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Basic Math Quiz
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Question 1WRONG
The reservoir is at full capacity at the beginning of summer. By the first day of fall, the level in the reservoir
is 40% below full capacity. Then during the fall, a period of heavy rains raises the level by 40%. After the
rains, the reservoir is at what percent of its full capacity?80%84%90%100%
Question 1 Explanation:
first day of the fall: the reservoir is 60% of full capacity during heavy rains, the reservoir raises 40% of 60%
full capacity of the reservoir after the rain = 60% + ( 0.4 x 0.6) = 60% + 24% = 84% full capacity of the
reservoirQuestion 2
WRONG
Of all the participants on a camping trip last summer, 70% were over 15 years old. If 63 of those who
attended were 15 years old or below, what was the total number of participants in the camp?200330120210
Question 2 Explanation:
let x = total number of participants (30%)x = 63 0.3x = 63 x = 63/0.3 x = 210Question 3
WRONG
The ratio of men to women at a concert was 2:3. If there were 350 people in the concert, how many women
were there?150140200210
Question 3 Explanation:
2:3, ratio of men to women. Let k = constant which we will use as multiplier to the ratio 2k + 3k = 350 5k =
350 k = 350/5 k = 70 the total number of women in the concert is (70)(3) = 210Question 4
WRONG
What is the difference between 72, 846 divided by twice of three and seventy-five multiplied twice?11, 99124, 13218, 6576, 516
Question 4 Explanation:
[72,846 / (2 X 3)] - (75)(75) = (72,846 / 6) - 5,625 = 12,141 - 5625 = 6,516Question 5
WRONG
Determine the value of k so that the line kx – 8 + 7y = 0 will be parallel to the line 2x – y + 1 = 0.9-146-3
Question 5 Explanation:
line 1: kx - 8 +7y = 0 y = -[k/7]x + 8/7 m1= -k/7 line 2: 2x-7+1 = 0 y = 2x+1 m2 = 2 if line 1 is parallel to
line 2, then their slope must be equal to each other. m1 = m2 -k/7 = 2 k = 2 X -7 k = -14Question 6
WRONG
The age of Jennilyn 3 years ago is ¼ her age 6 years from now. How old is Jennilyn?124618
Question 6 Explanation:
Let the present age of Jennilyn be equal to x. Present age = x 3 years ago = x-3 6 yrs from now = x +6 x – 3
= ¼ (x + 6) 4(x – 3) = x + 6 4x – 12 = x + 6 3x = 18 x = 6 , Jennilyn is 6 years oldQuestion 7
WRONG
Mrs. Isagani can embroider a tablecloth in 10 days while Mrs. Rosas can embroider the same tablecloth in 2
½ days. How long will it take both of them to embroider one such tablecloth?5/13 days7/10 days2 days1/2 days
Question 7 Explanation:
Mrs. Isagani: rate = 1/10 time = x work = x/10 Mrs. Rosas rate = 5/2 time = x work = 5/2 x The work Mrs.
Isagani and Mrs. Rosas did together equals one whole job = x/10 + 5x/2 = 1 Manipulating the equation, x +
25x = 10 26x = 10 x = 10/26 or 5/13 daysQuestion 8
WRONG
What is the sum of 2.45 multiplied by 0.06 and 0.057 divided by 0.3?1.662.0470.3373.37
Question 8 Explanation:
0.147 + 0.19 = 0.337Question 9
WRONG
Tuwing bakasyon, ginagamit ni Leah ang 30% ng kanyang oras sa pagbabasa ng mga nobela. Sa kabuuan,
kaya niyang matapos ang isang nobela ng pitong oras. Kung siya ay natutulog ng siyam na oras araw-araw,
ilang nobela ang kaya niyang tapusin sa loob ng dalawang linggo?8795
Question 9 Explanation:
24 hours – 9 hours (sleeping) = 15 hours (awake) 30% of 15 hours = 0.3 x 15 = 4.5 hours per day reading a
novel 4.5 x 14 days/2 weeks = 63 hours reading novels in 2 weeks 63 7 hours/novel = 9 novels she can read
in 2 weeksQuestion 10
WRONG
Rocky had a party. Midway in the party, half of the people left. A fifth of those remaining started to sing.
There were 16 remaining who did not sing. How many people came to Rocky’s party?30402050
Question 10 Explanation:
let x = total no. of people in Rocky’s party x[1 - 1/2] [ 1 - 1/5] = 16 x [1/2][4/5] = 16 4/10x = 16 x = 4 X 10 x
= 40Question 11
WRONG
At first stop on his route, a driver unloaded 1/5 of the packages in his truck. After he unloaded another 9
packages at his next stop, 1/2 of the original number of packages in the truck remained. How many
packages were in the van before at the first delivery?50204030
Question 11 Explanation:
let x = original number of packages before the 1st delivery [4/5]x - 9 = [1/2]x [4/5]x - [1/2]x = 9 [(8-5)/10] x
= 9 x = 90/3 x = 30Question 12
WRONG
A rope is cut into three and one-third is used. Then one-fourth of the remaining rope is cut of and used. The
piece left is 6 meters long. How many meters long was the rope originally?12896
Question 12 Explanation:
x [1-1/3] [ 3/4] = 6 x [2/3] [3/4] = 6 6/12 x = 6 x = 6 [12/6] x = 12Question 13
WRONG
If a and b are both odd numbers, then which of the following must be an even number?a + bab + 22a + ba + b + 1
Question 13 Explanation:
a and b are odd numbers, let a = 1 and b = 3 A. 5 = not an even number B. 5= not an even number C. 4 =
an even number D. 5 = not an even numberQuestion 14
WRONG
What is sixty-seven less than the sum of fifty-eight and forty-two?432333-33
Question 14 Explanation:
(58+42)-67 = 100-67 = 33Question 15
WRONG
When buying an item, a man was given a 10% discount on its original price, and then he was charged a 10%
tax on its selling price. Base from this transaction, which of the following is true?
The amount paid is 99% of the original price.The amount paid is 20% lower than the original price.The original price and the selling price are the same.The amount paid is 10% lower than the original price.
Question 15 Explanation:
let OP = original price discounted price = OP – 0.1OP = 0.9OP tax = 0.9OP x 0.1 = 0.09OP amount paid =
discounted price + tax = 0.9OP + 0.09OP = 0.99OPQuestion 16
WRONG
Two cars traveled at the rates of 50 kph and 60 kph respectively. The faster car traveled 2 hours longer than
the slower car and went 150 kms farther. Find the time traveled by the slower car.3745
Question 16 Explanation:
Rate x Time Distance Faster Car: rate = 60 time = t + 2 distance = d + 150 Slower Car: rate = 50 time = t
distance = d 60(t + 2) = d + 150 , 50 t = d 60t + 120 = 50t + 150 60t – 50t = 150 – 120 10t = 30 t = 3
hoursQuestion 17
WRONG
Six consecutive integers are given. The sum of the first three is 27. What is the sum of the last three?33363230
Question 17 Explanation:
six consecutive integers: x, x +1, x + 2, x +3, x + 4, x + 5 sum of first three terms: x + [x+1] + [x+2] = 27
3x + 3 = 27 3x = 24 x = 8 so the six consecutive integers are: 8, 9, 10, 11, 12, 13. The sum of last three
integers: 11 + 12 + 13 = 36Question 18
WRONG
Determine the equation of the line which passes through (4, -2) and has a slope of 3.y = -7x + 5y = 3x - 10y = 4x - 2y = 3x - 42
Question 18 Explanation:
Use point-slope formula, y - y1 = (x= x1)m y – (-2) = (x – 4)(3) y + 2 = 3x – 12 y = 3x – 10Question 19
WRONG
The sum of five consecutive integers is 35. How many of the five consecutive integers are prime numbers?2314
Question 19 Explanation:
five consecutive integers: x, x +1, x + 2, x +3, x + 4 x + [x+1] + [x+2] + [ x+3] + [x+4] = 35 5x + 10 = 35
x = 5 so the five consecutive integers are: 5, 6, 7, 8, 9 let check if their sum is 35: 5 + 6 + 7 + 8 + 9 = 11 +
7 + 8 + 9 = 18 + 8 + 9 = 26 + 9 = 35 the prime numbers are 5 and 7.Question 20
WRONG
A fruit salad mixture consists of apples, banana and peaches in the ratio of 6:5:4 respectively by weight. If
225 grams of mixture is prepared, how many more grams of apples than peaches?
60304575
Question 20 Explanation:
6:5:4 – ratio of apples, banana, & peaches respectively. Let k = constant which we will use as multiplier to
the ratio 6k + 5k + 4k = 225 15k = 225 k = 225/15 k= 15 weight of apple = (6)(15) = 90, weight of banana
= (5)(15) = 75, weight of peaches = (4)(15) = 60 weight of apple – weight of peaches = 90 – 60 = 30 gramsQuestion 21
WRONG
For any integer n, which of the following represents the sequence of three consecutive odd integers?2n + 1, 2n + 2, 2n + 3n, n + 2, n + 4n, n + 1, n + 32n +1, 2n + 3, 2n + 5
Question 21 Explanation:
n is any integer, let n = 1 for odd numbers & n = 2 for even numbers. If n = 1, A. n, n + 1, n + 3 = (1), (1) +
1, (1) + 3 = 1, 2, 4 not consecutive odd integers B. n, n + 2, n + 4 = (1), (1) + 2, (1) + 4 = 1, 3, 5
consecutive odd integers C. 2n + 1, 2n + 2, 2n + 3 = 2(1) + 1, 2(1) + 2, 2(1) + 3 = 3, 4, 5 not a consecutive
odd integers D. 2n + 1, 2n + 3, 2n + 5 = 2(1) + 1, 2(1) + 3, 2(1) + 5 = 3, 5, 7 a consecutive odd integers If
n = 2, A. n, n + 1, n + 3 = (2), (2) + 1, (2) + 3 = 2, 3, 5 not consecutive odd integers B. n, n + 2, n + 4 =
(2), (2) + 2, (2) + 4 = 2, 4, 6 not consecutive odd integers but consecutive even integers C. 2n + 1, 2n + 2,
2n + 3 = 2(2) + 1, 2(2) + 2, 2(2) + 3 = 5, 6, 7 not consecutive odd integers D. 2n + 1, 2n + 3, 2n + 5 = 2(2)
+ 1, 2(2) + 3, 2(2) + 5 = 5, 7, 9 consecutive odd integers D satisfy both sample value for n.Question 22
WRONG
Si Gng. Gonzales ay bumili ng kotse sa halagang P pesos. Pagkalipas ng tatlong taon, ibinenta niya ang kotse
ng 25% higit sa halaga ng pagkakabili niya. Binigyan siya ng babayarang buwis na 50% ng kanyang kita.
Magkano ang kailangang bayaran na buwis ni Gng. Gonzales?P/24P/2P/8P/4
Question 22 Explanation:
let P = original cost of car selling price of car = P + 0.25P = P + [1/4]P tax = 1/2 [(1/4)P] = 1/8 PQuestion 23
WRONG
What is the value of the digit x in order for 5719x to be divisible by 2, 3 and 6?6027
Question 23 Explanation:
5719x to be divisible by 2, 3, and 6 must follow the divisibility rule for 2, 3, and 6. Divisibility rule for 2: last
digit must be an even numbers (0, 2, 4, 6, 8) Divisibility rule for 3: sum of all digits must be divisible by 3.
Divisibility rule for 6: must follow the divisibility rule for 2 and 3. Applying the divisibility rule for 6, we now
get the sum of all digits to check if this number is divisible by 3. 5+7+1+9+x = 22+x, since we need an
even number for the last digit so that it can be divisible by 2, x = 2 so that 22 + 2 = 24, 24 is divisible by 3.Question 24
WRONG
If k = 2 x 10-2, then what does the expression 1/k equal to?50500
0.55
Question 24 Explanation:
k = 0.02 1/k = 1/0.02 = [1/0.02] [100/100] = 100/2 = 50Question 25
WRONG
Which of the following set of fractions arrange in ascending order?5/12, 1/9, 7/8, 11/83/16, 1/7, 2/5, 5/66/19, 7/12, 3/4, 4/513/15, 1/4, 3/8, 5/6
Question 25 Explanation:
A. 0.416, 0.111, 0.875, 0.611 not in ascending order B. 0.187, 0.143, 0.400, 0.833 not in ascending order C.
0.316, 0.583, 0.750, 0.800 in ascending order D. 0.867, 0.250, 0.375, 0.833 not in ascending orderQuestion 26
WRONG
[(800 ÷ 40) + (92 ÷ (17 – 8))] – (22 + 32) = _________.15291642
Question 26 Explanation:
= 20 + 981/9) - (4+9) = 20 + 9 - 13 = 16Question 27
WRONG
Simplify the expression: 5y – {3y + (2y – 5) – [3 – (2 + 4y)]}6 – 4y4y4y + 614y – 6
Question 27 Explanation:
5y – {3y + (2y – 5) – [3 – (2 + 4y)]} = 5y – {3y + (2y – 5) – [3 – 2 – 4y)]} = 5y – {3y + 2y – 5 – (1 – 4y)} = 5y
– {3y + 2y – 5 – 1 + 4y} = 5y – (9y – 6) = 5y – 9y + 6 = 6 – 4yQuestion 28
WRONG
(0.143 + 0.27 + 0.852 + 0.009) – (0.235 + 0.51 + 0.006) = _________.0.8510.7510.4230.523
Question 28 Explanation:
1.274 – 0.751 = 0.523Question 29
WRONG
If r, s, t are three consecutive integers such that r > s > t, then (r – s)(s – t)(r – t) equals:0-1-22
Question 29 Explanation:
Given three consecutive integers: r, s, t and r > s > t. let r = 3, s = 2, t = 1 (r-s)(s-t)(r-t) = (3-2)(2-1)(3-1) =
(1)(1)(2) = 2Question 30
WRONG
Lovely’s grade in four of her quizzes are 83, 86, 89, and 90. There is one more quiz for the grading period
and she does not want an average lower than 85, what is the lowest possible grade that she can get on her
fifth quiz to maintain that average?79777581
Question 30 Explanation:
[83+86+89+90+x]/5 = 85 [348 + x]/5 = 85 x = 77
Algebra Quiz
Congratulations - you have completed Algebra Quiz. You scored 0 out of 30. Your performance has been
rated as Need more practice!
Your answers are highlighted below.
Question 1WRONG
A tank can be filled in 6 hours by pipe A running alone, or in 4 hours by pipe B alone. How many hours would
be needed to fill the tank if both pipes were running?2 and 2/555/123 and 1/2
Question 1 Explanation:
A: Rate: 1/6, Time: x, Work: x/6, B: Rate: 1/4, Time: x, Work: x/4, x/6 + x/4 =1 ; multiply both sides by 12, 2x
+ 3x = 12, 5x = 12, x = 12/5 = 2 2/5Question 2
WRONG
Jack is now 14 years older than Jill. If in 10 years Jack will be twice as old as Jill, how many years old will Jack
be in 5 years?9192123
Question 2 Explanation:
let x = Jill’s age x + 14 = Jack’s age age 10 years from now: jill: x+10 jack: x+24, x + 24 = 2( x + 10 ), x +
24 = 2x + 20, 2x – x = 24 – 20, x = 4 , Jack’s present age: x + 14 = 4 + 14 = 18, 5 years from now: 18 + 5
= 23Question 3
WRONG
Which of the following equations has a root in common with x2 – 6x + 5 = 0?
Question 3 Explanation: Question 4
WRONG
A taxi driver must complete a 180 mile trip in 4 hours. If he averages 50 miles an hour for the first three
hours of his trip, how fast, in miles per hour, must he travel in the final hour?45403035
Question 4 Explanation:
180 miles in a 4-hour travel, 1st 3 hours: 50 mph, ( 50 m / hr )( 3 hr ) = 150 miles, 180 – 150 = 30, 30 miles
in 1 hr, speed on the 4th hr: 30 mphQuestion 5
WRONG
Kung ang a = b + 1/2 = [b+3]/2, ano ang halaga ng a?325/21/3
Question 5 Explanation:
a = b + ½ = [b+3]/2 b + ½ = [b+3]/2; multiply both sides by 2 2b + 1 = b + 3; 2b – b = 3 -1 b = 2 a = b +
½ = 2 + ½ = 2 ½ = 5/2Question 6
WRONG
How many liters of 60% solution of nitric acid should be added to 10 liters a 30% solution of nitric acid to
obtain a 50% solution?25201510
Question 6 Explanation:
10L + x =10+x 30% + 60% = 50% 0.3( 10 ) + 0.6x = 0.5( 10 + x ) 3 + 0.6x = 5 + 0.5x 0.1x = 2 x = 20 LQuestion 7
WRONG
If 2x + 4y – 5z = 19 and z = 3, what is the value of x + 2y + z?1020515
Question 7 Explanation:
2x + 4y - 5z = 19; where z = 3 2x + 4y – 5(3) = 19 2x + 4y = 19 + 15; 2x + 4y = 34, divide both sides by 2
x + 2y = 17, thus, x + 2y + z = 17 + 3 = 20Question 8
WRONG
Grace can finish cleaning their room in 45 minutes. When her sister Abby helps her, it takes them 18 minutes
to clean the room completely. How many minutes would it take Abby to clean their room alone?25303520
Question 8 Explanation:
Grace: Rate: 1/45. Time: 18, Work: 18/45, Abby: Rate: 1/x, Time: 18, Work: 18/x, 18/45 + 18/x = 1 ; multiply
both sides by 45x, 18x + 18( 45 ) = 45x, 45x – 18x = 810, 27x = 810, x = 30 minQuestion 9
WRONG
A man is thrice as old as his son. In five years, he will be three years more than twice his son’s age. How
many years old is the man now?36241041
Question 9 Explanation:
let x – son 3x – man age 5 years from now: son = x+5 man = 3x+5 5 yrs from now, the man’s age is 3 more
than twice the age of his son. 3x + 5 = 3 + 2( x + 5 ), 3x + 5 = 2x + 10 + 3, 3x – 2x = 10 + 3 – 5, x = 8,
man = 3x = 3(8) = 24Question 10
WRONG
Kung ang (x + y)2 = 20 at ang xy = 4, ano ang halaga ng x2 + y2?10141612
Question 10 Explanation: Question 11
WRONG
If -6 is one solution of the equation x2 + 5x + k = 7, where k is constant, what is the other solution?20-11
Question 11 Explanation:
-6 is a solution to x^2 + 5x + k = 7, substitute -6 to all values of x: (-6)^2 + 5(-6) + k = 7, k = 7 – 36 + 30,
k = 1, x^2 + 5x + 1 = 7; x^2 + 5x + 1 - 7 = 0, x^2 + 5x – 6 = 0; factoring: ( x + 6 )( x – 1 ) = 0, x = -6 and
1Question 12
WRONG
Simplify the following expression :
Question 12 Explanation:
, then we multiply by , =Question 13
WRONG
Ano ang halaga ng q sa tumbasang radikal na ?5432
Question 13 Explanation:
we raise both sides to the 2nd power 21 + q = = 9 + 6 + q =21-9 + q - q = 6 12 = 6 = 2 q = 4Question 14
WRONG
What is the equation of the line that passing through (1,1) and parallel to line y = 2x– 5?y = 2x + 1y = 2x - 1y = -(1/2)x + 1y = 2x
Question 14 Explanation:
line parallel to: y = 2x – 5 Passing through pt. (1, 1) Since y = mx + b; m = 2 y = 2x + b; then substitute the
coordinates of pt. (1, 1) 1 = 2(1) + b; b = 1 – 2 b = -1 y = 2x - 1Question 15
WRONG
Bruno raises a number of ducks and carabaos in his farm, all of which are normal. If his animals have a total
of 44 feet and a total of 16 heads, how many carabaos does Bruno have?6578
Question 15 Explanation:
let x – number of ducks, y – number of carabaos, there are 44 feet ( carabaos has 4 and ducks has 2 ) 2x +
4y = 44, there are 16 heads, x + y = 16, x = 16 – y, 2( 16 – y ) + 4y = 44, 32 – 2y + 4y = 44, 2y = 44 – 32 =
12, y = 6 --- carabaosQuestion 16
WRONG
Aling pangungusap ang totoo sa mga graph ng mga tumbasan sa sistemang y = -x + 3 at y = -x – 2?Ang mga graph ng linya ay dumaraan sa mga point (0, 2) at (0, 3).Ang graph ay may iisang linya.Ang mga graph ng dalawang linya ay nagtatagpo sa point (-2, 3).Ang graph ng dalawang linya ay parallel.
Question 16 Explanation:
y = -x + 3, y = -x – 2 from the general form: y = mx + b, where the m is the slope. both equations have
slopes equal to -1 since the have the same slope, these lines are parallel.Question 17
WRONG
One number is 17 less than another. Their sum is 125. What is the smaller number?108715460
Question 17 Explanation:
let x – smaller number, then x + 17 is the bigger number, the sum of the two numbers is 125, x + x + 17 =
125, 2x = 108, x = 54 --- smaller number,Question 18
WRONG
In the diagram at the right, line AB and AC have equal lengths. What is the value of k?
1211109
Question 18 Explanation:
A (1,2) B (9,2) C (1,k) Segment AB = AC AB = X2 – X1 = 9-1 = 8 AC = Y2 – Y1 = k – 2 = 8 k – 2 = 8; k = 8 +
2 k = 10Question 19
WRONG
Which of the following can best describe the graph?cannot be determinedy > 4 – 2xy = 4 – 2xy < 4 – 2x
Question 19 Explanation:
inspect the graph: the line passes through pts. (1, 2) and (4, -4) slope = m = [-4-2]/[4-1] = -6/3 = -2 y = -2x
+ b; then substitute any point. We use pt. (1, 2) 2 = -2(1) +b; b = 2 + 2 b = 4 y = -2x + 4 or y = 4 – 2xQuestion 20
WRONG
What is the slope of the line containing the points (2, -4) and (-5, 7)?-11/7-7/1111/77/11
Question 20 Explanation:
Slope of the line containing pts. (2, -4) and (-5, 7) Slope = m = [y2-y1]/[x2-x1] = [7- (-4)]/[-5-2] = -11/7Question 21
WRONG
Ang eksponensyal na ekspresyong 32/n sa pormang radical ay _______.
Question 21 Explanation: Question 22
WRONG
How many students are there in a class if two students are not seated when 4 rows of seat are filled and 9
students are not seated when 3 rows of seats are filled?28363034
Question 22 Explanation:
4x + 2 = 3x + 9, where x is the number of students per row, 4x – 3x = 9 – 2 , x = 7, then substitute to above
equation, 4(7) + 2 = 30 --- studentsQuestion 23
WRONG
Factor out the expression ab – 1 – b + a completely:(b + 1)(a + 1)(b – 1)(a – 1)(b – 1)(a + 1)(b + 1)(a – 1)
Question 23 Explanation:
ab – 1 – b + a = ( ab – b) + ( a – 1) = b ( a – 1) + ( a – 1) = ( b + 1) ( a – 1)Question 24
WRONG
A train covers the distance d between two cities in h hours arriving 2 hours late. What speed would permit
the train to arrive on schedule?[d/h]-2dh-2d/[h-2]h-2
Question 24 Explanation:
d/h is the speed arriving 2 hrs late. Where d is the distance and h is time ( hrs.). To arrive in schedule, the
train has to travel distance d in h – 2 hours. Rate = distance/time = d/[h-2]Question 25
WRONG
Alin sa mga sumusunod na ekspresyon ang perfect square trinomial?
Question 25 Explanation:
perfect square trinomial:Question 26
WRONG
Pasimplehin ang ekspresyong:
Question 26 Explanation: Question 27
WRONG
What is the solution set (x, y) in system of equations: 2x – 3y = 12 and 3x + y = 7?(3, -2)(-2, 3)(-3, 2)(2, -3)
Question 27 Explanation:
2x – 3y = 12, 3x + y = 7, using substitution method: 3x + y = 7, y = 7 – 3x; then substitute to the other
equation 2x – 3( 7 – 3x ) = 12, 2x – 21 + 9x = 12, 11x = 33, x = 3, y = 7 – 3x = 7 – 3(3) = 7 – 9, y = -2,
solution: ( 3,-2 )Question 28
WRONG
Jerry ran a 200 – meter dash race at an average speed of 2.4 kph. If Ryan ran the same race at an average
speed of 3 kph, how many minutes longer did it take for Jerry to complete the race?1 min2 min3 min4 min
Question 28 Explanation:
Ryan – 3 kph, Jerry – 2.4 kph, Ryan: ( 200m )( 1 hr / 3000m ) = 1/15 hr = 4min, Jerry: ( 200m )( 1 hr /
2400m ) = 1/12 hr = 5min, Difference: 1 minQuestion 29
WRONG
For which value of p in the division (2x2 + 11x – p) ÷ (2x – 3) is the remainder zero?182135
Question 29 Explanation:
( 2x^2 + 11x – p ) / ( 2x – 3 ) divisor: 2x – 3 = 0; 2x = 3; x = 3/2 using factor theorem, 2( 3/2 )^2 + 11( 3/2 )
– p = 0, 2(9/4) + 33/2 – p = 0 9/2 + 33/2 – p = 0 42/2 – p = 0 p = 21Question 30
WRONG
The attendance at Enchanted Kingdom on a certain day was 737 persons. If there were 289 more adults than
children, how many children were there? 548513250224
Question 30 Explanation:
let x – adults, then x – 289 is the number of children, there are a total of 737 persons, thus x + x – 289 =
737, 2x = 1026, x = 513 --- adults, children: x – 289 = 513 – 289 = 224
Geometry / Trigonometry Quiz
Congratulations - you have completed Geometry / Trigonometry Quiz. You scored 0 out of 30. Your
performance has been rated as Need more practice!
Your answers are highlighted below.
Question 1WRONG
In the figure to the right, QRST is a parallelogram. If the
measure of angle TQR = 85o, then what is the measure of angle TSR??1051158595
Question 1 Explanation:
Opposite angle of a parallelogram are congruent.Question 2
WRONG
what is the value of tan θ? 3/45/34/5
4/3
Question 2 Explanation:
tan = y/x = opposite/adjacent = 8/6 = 4/3Question 3
WRONG
In the diagram, each small square is 1 cm by 1 cm. What is the area
of the non-shaded region? 632.754.5
Question 3 Explanation:
A=bh/2, b=2cm, h=3cm, A=[1/2] [2] [3] = 3 cm^2Question 4
WRONG
Which of the following statements is/are true? I. Two points are contained in one and only one line.
II. A segment has a unique midpoint. III. On a ray, there are many points given distance from
the endpoint to the ray.I and II onlyI onlyII onlyIII only
Question 4 Explanation:
A segment has a unique midpoint. Two points are contained in one and only one line.Question 5
WRONG
In the figure at the above, what is the value of y?
cannot be determined604530
Question 5 Explanation:
Vertical angles are congruent 2y = x x+x+2x+2x = 360 6x = 360 x = 60 60 = 2y y = 30°Question 6
WRONG
In a regular hexagon, the measure of each interior angle is ________.100160140120
Question 6 Explanation:
Regular hexagon, n = 6, 6 angles, (n-2)(180) = (6-2)(180) 180(4) = 720 = total interior angles 720/6 = 120Question 7
WRONG
Given three squares of different areas, the perimeter of square A is 2/3 the perimeter of square B, and the
perimeter of square B is 2/3 the perimeter of square C. If the area of square A is 16 square units, what is the
area of square C?36816472
Question 7 Explanation:
PA= 2/3 PB PB = 2/3 PC A[A]= 16units = S^2 S^2 = 16 S = 4 P[A] = 16 = 2/3 P[B] P[B] = 24 24 = 2/3 P[C]
PC = 36 4S = 36 S = a A[C] = S^2 = 81Question 8
WRONG
From the figure above, what is the value of x if TP= 2x +
1; SP= 4 – 3y; RP= y + 5; QP=x – 5?11/323/717/415/2
Question 8 Explanation:
TP = 2x+1 RP =y+5 SP = 4-3y QP = x-5 TP = RP SP = QP diagonals of a parallelogram bisect each other.
Substituting and Equating 1. 2x+1 = y+5 2. 4-3y = x-5 using equation 2: x = 9-3y substituting to equation 2:
2(9-3y) = y+5 18-6y = y+5 7y = 11 y = 11/7 x = 9-3 (11 / 7) = (8- 33) / 7 = (56-33) / 7 x = 23/7Question 9
WRONG
How many different segments are determined by four collinear points A, B,
C, D?
84106
Question 9 Explanation:
1. AD 2. AC 3. BD 4. AB 5. BC 6. CDQuestion 10
WRONG
What is the height of Quezon City Hall if the shadow of the building is 20 meters and the angle of elevation of
the sun is 300?
Question 10 Explanation:
Question 11WRONG
If the lengths of the sides of a square are doubled, what is the effect on the area?The area will increase 8 times.The area will increase 4 times.The area will increase twice.The area will remain the same.
Question 11 Explanation:
let: s=2 s1=4 A = s^2 2^2 = 4 A1 = s1^2 4^2 = 16 4 = 4X4 s = 4 X s1Question 12
WRONG
The figure above shows a rectangular parcel of land
divided into lots of equal size, as shown by the dotted lines. If the area of three of the lots is equal to one-
fourth of the total area in the parcel, then how many feet wide is each lot?60
409030
Question 12 Explanation:
Area of 3 lots = ¼ of area of rectangle, ¼ * 360 = width of lot = 90, 90/3 = width of 3 lots = 30ftQuestion 13
WRONG
ABCD is a trapezoid with AB parallel to CD. XY is the
median. If AB = 6 and XY = 13, then what is the length of CD?20221618
Question 13 Explanation:
13 = [AB + CD]/2 13 = [6+CD]/2 = 26 = 6+CD CD = 26-6 CD = 20Question 14
WRONG
is equal to?
Question 14 Explanation:
Question 15WRONG
In the right triangle ABC, what is the value of cos θ?3/54/55/33/4
Question 15 Explanation:
cos = adjacent / hypotenuse = 6/10 = 3/5Question 16
WRONG
A rectangular solid with dimensions 2, 12, and q has the same volume as a cube with an edge length of 6.
What is the value of q?75119
Question 16 Explanation:
V = 2 * 12 * q = 24q V = 6^3 =216 V solid rectangle = V cube 216 = 24q q = 216/24 = 36*6/24 = 9 q =
9Question 17
WRONG
How many sides of a regular polygon if has a sum of 1, 800o in its interior angle?10121311
Question 17 Explanation:
Total interior angles = (n-2)(180) 1800= (n-2)(180) n-2 = 1800/180 = 10 n-2 = 10 n = 10+2 n = 12Question 18
WRONG
Given the figure, AB = CD, AC = BC = 4. What is AD?
Question 18 Explanation:
Question 19WRONG
Find tan θ if sin θ = 2 / 3 and θ is not in the first quadrant
Question 19 Explanation:
Question 20WRONG
The longest side of ΔABC is ______.BC
cannot be determinedACBA
Question 20 Explanation:
angle A: 25 angle B: 75 angle C: 80 Longest side is side opposite the largest angle. AB is the longest side.Question 21
WRONG
Which of the following statements is/are false? I. A square is a rectangle with four congruent sides. II.
Rectangles have no congruent angles. III. A rhombus is a parallelogram with four congruent sides.II onlyI onlyI and II onlyIII only
Question 21 Explanation:
Rectangle have no congruent angles: False Rectangle is quadrilateral with four congruent angles.Question 22
WRONG
What is the area of the kite whose diagonals have lengths 12 and 7?40422430
Question 22 Explanation:
Question 23WRONG
Convert 225o to radians:
Question 23 Explanation:
5 * \frac{\Pi radians}{4} Question 24
WRONG
In the coordinate system given, in which quadrant is sin
θ positive and cos θ negative? IIIIIIIV
Question 25WRONG
If the area of the triangle in the figure above is 12, then what
is the value of r?1342
Question 25 Explanation:
Question 26WRONG
An equilateral triangle has the same perimeter as a square. What is the area of the square if the triangle has
side equal to 16?16914410081
Question 26 Explanation:
P[triangle] = P[square], s=16, P=48 P=48 = 4S and S=12, A= S^2 = 12^2 =144Question 27
WRONG
The length of a rectangle is twice the width and is equal to the side of a square. Which of these statements
is true?The area of the square is 1 / 2 times that of the rectangle.The area of the rectangle is 1 / 4 times that of the square.The area of the rectangle is 1 / 2 times that of the square.The area of the square is 1 / 4 times that of the rectangle.
Question 27 Explanation:
Rectangle: L = 2x, w = x area: L X W = 2x * X area of rectangle = 2x^2 Square: side = 2x Area = S^2 =
(2x)^2 area of square = 4x^2 Area of rectangle is ½ the area of squareQuestion 28
WRONG
What is the value of x in the diagram shown?22
4422/340
Question 28 Explanation:
Vertical angles are congruent 2x = x+22 2x-x = 22 x = 22Question 29
WRONG
In the figure, the side of each small square is 27
centimeters. What is the length of MN?24 cm21 cm15 cm18 cm
Question 29 Explanation:
Question 30WRONG
Convert to degrees:
Question 30 Explanation:
Advanced Math Quiz
Congratulations - you have completed Advanced Math Quiz. You scored 0 out of 30. Your performance has
been rated as Need more practice!
Your answers are highlighted below.
Question 1WRONG
What is the 25th term of an arithmetic sequence whose 7th and 20th terms are 20 and 59 respectively?517455
77
Question 1 Explanation:
Given :
a7 = 20
a20 = 59
a7 = a1 +(7-1)d
a20 = a1 +(20-1)d
20 = a1+6d 59 = a1+19d
Solving by elimination, we can solve the value of d.
a1+19d = 59 a1+19d = 59
- a1+6d = 20 +- a1-6d = -20
13d/13 = 39/13
d = 3
Solving for a1: Solving for a25:
20=a1+6(3) a25 = a1+24d
20 = a1+18 = 2 + 24(3)
a1 = 20-18 = 2+72
a1 = 2 a25 = 74Question 2
WRONG
If x1 = 5, x2 = 6, x3 = 9, x4 = 13, x5 = 14, x6 = 16, what is the value of ?45504749
Question 2 Explanation:
= x1+x2+x3+x4+x5 = 5+6+9+13+14 = 47Question 3
WRONG
Which of the following expressions is not a function?y = 9 – xy = 2x + 1
Question 3 Explanation:
Function - defined as a relation with one-to-one correspondence. It means that for every value of X in the
given equation, there corresponds a unique value of Y.
, is not a function because given a value of x say x=4, there corresponds two values for Y, 2 and -2Question 4
WRONG
A box contains 5 red balls, 4 blue balls, and 3 white balls. If a ball is chosen at random, what is the
probability that it is not blue?2/33/41/37/12
Question 4 Explanation:
Probability not blue = [5+3]/12
= 8/12
= 2/3Question 5
WRONG
In how many ways can the letters of the word MERCY be arranged?5025120100
Question 5 Explanation:
Solving for permutation for different objects nPn =n(n-1)(n-2)...(3)(2)(1) or n! 5! = 5*4*3*2*1 = 120 waysQuestion 6
WRONG
Which of the following is/are TRUE? I. Given the sequence 5, 10, 20, 40, 80, . . . is an arithmetic
sequence II. In the sequence 7, 14, 21, 28, 35, . . the next term is 70 III. Given the sequence 2, 5, 8, 11,
14, 17 the common difference is 3II onlyI and II onlyI onlyIII only
Question 6 Explanation:
Statement I is false because it shows geometric sequence. Statement II is false because the next term is 42.Question 7
WRONG
On a certain street, there are an odd number of houses in a row. The houses in the row are painted
alternately blue and yellow, with the first house painted blue. If n is the total number of houses in the row,
how many of the houses are painted blue?n/2 + 1[n+1]/2n/2 - 1[n-1]/2
Question 7 Explanation:
Let n = Total number of houses
n-1 = Odd number of house
[n-1]/2 = Houses that are painted blueQuestion 8
WRONG
If an amoeba can produce 4 amoebas every six hours, how many amoebas will there be after one day if the
reproduction started with one amoeba?82256374312
Question 8 Explanation:
After 6 hrs = 4 amoebas After 12 hrs = 4*4= 16 amoebas After 18 hrs =16*4= 64 amoebas After 24 hrs
=64*4=256 amoebasQuestion 9
WRONG
A sample of 30 companies belonging to a certain industry reported the following number of employees.43 33 24 51 36 3150 46 50 29 40 2538 35 31 35 42 5047 21 45 45 28 3658 62 37 55 52 49
What is the range of given set of data? 63415640
Question 9 Explanation:
Range = Highest value – Lowest Value
= 62 – 21 = 41Question 10
WRONG
A committee consists of three girls (Ana, Betty, Connie) and five boys (Ryan, Ben, Ceasar, Francis, Dan). A
delegate to a conference is to be chosen from the committee. What is the chance that a boy will be
selected?3/81/81/75/8
Question 10 Explanation:
Total number of delegates = 8
Total number of boys = 5
Probability = 5/8Question 11
WRONG
What is the sum of the first six terms in the arithmetic progression whose first three terms are –1, 1, and 3?26252324
Question 11 Explanation:
Sum of first 6 terms:
a1= -1
a6 = -1 + 5(2) = 9
sn = n/2(a1+a6)
s6 = 6/2(-1+9)
= (3)8
= 24Question 12
WRONG
What is the range of g(x) =all real numbersall real numbers greater than or equal to -1/5all real numbers greater than -1/5all real numbers greater than 0
Question 12 Explanation:
Solving for the range is also the same as solving for the domain.
y =
5y = 2x^2-1
5y + 1 = 2x^2
Range is defined as all possible values of y correspond to value of x. From the given equation must be
greater than or equal to zero.
Therefore, range for given equation: all real numbers greater than or equal to -1/5 5y +1 Therefore, range
for given equation: all real numbers greater than or equal to zero.Question 13
WRONG
A sample of 30 companies belonging to a certain industry reported the following number of employees.43 33 24 51 36 3150 46 50 29 40 2538 35 31 35 42 5047 21 45 45 28 3658 62 37 55 52 49
What is the population mean if the sum is 1224? 46.440.840.648.3
Question 13 Explanation:
n = 30
sum = 1224
average: 1224/30 = 40.8Question 14
WRONG
Linda started working at a monthly salary of P5, 600.00 and steadily received an annual increase of P250.
How much did she earn in the 11 years that she worked in that office?P69, 700.00P69, 950.00P64, 100.00P67, 200.00
Question 14 Explanation:
a1= 5,600 * 12
= 67,200 (starting annual salary)
n = 1 d = 250
a11 = a1+(11-1)d
= 67,200 +10 (250)
= 67,200 +2,500
= 69,700Question 15
WRONG
If Nelly gets 3 in his first quiz and 6 in his second quiz, and doubles his quiz everytime they have quiz, what
will be his average score after their fifth quiz?18.621.520.422.8
Question 15 Explanation:
1st Quiz = 3
2nd Quiz = 6
3rd Quiz = 12
a1 = 3 r = 2
93/5 = 18.16Question 16
WRONG
Fifty-one electric poles are placed along a straight highway such that the distance between the first and the
last pole is 2 250 meters and the distance between any two consecutive poles are equal. How many meters
apart are any two successive poles?50 meters40 meters45 meters30 meters
Question 16 Explanation:
Getting the distance between the two poles, we must get the number of between the two poles:
51-1 = 50
2,250 / 50 = 45 metersQuestion 17
WRONG
In statistics, a/an __________ is an arrangement of data according to size or magnitude.DiscriminantFrequencyArrayMatrix
Question 17 Explanation:
Array is the arrangement of data according to size or magnitudeQuestion 18
WRONG
The first term of an arithmetic progression is 6 and the common difference is –3. What term is –51?21202223
Question 18 Explanation:
Given: a1= 6 d = -3
an= -51 n = ?
an = a1+ (n-1)d
-51 = 6+(n-1)(-3)
-51 = 6 +-3n+3
-51 = 9 + -3n
-51-9 = -3n
-60 = -3n
n = 20Question 19
WRONG
In a circular dining table, 5 guests are to be seated. In how many ways can the five guests sit?10241230
Question 19 Explanation:
Solving by circular permutation P = (n-1)! = (5-1)! = 4! = 24Question 20
WRONG
In how many ways can a committee of 4 be chosen from a group of 8 people?
48702432
Question 20 Explanation:
Solving by combination
C = n!/[(n-r)!r!]
n = 8 r = 4
8!/[(8-4!)4!
[4x2x7x6x5]/[4x3x2x1]
=2x7x5
C = 70Question 21
WRONG
A sample of 30 companies belonging to a certain industry reported the following number of employees.43 33 24 51 36 3150 46 50 29 40 2538 35 31 35 42 5047 21 45 45 28 3658 62 37 55 52 49
What is the median?41404342
Question 21 Explanation:
To solve for the median, arrange the set of data in increasing order.
21 24 25 28 29 31 31 33 35 35 36 36 37 38 40 42 43 45 45 46 47 49 50 50 50 51 52 55 58 62
15th = 40
16th = 42
median = [N+1]/2 = [30+1]/2 = 31/2 = 15.5th score
x15 = 40
x16 = 42
[40+42]/2 = 41Question 22
WRONG
In a geometric progression 1, 2, 4, 8, . . . how many terms are added if the sum is 127?6789
Question 22 Explanation:
Given: a1 =1
sn = 127
a2 =2
n = ?
r=a2/a1 = 2/1 = 2
sum of nth terms in geometric progression:
sn = [a1(1-r^n)]/ [1-r]
127 = [1(1-2^n)]/(1-2)
-127 = 1-2^n
-2^7= -2^n
n=7 -127 = 1-2n -127-1 = -2n -27= -2n n = 7Question 23
WRONG
The percentiles are the scores-points that divide a distribution into 100 equal parts. What do you call a
distribution that divides into 10 equal parts?inter quartileDecileQuartiletenths
Question 24WRONG
If Jun saves P10.00 on the first week and adds P4.00 each week, how much will he save on the last week of
the 3rd month?P40.00P54.00P50.00P58.00
Question 24 Explanation:
a1= 10.00
d = 4.00
an= 4 * 3 = 12wks
a12 = a1+(12-1)d
= 10.00 + (11) 4.00
= 10.00 + 44.00
= 54.00Question 25
WRONG
If f(x) = , what is the domain of f(x)?The domain of f(x) are all real numbers.The domain of f(x) are all real numbers except 3.The domain of f(x) are all real numbers except 0.The domain of f(x) are all real numbers except -3.
Question 25 Explanation:
Solving for the domain, take note that division by zero is undefined. From the given equation, x-3 must not
be equal to zero and must not be included into the domain. Therefore the domain of f(x) are all real number
except x = 3Question 26
WRONG
In the geometric progression 4, 12, 36, 108, . . . the common ratio is:211/33
Question 26 Explanation:
solving for the common ratio:
r = a2/a1 = a3/a2 = a4/a3
r = 12/4 = 36/12 = 108/36
r = 3Question 27
WRONG
Given the table below, what is the equation of the given relation?X 0 1 2 3 4 5
y 1 3 5 7 9 11y = x
y = 2x
y = 2x – 1
y = 2x + 1
Question 27 Explanation:
SLOPE (m)= (y2-y1)/(x2-x1)
=(3-1)/(1-0)
m=2
(y-intercept) b=1
y=mx+b
y=2x+1Question 28
WRONG
If two dice are tossed together, in how many ways can they fall?3612246
Question 28 Explanation:
each die has 6 possible outcomes, so 6x6 = 36Question 29
WRONG
A sample of 30 companies belonging to a certain industry reported the following number of employees.43 33 24 51 36 3150 46 50 29 40 2538 35 31 35 42 5047 21 45 45 28 3658 62 37 55 52 49
What is/are the mode/s of the set of data? 4545 and 355050 and 45
Question 29 Explanation:
Most Frequent data is 50Question 30
WRONG
What is the value of 3! (3 factorial)?cannot determine136
Question 30 Explanation:
3! = 3*2*1 = 6