Basic Math Quiz

Basic Math Quiz

Congratulations - you have completed Basic completed  Basic Math Quiz  Quiz . You scored 0 out of 30. Your performance has been rated as Need more  practice! Post your Results on our Fanpage or the comments section below to view how well you did compared to others [UPCAT is a ranking system afterall.:D] and please dont forget to click the share button to share the quiz with your classmates!^^ ps. you

still have to adjust your scores for the UPCAT Penalty of correct - 1/4 wrong. Your answers are highlighted below.

Question 1 WRONG

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 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 reservoir  Question 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 was the total total number of of participants in the camp? camp? 200 330 120 210 Question 2 Explanation Explanation::

let x = total number of participants (30%)x = 63 0.3x = 63 x = 63/0.3 x = 210 Question 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? 150 140 200 210 Question 3 Explanation 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) = 210 Question 4 WRONG

What is the difference between 72, 846 divided by twice of three and seventy-five multiplied twice? 11, 991 24, 132 18, 657 6, 516 Question 4 Explanation Explanation::

[72,846 / (2 X 3)] - (75)(75) = (72,846 / 6) - 5,625 = 12,141 - 5625 = 6,516 Question 5 WRONG Determine the value of k  of  k so so that the line kx –  kx  – 8 8 + 7y = 0 will be parallel to the line 2x  –   – y y + 1 = 0. 9 -14 6 -3

Question 5 Explanation 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 = -14 Question 6 WRONG

The age of Jennilyn 3 years ago is ¼ her age 6 years from now. How old is Jennilyn? 12 4 6 18 Question 6 Explanation 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 3 = ¼ (x + 6) 4(x –  4(x  – 3) 3) = x + 6 4x –  4x  – 12 12 = x + 6 3x = 18 x = 6 , Jennilyn is 6 years old Question 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 days 7/10 days 2 days 1/2 days Question 7 Explanation 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 days Question 8 WRONG What is the sum of 2.45 multiplied by 0.06 and 0.057 divided by 0.3? 1.66 2.047 0.337 3.37 Question 8 Explanation Explanation::

0.147 + 0.19 = 0.337 Question 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? 8 7 9 5 Question 9 Explanation Explanation::

24 hours –  hours – 9 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 weeks Question 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? 30 40 20 50 Question 10 Explanation:

Question 5 Explanation 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 = -14 Question 6 WRONG

The age of Jennilyn 3 years ago is ¼ her age 6 years from now. How old is Jennilyn? 12 4 6 18 Question 6 Explanation 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 3 = ¼ (x + 6) 4(x –  4(x  – 3) 3) = x + 6 4x –  4x  – 12 12 = x + 6 3x = 18 x = 6 , Jennilyn is 6 years old Question 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 days 7/10 days 2 days 1/2 days Question 7 Explanation 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 days Question 8 WRONG What is the sum of 2.45 multiplied by 0.06 and 0.057 divided by 0.3? 1.66 2.047 0.337 3.37 Question 8 Explanation Explanation::

0.147 + 0.19 = 0.337 Question 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? 8 7 9 5 Question 9 Explanation Explanation::

24 hours –  hours – 9 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 weeks Question 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? 30 40 20 50 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 = 40 Question 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? 50 20 40 30 Question 11 Explanation:

let x = original number of packages before the 1st delivery delivery [4/5]x - 9 = [1/2]x [4/5]x - [1/2]x = 9 [(8-5)/10] x = 9 x = 90/3 x = 30 Question 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? 12 8 9 6 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 = 12 Question 13 WRONG If a If  a and b are both odd numbers, then which of the following must be an even number? a+b ab + 2 2a + b a+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 number  Question 14 WRONG

What is sixty-seven less than the sum of fifty-eight and forty-two? 43 23 33 -33 Question 14 Explanation:

(58+42)-67 = 100-67 = 33 Question 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 0.1OP = 0.9OP tax = 0.9OP x 0.1 = 0.09OP amount paid = discounted price + tax = 0.9OP + 0.09OP = 0.99OP Question 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.

3 7 4 5 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 hours Question 17 WRONG Six consecutive integers are given. The sum of the first three is 27. What is the sum of the last three? 33 36 32 30 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 = 36 Question 18 WRONG Determine the equation of the line which passes through (4, -2) and has a slope of 3. y = -7x + 5 y = 3x - 10 y = 4x - 2 y = 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 – 10 Question 19 WRONG The sum of five consecutive integers is 35. How many of the five consecutive integers are prime numbers? 2 3 1 4 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? 60 30 45 75 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 grams Question 21 WRONG

For any integer n, which of the following represents the sequence of three consecutive odd integers? 2n + 1, 2n + 2, 2n + 3 n, n + 2, n + 4 n, n + 1, n + 3

2n +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/24 P/2 P/8 P/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 P Question 23 WRONG What is the value of the digit  x in order for 5719 x to be divisible by 2, 3 and 6? 6 0 2 7 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 -2

If k = 2 x 10 , then what does the expression 1/k equal to? 50 500 0.5 5 Question 24 Explanation:

k = 0.02 1/k = 1/0.02 = [1/0.02] [100/100] = 100/2 = 50 Question 25 WRONG

Which of the following set of fractions arrange in ascending order? 5/12, 1/9, 7/8, 11/8 3/16, 1/7, 2/5, 5/6 6/19, 7/12, 3/4, 4/5 13/15, 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 order  Question 26

WRONG

[(800 ÷ 40) + (9 2 ÷ (17 – 8))] – (22 + 32) = _________. 15 29 16 42 Question 26 Explanation:

= 20 + 981/9) - (4+9) = 20 + 9 - 13 = 16 Question 27 WRONG

Simplify the expression: 5y – {3y + (2y – 5) – [3 – (2 + 4y)]} 6 – 4y 4y 4y + 6 14y – 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 – 4y Question 28 WRONG

(0.143 + 0.27 + 0.852 + 0.009)  – (0.235 + 0.51 + 0.006) = _________. 0.851 0.751 0.423 0.523 Question 28 Explanation:

1.274 – 0.751 = 0.523 Question 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 -2 2 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) = 2 Question 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? 79 77 75 81 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 1 WRONG

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 2/5 5 5/12 3 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 2/5 Question 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? 9 19 21 23 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 = 23 Question 3 WRONG Which of the following equations has a root in common with  x2 – 6 x + 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? 45 40 30 35 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 mph Question 5 WRONG

Kung ang a = b + 1/2 = [b+3]/2, ano ang halaga ng a? 3 2 5/2 1/3 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 = 5/2 Question 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? 25 20 15 10 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 L Question 7 WRONG If 2 x + 4 y – 5 z = 19 and z = 3, what is the value of  x + 2 y + z ? 10 20 5

15 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 = 20 Question 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? 25 30 35 20 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 min Question 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? 36 24 10 41 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) = 24 Question 10 WRONG Kung ang ( x + y)2 = 20 at ang xy = 4, ano ang halaga ng x2 + y2? 10 14 16 12 Question 10 Explanation: Question 11 WRONG 2

If -6 is one solution of the equation x + 5 x + k = 7, where k is constant, what is the other solution? 2 0 -1 1 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 1 Question 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 ? 5 4 3

2 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 = 4 Question 14 WRONG What is the equation of the line that passing through (1,1) and parallel to line y = 2 x – 5? y = 2x + 1 y = 2x - 1 y = -(1/2)x + 1 y = 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 - 1 Question 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? 6 5 7 8 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 --- carabaos Question 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? 108 71 54 60 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 ?

12 11 10 9 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 = 10 Question 19 WRONG

Which of the following can best describe the graph? cannot be determined y > 4 – 2x y = 4 – 2x y < 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  – 2x Question 20 WRONG What is the slope of the line containing the points (2, -4) and (-5, 7)? -11/7 -7/11 11/7 7/11 Question 20 Explanation:

Slope of the line containing pts. (2, -4) a nd (-5, 7) Slope = m = [y2-y1]/[x2-x1] = [7- (-4)]/[-5-2] = -11/7 Question 21 WRONG Ang eksponensyal na ekspresyong 3 2/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? 28 36 30 34 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 --students Question 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]-2 dh-2 d/[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 min 2 min

3 min 4 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 min Question 29 WRONG 2

For which value of p in the division (2 x + 11 x –  p) ÷ (2 x – 3) is the remainder zero? 18 21 3 5 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 = 21 Question 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? 548 513 250 224 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 1 WRONG

In the figure to the right, QRST is a parallelogram. If the measure of  angle TQR = 85 o, then what is the measure of angle TSR?? 105 115 85 95 Question 1 Explanation:

Opposite angle of a parallelogram are congruent. Question 2 WRONG

what is the value of tan θ? 3/4 5/3 4/5 4/3 Question 2 Explanation:

tan = y/x = opposite/adjacent = 8/6 = 4/3 Question 3 WRONG

In the diagram, each small square is 1 cm by 1 cm. What is the area of the non-shaded region? 6 3 2.75 4.5 Question 3 Explanation:

A=bh/2, b=2cm, h=3cm, A=[1/2] [2] [3] = 3 cm^2 Question 4 WRONG

Which of the following statements is/are true? I. unique midpoint. III. I and II only I only II only III only

Two points are contained in one and only one line. II.

On a ray, there are many points given distance from the endpoint to the ray.

Question 4 Explanation:

A segment has a unique midpoint. Two points are contained in one and only one line. Question 5

A segment has a

WRONG

In the figure at the above, what is the value of  y? cannot be determined 60 45 30 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 ________. 100 160 140 120 Question 6 Explanation:

Regular hexagon, n = 6, 6 angles, (n-2)(180) = (6-2)(180) 180(4) = 720 = total interior angles 720/6 = 120 Question 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? 36 81 64 72 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 = 81 Question 8 WRONG

From the figure above, what is the value of  x if TP= 2 x + 1; SP= 4 –  3 y; RP= y + 5; QP= x – 5?

11/3 23/7 17/4 15/2 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 = 23/7 Question 9 WRONG

How many different segments are determined by four collinear points A, B, C, D? 8 4 10 6 Question 9 Explanation:

1. AD 2. AC 3. BD 4. AB 5. BC 6. CD Question 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 30 0? Question 10 Explanation:

Question 11 WRONG

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 s1 Question 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 40 90 30 Question 12 Explanation:

Area of 3 lots = ¼ of area of rectangle, ¼ * 360 = width of lot = 90, 90/3 = width of 3 lots = 30ft Question 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? 20 22 16 18 Question 13 Explanation:

13 = [AB + CD]/2 13 = [6+CD]/2 = 26 = 6+CD CD = 26-6 CD = 20 Question 14 WRONG is equal to? Question 14 Explanation:

Question 15 WRONG

In the right triangle ABC, what is the value of cos θ? 3/5 4/5 5/3 3/4 Question 15 Explanation:

cos = adjacent / hypotenuse = 6/10 = 3/5 Question 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? 7 5 11 9 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 = 9 Question 17 WRONG How many sides of a regular polygon if has a sum of 1, 800 o in its interior angle? 10 12

13 11 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 = 12 Question 18 WRONG

Given the figure, AB = CD, AC = BC = 4. What is AD? Question 18 Explanation:

Question 19 WRONG

Find tan θ if sin θ = 2 / 3 and θ is not in the first quadrant Question 19 Explanation:

Question 20 WRONG

The longest side of ΔABC is ______. BC cannot be determined AC BA 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.

congruent angles. III. A rhombus is a parallelogram with four congruent sides. II only I only I and II only III 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? 40 42 24 30 Question 22 Explanation:

Rectangles have no

Question 23 WRONG

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? I III II IV Question 25 WRONG

If the area of the triangle in the figure above is 12, then what is the value of r ? 1 3 4 2 Question 25 Explanation:

Question 26 WRONG

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? 169 144 100 81 Question 26 Explanation:

P[triangle] = P[square], s=16, P=48 P=48 = 4S and S=12, A= S^2 = 12^2 =144 Question 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 square Question 28 WRONG

What is the value of x in the diagram shown? 22 44 22/3 40 Question 28 Explanation:

Vertical angles are congruent 2x = x+22 2x-x = 22 x = 22 Question 29 WRONG

In the figure, the side of each small square is 27 centimeters. What is the length of  MN ? 24 cm 21 cm 15 cm 18 cm Question 29 Explanation:

Question 30 WRONG

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 1 WRONG

What is the 25 th term of an arithmetic sequence whose 7 th and 20th terms are 20 and 59 respectively? 51 74 55 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 = 74 Question 2 WRONG

If x1 = 5, x2 = 6, x3 = 9, x4 = 13, x5 = 14, x 6 = 16, what is the value of ? 45 50 47 49 Question 2 Explanation:

= x1+x2+x3+x4+x5 = 5+6+9+13+14 = 47 Question 3 WRONG

Which of the following expressions is not a function? y = 9 – x y = 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 -2 Question 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? 2/3 3/4 1/3 7/12 Question 4 Explanation:

Probability not blue = [5+3]/12 = 8/12 = 2/3 Question 5 WRONG

In how many ways can the letters of the word MERCY be arranged? 50 25 120 100 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 ways Question 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 3 II only I and II only I only III 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]/2 n/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 blue Question 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? 82 256 374 312 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 amoebas Question 9 WRONG A sample of 30 companies belonging to a certain industry reported the following number of employees. 43 33 24 51 36 31 50 46 50 29 40 25 38 35 31 35 42 50 47 21 45 45 28 36 58 62 37 55 52 49 What is the range of given set of data? 63 41 56 40 Question 9 Explanation:

Range = Highest value – Lowest Value = 62 – 21 = 41 Question 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? 3/8 1/8 1/7 5/8 Question 10 Explanation:

Total number of delegates = 8 Total number of boys = 5 Probability = 5/8 Question 11 WRONG

What is the sum of the first six terms in the arithmetic progression whose first three terms are  – 1, 1, and 3? 26 25 23 24 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 = 24 Question 12 WRONG

What is the range of g(x) = all real numbers all real numbers greater than or equal to -1/5 all real numbers greater than -1/5 all 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 31 50 46 50 29 40 25 38 35 31 35 42 50 47 21 45 45 28 36 58 62 37 55 52 49 What is the population mean if the sum is 1224? 46.4 40.8 40.6 48.3 Question 13 Explanation:

n = 30 sum = 1224 average: 1224/30 = 40.8 Question 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, 700.00 P69, 950.00

P64, 100.00 P67, 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 = 69,700 Question 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? 18.6 21.5 20.4 22.8 Question 15 Explanation:

1st Quiz = 3 2nd Quiz = 6 3rd Quiz = 12 a1 = 3 r = 2

93/5 = 18.16 Question 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 meters 40 meters 45 meters 30 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 meters Question 17 WRONG

In statistics, a/an __________ is an arrangement of data according to size or magnitude. Discriminant Frequency Array Matrix Question 17 Explanation:

Array is the arrangement of data according to size or magnitude Question 18 WRONG The first term of an arithmetic progression is 6 and the common difference is  – 3. What term is – 51? 21

20 22 23 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 = 20 Question 19 WRONG

In a circular dining table, 5 guests are to be seated. In how many ways can the five guests sit? 10 24 12 30 Question 19 Explanation:

Solving by circular permutation P = (n-1)! = (5-1)! = 4! = 24 Question 20 WRONG In how many ways can a committee of 4 be chosen from a group of 8 people? 48 70 24 32 Question 20 Explanation:

Solving by combination C = n!/[(n-r)!r!] n=8r=4 8!/[(8-4!)4! [4x2x7x6x5]/[4x3x2x1] =2x7x5 C = 70 Question 21 WRONG

A sample of 30 companies belonging to a certain industry reported the following number of employees. 43 33 24 51 36 31 50 46 50 29 40 25 38 35 31 35 42 50 47 21 45 45 28 36 58 62 37 55 52 49 What is the median? 41 40 43 42 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 = 41 Question 22 WRONG

In a geometric progression 1, 2, 4, 8, . . . how many terms are added if the sum is 127? 6 7 8 9 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 = 7 Question 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 quartile Decile Quartile tenths Question 24 WRONG

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 3 P40.00 P54.00 P50.00 P58.00 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 = 54.00 Question 25 WRONG

If f(x) = , what is the domain of f(x)?

rd

month?

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 = 3 Question 26 WRONG In the geometric progression 4, 12, 36, 108, . . . the common ratio is: 2 1 1/3 3 Question 26 Explanation:

solving for the common ratio: r = a2/a1 = a3/a2 = a4/a3 r = 12/4 = 36/12 = 108/36 r=3 Question 27 WRONG

Given the table below, what is the equation of the given relation? 0 1 2 3 X 1 3 5 7 y y=x y = 2x y = 2x – 1 y = 2x + 1

4 9

5 11

Question 27 Explanation:

SLOPE (m)= (y2-y1)/(x2-x1) =(3-1)/(1-0) m=2 (y-intercept) b=1 y=mx+b y=2x+1 Question 28 WRONG

If two dice are tossed together, in how many ways can they fall? 36 12 24 6 Question 28 Explanation:

each die has 6 possible outcomes, so 6x6 = 36 Question 29 WRONG

A sample of 30 companies belonging to a certain industry reported the following number of employees. 43 33 24 51 36 31 50 46 50 29 40 25 38 35 31 35 42 50 47 21 45 45 28 36 58 62 37 55 52 49 What is/are the mode/s of the set of data? 45 45 and 35