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WorksheetsMath 3
Total questions: 100
Worksheet time: 50mins
Name
Class
Date
1.
How much will an amount (in Php) be after 7 years when Php60,000 is invested at 2% compounded annually?
a)
68921.14
b)
70837.18
c)
72148.19
d)
73150.91
2.
Evaluate the limit of
(x^2 - 10x + 25) / (x^2 - 25)
as x approaches to 5
a)
0
b)
-1/3
c)
-1/8
d)
1/2
3.
To prove a conjecture, Maria checked if it worked for n = 1. She assumed it to be true for n = k and she is trying to prove that the conjecture is true for n = k + 1. What method of proof was used by Maria?
a)
mathematical induction
b)
direct substitution
c)
direct
d)
indirect
4.
Evaluate the limit of
(3x - 5) / (2x - 8)
as x approaches to infinity
a)
1.5
b)
0
c)
2
d)
3
5.
Mr. Pedros utilized the following image for his Math class? A scale in balanced with x box and 3 circle on left and 7 circle on right. What is he most likely trying to model here?
a)
x + 3 =7
b)
3x = 7
c)
x/3 = 7
d)
x - 3 = 7
6.
If sin θ = 4/5, and 0 < θ < π/2, then cos 2θ is equal to _______.
a)
-7/25
b)
44/125
c)
24/25
d)
7/25
7.
Find the probability of getting a face card if a card is picked at random from a standard deck of cards.
a)
3/13
b)
4/13
c)
5/13
d)
7/13
8.
Evaluate: ∫(3x^2 + 4x) dx
a)
x^3 + 2x^2 + C
b)
x^3 + 2x + C
c)
x^3 - 2x^2 + C
d)
x^2 + 2x + C
9.
Which of the following has a value that is different from the rest?
a)
3.34
b)
15/4
c)
3.75
d)
3.75
10.
What is the antiderivative of a constant 𝑎?
a)
ax + C
b)
0
c)
-ax + C
d)
does not exist
11.
Which of the following is true about disjunction statements?
a)
If at least 1 proposition is true, then the whole statement is true.
b)
If at least 1 proposition is false, then the whole statement is false.
c)
If all propositions are false, then the whole statement is true.
d)
None of these
12.
A square and a 14 cm by 10 cm rectangle have the same perimeter. What is the area (in cm^2) of the square?
a)
144
b)
64
c)
100
d)
121
13.
A certain product was given successive discounts of 10% and 20%, in this order. Overall, the original price of the product was decreased by how many percent?
a)
28
b)
30
c)
32
d)
33
14.
When a logarithm is expressed as an integer plus a decimal, the decimal part is called the ___________.
a)
mantissa
b)
characteristic
c)
base
d)
antilogarithm
15.
Given the functions f(x) = x2 + 2x – 24 and g(x) = x + 6. What is (f/g)(x)?
a)
x-4
b)
x+4
c)
x-6
d)
x+6
16.
After investing Php15,000 at 7% simple interest for x years, it became Php20,250. What is x?
a)
5
b)
6
c)
7
d)
8
17.
Express in general form: (x + 3)2 + (y − 1)2 = 4.
a)
x2 + y2 + 6x − 2y + 6 = 0
b)
x2 + y2 - 6x − 2y + 6 = 0
c)
x2 + y2 - 6x + 2y - 6 = 0
d)
x2 + y2 + 6x − 2y - 6 = 0
18.
The conjunction of a true and a false statement is
a)
false
b)
True
c)
may be true or false
d)
neither true nor false
19.
Point M(2,-3) is the midpoint of segment KJ. If K has coordinates (4, -1), find the coordinates of J.
a)
(0, -5)
b)
(1, -3)
c)
(-5, 0)
d)
(2, -4)
20.
Which of the following is done to improve the quality of multiple choice tests?
a)
Item analysis
b)
Difficulty index computation
c)
Discrimination index computation
d)
Plausibility of Distracters
21.
The graph of y = x^2 + 3x – 40 passes through what points on the x-axis?
a)
(-8, 0) & (5, 0)
b)
(8, 0) & (5, 0)
c)
(0, -8) & (0, 5)
d)
(8, 0) & (-5, 0)
22.
The set of natural numbers N = {1, 2, 3, 4, …} is an example of an/a _______ set
a)
infinite
b)
finite
c)
null
d)
equivalent
23.
2 box is balanced with a circle, how many box is needed to balance 3 circle?
a)
6
b)
2
c)
3
d)
4
24.
A teacher is replaceable by technology so teachers may not be needed.
a)
false
b)
True
c)
maybe
d)
undetermined
25.
This type of number system has made use of some of the letters in the English alphabet to
represent quantities.
a)
Roman
b)
Akkadian
c)
Decimal
d)
English
26.
Twice a number added by 8 is equal to 4 times the number subtracted by 40. What is the
number?
a)
24
b)
23
c)
25
d)
27
27.
Maria rejected a true null hypothesis and reported a false alternative hypothesis. What kind of error is this?
a)
type 1
b)
type 2
c)
type 3
d)
type 4
28.
The diagonals of a rhombus measure 10 and 24. How long is the height of the rhombus?
a)
120/13
b)
12/50
c)
53/12
d)
130/12
29.
Find the area of the region bounded by x = 3 - y2 and the line y = x - 1
a)
9/2
b)
12/25
c)
13/2
d)
18/25
30.
The domain of y = (x + 1) / (x^2 - 9)
is the set of real numbers except
a)
-1, 3
b)
-3, 3
c)
-1, 3, -3
d)
1, -3
31.
Of the 10 girls in a class, 3 have blue eyes. If two of the girls are chosen at random, find the probability that at least one has blue eyes.
a)
8/15
b)
6/17
c)
7/15
d)
5/17
32.
Evaluate: ∫√(1 + 3x) dx from 1 to 8.
a)
26
b)
27
c)
24
d)
25
33.
What is the range of y = 3x – 4?
a)
all real numbers
b)
positive reals
c)
negative reals
d)
y ≠ 0
34.
A certain product was given successive discounts of 20% and 30%, in this order. Overall, the original price of the product as decreased by how many percent?
a)
44
b)
56
c)
28
d)
65
35.
Three concentric circles have radii 3, 4, and 5 cm. What percent of the area of the largest circle lies between between the other two circles?
a)
28
b)
30
c)
32
d)
34
36.
Simplify: cos x (csc x - sec x) - cot x
a)
-1
b)
1
c)
sec x
d)
tan x
37.
Teacher Angelica made use of information found in Math books for her class. Data found from such sources is an example of ___ data.
a)
secondary
b)
primary
c)
tertiary
d)
null
38.
He is an Italian mathematician who was famed for his algebraic solution of cubic equations
which was eventually published in Ars Magna.
a)
Niccolo Tartaglia
b)
Isaac Newton
c)
Leonardo Pisano
d)
Blaise Pascal
39.
How many triangles can be made from 10 points of which no three points are collinear?
a)
120
b)
720
c)
30
d)
210
40.
The number 0.06906906907... is
a)
rational
b)
irrational
c)
surd
d)
transcendental
41.
A farmer with 200 m of fence plans to enclose a rectangular piece of land using a river on one side and a fence on the other three sides. Solve the maximum area (in m2) that the farmer can obtain.
a)
5000
b)
5600
c)
5400
d)
5200
42.
Find the equation of a line that has a slope of 3 and passes through (-3, 4)
a)
y = 3x + 13
b)
y = 3x - 13
c)
y = 3x + 5
d)
y = 3x + 10
43.
Which of the following statements is correct about mathematical investigation?
a)
Mathematical investigation is an open-ended exploration of a mathematical problem
or situation
b)
In doing Mathematical Investigation, one visits the internet to determine the formula
that leads to answers to questions.
c)
Mathematical Investigation should be done in a short amount of time regardless of the
problem’s difficulty.
d)
Mathematical Investigation is teacher- centered inquiry and hence students should
follow steps indicated by teachers.
44.
Which of the following concepts could be used to make students realize that Mathematics is also applicable to other areas of knowledge or discipline?
a)
Integration
b)
Contextualization
c)
Differentiated Instruction
d)
all of these
45.
What is the circumference (in cm) of a circle with r = 10 cm? Use 𝜋 = 3.14.
a)
62.8
b)
125.6
c)
157
d)
314
46.
Find the equation of a line that passes through
(-1, 5) and (3, -3)
a)
2x + y = 3
b)
2x - y = 3
c)
3x + y = 2
d)
x - 3y = 2
47.
Consider right triangle ABC with angle B = 90°. Let D be a point on line AC such that line BD is perpendicular to line AC. If line AB = 3 and line BC = 4, how long is line BD?
a)
12/5
b)
5/12
c)
13/12
d)
12/13
48.
Which of the following ancient number systems which used a base 60?
a)
Babylonians
b)
Hittites
c)
Egyptians
d)
Akkadians
49.
Which of the following is the converse of p → q?
a)
q → p
b)
~p → ~q
c)
~q → ~p
d)
~q → p
50.
Evaluate: ∫(√x) dx from 1 to 4.
a)
14/3
b)
8/5
c)
10/3
d)
5/3
51.
Find the equation of a line through (1, 2) parallel to the line 3x – 2y = 4
a)
3x – 2y = -1
b)
2x + 3y = 4
c)
3x – 2y = 2
d)
2x + 3y = 8
52.
Find the value of k if 4x2 + 6x + k will have equal roots.
a)
9/4
b)
4
c)
8/3
d)
2
53.
If sec θ − tan θ = 25, which of the following must be the value of sec θ + tan θ?
a)
5/2
b)
2/5
c)
3/4
d)
7/3
54.
In one class, 1/3 of the students are male students. Of these male students, 2/7 are varsity athletes. If there are four male varsity athletes in the class, how many students are there in the class?
a)
42
b)
52
c)
60
d)
84
55.
What is the probability of getting a sum of 9 when a pair of dice is rolled?
a)
1/9
b)
5/36
c)
2/3
d)
5/6
56.
Which of the following is important when you are able to determine that students do not pay attention in class?
a)
motivate them
b)
ask them what is wrong
c)
scold them
d)
assign them internet-related works
57.
What is the sum of the prime factors of 360?
a)
10
b)
9
c)
12
d)
15
58.
Which of these could be utilize for online synchronous classes in Mathematics?
a)
all of these
b)
Google Meet
c)
Microsoft Teams
d)
Zoom
59.
She is one of the earliest known female mathematicians who invented the astrolabe for ship
navigation and devices for measuring the density of fluids.
a)
Hypatia
b)
Ada Lovelace
c)
Valentina Tereshkova
d)
Victoria Komova
60.
This refers to the collection of objects with a common characteristic.
a)
set
b)
aggregate
c)
group
d)
power
61.
There are 1, 3, 6, and 10 unit squares in Figures 1, 2, 3, and 4, respectively. If the pattern continues, how many unit squares will there be in Figure 15?
a)
120
b)
100
c)
110
d)
115
62.
Which of the following sequences in doing research is correct?
i. problem identification iii. data analysis
ii. stating conclusion iv. data-gathering
a)
i, iv, iii, ii
b)
i, iii, iv, ii
c)
i, ii, iv, iii
d)
i, ii, iii, iv
63.
A teacher wishes to determine the reason why the student employed a particular solution to a problem. Which is the best thing to use?
a)
interview
b)
experimentation
c)
questionnaire
d)
observation
64.
Find the equation of a line passing through (1, 4) and (4, 1)
a)
x + y = 5
b)
x – y = 5
c)
x – y = 3
d)
x + y = 3
65.
After investing a certain amount of money at 5% simple interest rate for 4 years, my money became Php102,000 in all. How much was invested?
a)
Php85,000
b)
Php84,000
c)
Php80,000
d)
Php75,000
66.
What is the minimum point of the parabola y = x^2 – 4x + 1?
a)
(2, -3)
b)
(-2, 3)
c)
(-3, 2)
d)
(3, -2)
67.
Evaluate the limit of (√x - 4) / (x - 16) as x approaches to 16
a)
1/8
b)
3/8
c)
1/4
d)
1/2
68.
How many 4-digit numbers do not contain at least one of the digits 2 and 6?
a)
3584
b)
3854
c)
3845
d)
3548
69.
A side of a square has been tripled. The new area will be _____ times that of the original.
a)
9
b)
3
c)
6
d)
12
70.
A man invests 1/3 of his capital at 6% and the remainder at 8%. Find his capital if his total income is Php4,400.
a)
Php60,000
b)
Php55,000
c)
Php65,000
d)
Php70,000
71.
A certain amount of money was invested at 3% simple interest and it gained Php400 in a span of 4 years. How much (in Php) was invested then?
a)
3333.33
b)
3334.33
c)
3433.33
d)
3443.33
72.
Mrs. Gonzales considers the ranking of the total scores of learners as basis for giving grades. Rank 1 got 99, rank 2 got 97, and so on. Which of the following concepts is involved
here?
a)
norm-referenced
b)
criterion-referenced
c)
averaging
d)
cumulative
73.
If a certain amount of money will be shared equally by 12 people, then each one will get Php360. How much(in Php) will each one get if there are 18 people who will share the same amount?
a)
240
b)
200
c)
280
d)
300
74.
This refers to the if-part of a conditional statement.
a)
hypothesis
b)
conclusion
c)
converse
d)
inverse
75.
Which of the following units of measure could best measure the height of a flagpole?
a)
m
b)
km
c)
mm
d)
cm
76.
What is the sum of the interior angles (in degrees) of an octagon?
a)
1080
b)
720
c)
900
d)
1260
77.
Evaluate: ∫(x^2) dx from 0 to 2.
a)
8/3
b)
5/3
c)
2/5
d)
8/5
78.
In how many ways can you line up 5 persons to get on a bus?
a)
120
b)
1
c)
5
d)
60
79.
What part of an hour has passed from 2:48 pm to 3:32 pm of the same day?
a)
11/15
b)
13/15
c)
11/12
d)
14/15
80.
How many positive factors does 120 have?
a)
16
b)
12
c)
18
d)
20
81.
Suppose a conditional has a false premise and a true conclusion. The inverse of this conditional is
a)
false
b)
True
c)
no value
d)
unknown
82.
What is the center of the circle (x + 3)^2 + (y + 2)^2 = 9?
a)
(-3, -2)
b)
(3, -2)
c)
(3, 2)
d)
(-3, 2)
83.
What is the equation of a line parallel to x – 3y = 5 passing through (-1, -4)?
a)
x – 3y = 11
b)
x – 3y = 10
c)
x – 3y = 9
d)
x – 3y = 8
84.
Which of the following softwares below is best for statistical analysis?
a)
SPSS
b)
GeoGebra
c)
Quizizz
d)
Microsoft Office
85.
About how many percent of the class fall between -2SD and +2SD in the normal curve?
a)
95.44
b)
99.85
c)
99.72
d)
68.26
86.
In how many ways can 10 flowers be planted in a circular lot?
a)
362880
b)
380628
c)
388620
d)
328860
87.
If 7 coins are tossed together, in how many ways can they fall with at most 3 heads?
a)
64
b)
63
c)
260
d)
259
88.
B is a point on Circle A with diameter CD. If BC = 6 and BD = 8. What is the area of the circle (in square units)?
a)
25π
b)
50π
c)
75π
d)
100π
89.
You would like your students to understand the trend of sales of the school canteen. Which of the following graphs is best to use?
a)
line graph
b)
pie graph
c)
frequency polygon
d)
pictograph
90.
The sum of 2 numbers is 36 and their difference is 14. What is their product?
a)
275
b)
250
c)
257
d)
259
91.
A rectangle has a perimeter of P = 18x – 14. If the length is 6x + 3, find the area?
a)
18x^2 – 51x – 30
b)
18x^2 + 51x – 30
c)
9x^2 – 21x + 30
d)
15x^2 + 31x – 20
92.
How long (in years) should Php25,000 be invested at 5% simple interest so that it would become Php30,000?
a)
4
b)
4.5
c)
5
d)
5.5
93.
It is a part of the mathematical investigation paper where the investigators check if the formulas found is true for all cases
a)
Justifying
b)
Deriving
c)
Verifying
d)
Summarizing
94.
Find the equation of an ellipse in the general form if the equation of the ellipse in the standard form is given by:
[(x - 7)^2 / 4] + [(y - 2)^2 / 25] = 1
a)
25x^2 + 4y^2 - 350x - 16y + 1241 = 0
b)
25x^2 + 4y^2 - 350x - 16y - 1241 = 0
c)
25x^2 - 4y^2 - 350x - 16y + 1241 = 0
d)
25x^2 - 4y^2 - 350x + 16y + 1241 = 0
95.
Suppose p is a proposition. What is the truth value of
(p V ¬ p)?
a)
always true
b)
never true
c)
always false
d)
sometimes true
96.
Find the area of the region bounded by
y = 2 − x^2 and y = −x
a)
9/2
b)
11/3
c)
10/3
d)
14/3
97.
Higher scores in Test A are associated with high scores in Test B. There is _____ correlation between the two tests.
a)
a positive
b)
a negative
c)
no
d)
absolute
98.
The numbers 1, 2, and 3 are said as yi, er, san in this language. What is this language?
a)
Chinese
b)
Japanese
c)
Koreans
d)
Mongolia
99.
How much will an amount (in Php) be after 7 years when Php120,000 is invested at 4% compounded quarterly?
a)
158554.92
b)
173154.95
c)
174554.92
d)
175554.93
100.
Item #7 got a difficult index of 0.01. What does it imply about item #7?
a)
very difficult
b)
very easy
c)
moderately easy
d)
moderately difficult
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