersects the
C) intersects the
D) intersects the
41) 3 3 = 815+x
A) -57/11
B) 57/11
C) 11/57
D) -11/57
42) 2|x-7| = 8
A) 9
B) 10
C) 11
D) 12
43) 73x+2 = 49x
A) 2
B) 1
C) -2
D) -1
44) Which of the following is an inverse of f(x) = 2x – 7?
A) f -1(x) = x + 7
B) f -1(x) =
2__
2
x+7
-1
C) f -1(x) = x – 7
D) f (x) = 2__
2
x–7
....
x-axis
y-axis
both x-axis and y-axis
neither x-axis and y-axis
45) Find the inverse for the function
30) Find the domain of
.
A) all real numbers
B) all positive real numbers
C) all real numbers greater than one
D) all real numbers less than zero
31) For what values of x will the function
be
greater than or equal to one?
A) all values of x
B) all x > 0
C) all x > 0
D) all x < 0
32) For the graph below shows the function f (x) = bx ,
which statement must be true about b?
A) b > 1
B) 0 < b < 1
C) b < 0
D) b < -1
33) Which expression indicates an exponential function?
A) f(x) = x2
B) f(x) = 2x
C) f(x) = 2x
D) f(x) = x
34) The expression 4-2 is equal to
A) -8
B) -16
C) 1/8
D) 1/16
35) The expression –(3√2) is approximately
A) -4.73
B) -9
C) -3.14
D) -5.73
(x is not zero).
A)
B)
C)
D)
46) Which of the following graphs below show that for
every x there corresponds one value of y?
y
A)
B)
y
x
C)
x
D)
y
x
y
x
47) Which of the following represents the inverse of f(x)
= 8x, given that the function f is one-to-one?
A)
x
0 1
2
3
4
f(x) 0 -⅛ -¼ -⅜ -½
B)
x
0 1
2
3
4
f(x) 0 -8 -16 -24 -32
C)
x
0 1 2
3
4
f(x) 0 8 16 24 32
D)
x
0 1
2
3
4
f(x) 0 ⅛ ¼ ⅜ ½
48) A town has a population of 50,000. Its rate increases
8% each year. Find the population after 4 years.
A) 68,224.45
B) 68,444.45
C) 68,222.45
D) 68,024.45
49) Suppose a culture of 100 bacteria is put in a Petri dish
and the culture triples every hour. How many bacteria
will there be after 6 hours?
A) 72,900 B) 73,900
C) 74,900
D) 75,900
50) Which of the following represents a one-to-one
function?
A)
B)
C)