General Education Review - SEMINAR 1 MATHEMATICS

Refer to the given figure (81-85 on the given material) If LM = 5x - 8 and UQ = 3x + 4, then what is x? a. 8 b. 6 c. 4 d. 2

Answer: B Solution: Since LM = UQ, we get: 5x - 8 = 3x + 4 5x - 3x = 4 + 8 2x = 12 and x = 6

Refer to the given figure (81-85 on the given material) Using number 18, what is MU + LQ? a. 122 b. 102 c. 82 d. 62

Answer: B Solution: Since LQ = MU = 51, thus LQ + MU = 51 + 51 = 102

How many three digit numbers can be formed using 0, 1, 2, 3, 4, and 5 if repetition is allowed? a. 80 b. 1080 c. 1296 d. 300

Answer: B Solution: Since repetition is allowed, probability can be computed as: 5 x 6 x 6 x 6 = 1080

In a normal curve, if there are more high scores than low scores then the graph can be described as? a. Skewed to right b. Skewed to the left c. Leptokurtic d. Mesokurtic

Answer: B Solution: Skewed to right means that most of the scores are low. Leptokurtic and mesokurtic are measures of skewness

Evaluate: 2x3 - x 2 + y if x = 3 and y = -2? a. 38 b. 43 c. 59 d. 61

Answer: B Solution: Substitute x and y. We get: 2(3)3 - (3)2 + (-2) = 2(27) -(9) + (-2) = 54 - 9 - 2 = 43

What is the prime factorization of 2850? a. 2 x 2 x 5 x 7 x 11 b. 2 x 5 x 5 x 7 x 11 c. 2 x 5 x 7 x 7 x 11 d. 2 x 5 x 7 x 11

Answer: B Solution: By checking, multiply each factor to get 2850.

Find the values of x and y given x + 2y = 16 and x - 3y = -19. a. (2, 7) b. (7, 2) c. (2, -7) d. (-2, 7)

Answer: B Solution: By elimination method x + 2y = 16 Using x + 2y = 16, when y =7 x - 3y = -19 x + 2(7) = 16 5y = 35 x + 14 = 16 y = 7 x = 16 - 14 = 2

What are the roots of b2 + 4b - 21 = 0? a. 3 or -7 b. -3 or - 7 c. -3 or 7 d. 3 or 7

Answer: A Solution: b 2 + 4b - 21 = 0 (b + 7)(b - 3) = 0 ; Factor the equation b = -7 or b = 3 ; Zero Product Property

Which of the following is not divisible by 17? a. 51 b. 117 c. 187 d. 391

Answer: B Solution: 117 when divided by 17 has a remainder of 15.

Determine the LCM of 12, 16, and 18. a. 288 b. 144 c. 64 d. 36

Answer: B Solution: 12 = (2)(2)(3) 18 = (2)(3)(3) 16 = (2)(2)(2)(2) LCM = (2)(2)(2)(2)(3)(3) = 144

Which of the following the GCF of 144, 64, and 224? a. 8 b. 16 c. 32 d. 64

Answer: B Solution: 144 = (2)(2)(2)(2)(3)(3) 224 = (2)(2)(2)(2)(2)(7) 64 = (2)(2)(2)(2)(2)(2) GCF = (2)(2)(2)(2) = 16

Which of the following is the GCF of 16x2y 3 and 24x5yz? a. 16x5y 2 b. 8x2y c. 16x2y 3 d. 8x5y 2

Answer: B Solution: 16x2y 3 = (24 )(x2 )(y3 ) 24x5yz = (23 )(3)(x5 )(y)(z) GCF = 23 x 2y = 8x2y Note: When getting the GCF, choose the all common factors with the smallest exponent.

What must be added to 2 2 3 to make it 3 3 5 ? a. - 15/14 b. 14/15 c. - 14/15 d. 15/14

Answer: B Solution: 3 3/5 - 2 2/3 = 18/5 I-I8/3 = 54−40/15 = 14/15

Find the point of intersection of the lines x + 2y = 5 and x - 5y = 19. a. (2, -7) b. (9, -2) c. (-9, 2) d. (-2, -7)

Answer: B Solution: By elimination method, x + 2y = 5 If y = -2 and x + 2y = 5, then: x - 5y = 19 x + 2(-2) = 5 7y = - 14 x - 4 = 5 y = -2 x = 9

In a circular table, in how many ways can you arrange the five guests? a. 5! b. 4! c. 5P4 d. 5C4

Answer: B Solution: Circular permutation is computed as (n - 1)!.

What property of real numbers is shown in: (M + N) + P = P + (M + N) a. Associative property b. Commutative property c. Transitive property d. Distributive property

Answer: B Solution: Commutative property is about changing the position of one term and another. Associative is about changing of groupings of the terms.

Find the geometric mean of 12 and 24. a. 12 b. 12√2 c. 8√2 d. 4√2

Answer: B Solution: Geometric mean can be computed as GM = √𝑎𝑏. Thus we get GM = √12(24) = 12√2

If 3p - 5 is an odd integer, which of the following can be a value for p? a. P is a prime number b. P is an odd number c. P is an even number d. P is composite number

Answer: B Solution: If we substitute p as a prime, composite or odd, 3p - 5 would be an even integer.

Find the area of a triangle whose sides are 5 cm, 12, cm, and 13cm. a. 20 sq cm b. 30 sq cm c. 60 sq cm d. 390 sq cm

Answer: B Solution: Since 5, 12, 13 will form a right triangle, hence 5 and 12 will be the base and height. Thus A = 5(12)/2 = 30 sq cm

Suzette wants to make a fruit salad. She now bought 8 apples, 12 oranges and 6 mangoes. Find its corresponding ratio? a. 8:12:6 b. 4:6:3 c. 3:4:8 d. 4:3:2

Answer: B Solution: The common ratio of 8, 12, and 6 is 2. Thus its dividing all by the common ratio we get, 4:6:3 respectively.

What is the complement of 430? a. 430 b. 470 c. 1370 d. 1430

Answer: B Solution: The sum of the complementary angles is equal to 900 .

The diagonal of a square table is 4 meters. What is the total area of the table? a. 4 m2 b. 8 m2 c. 16 m2 d. 32 m2

Answer: B Solution: Using A = (d1d2)/2, then A = (4m)(4m)/2 = 8 m2

Find the area of a rectangle whose width is 12 inches and has a perimeter of 36 inches. a. 3 inches b. 6 inches c. 12 inches d. 18 inches

Answer: B Solution: Using P = 2l + 2w, we get: 36 = 2l +2(12) 36 = 2l + 24 36 - 24 = 2l 12 = 2l and l = 6 inches.

What is the volume of a sphere whose radius is 15 cm? a. 2250π cm3 b. 4500π cm3 c. 5400π cm3 d. 6000π cm3

Answer: B Solution: Using V = 4πr3 /3, we get: V = 4π(153 )/3 = 4500 π cm3

Find the height of a triangular prism whose volume is 100 cu. meters with a base having an area of 20 sq. meters. a. 3 meters b. 5 meters c. 0.6 meters d. 1.67 meters

Answer: B Solution: Using V = Bh, we get: 100 = (20)h and h = 5 meters

What is the 3rd term of the geometric sequence if the 1st term is 3 and 7th term is 64/243? a. ±2 b. ± 4/3 c. ±8/9 d. ±16/2 7

Answer: B Solution: Using an = a1r n - 1 , we get: 64 243 = 3(𝑟 7−1 ) 64 729 = (𝑟 6 ) r = ±2/3 Then, a3 = 3(r3 -1 ) a3 = 3(2/3)2

Two numbers have a sum of 69 and their difference is 25. What are the two numbers? a. 42 and 27 b. 47 and 22 c. 45 and 24 d. 44 and 25

Answer: B Solution: Using backward method, 47 + 22 = 29 and 47 - 22 = 25.

. Lebron is seven years older than Stephen. The sum of their ages is 49. How old is Lebron at present? a. 21 years old b. 28 years old c. 42 years old d. 56 years old

Answer: B Solution: Using backward method, If Lebron is 28 y/o and he is 7 years older than Stephen, then Stephen is 21 y/o. Since 21 + 28 = 49, and that is true, thus, assumption is TRUE.

If x2 -5x - 6 = 0, then find the value of x. a. -2 or 3 b. -1 or 6 c. 1 or -6 d. -2 or -3

Answer: B Solution: x 2 - 5x - 6 = 0 (x - 6)(x + 1) = 0 : Factor the equation X = 6 or x = -1 : Zero Product Property

If m<U= 5x + 38 and m<L= 3x + 50, solve for m<M a. 68 b. 86 c. 112 d. 104

Answer: C Solution: refer to the given material

How many millimetres are there in 2.3 kilometers? a. 23 000 000 000 mm b. 23 000 000 mm c. 2 300 000 mm d. 230 000 mm

Answer: C Solution: (2.3 km)(1 000m/1km)(100cm/1m)(10mm/1cm) = 2 300 000mm

What is the mean of the given math scores above? a. 24 b. 26 c. 27 d. 31

Answer: C Solution: (31 + 26 + 24 + 31 + 28 + 25 + 24)/7 =27

Simplify: (7x - 9) - [7x - (-5x + 3) - 7] a. 5x - 19 b. 19 - 5x c. -5x - 19 d. 5x + 19

Answer: C Solution: (7x - 9) - (12x + 10) = -5x - 19

Find the value of x in 3x - 19 = -2x + 1 a. 20 b. -20 c. 4 d. -4

Answer: C Solution: 3x - 19 = -2x + 1 3x + 2x = 1 + 19 5x = 20 and x = 4

Which of the following is a composite number? a. 117 b. 91 c. 87 d. 89

Answer: C Solution: 87 has other factors which are 3 and 29.

How many sides does isocagon have? a. 10 b. 15 c. 20 d. 25

Answer: C Solution: A 20-sided is known as isocagon. Moreover, 10-sided is called decagon while 15-sided is known as pentadecagon.

A square has an area of 784 sq. cm., find its perimeter. a. 28 cm b. 56 cm c. 112 cm d. 224 cm

Answer: C Solution: If A = s 2 then, 784 = s2 and s = 28 cm. Since P = 4s and s = 28cm, then P = 4(28 cm) = 112 cm.

At what quadrant can we locate the point (10, -28)? a. Q1 b. Q2 c. Q3 d. Q4

Answer: D Solution: Each quadrant has its corresponding signs. Q1(+, +), Q2(-, +), Q3(-, -), and Q4(+, -)

Which of the following is an irrational number? a. √36 b. √25 c. √16 d. √8

Answer: D Solution: Irrational number is a number which can't be transformed to a fraction. √8 = 2√2

Three brothers agreed to share on the expenses on the renovation of their parents' house in the ratio of 12:7:5. If the youngest with the least number gave P20, 000.00, then what is the difference between the shares of the remaining two brothers? a. P4 000.00 b. P20 000.00 c. P28 000.00 d. P48 000.00

Answer: D Solution: Let x := common share amount of the three brothers 12x := biggest share among the three brothers 7x := share of the middle among the three brothers 5x := share of the youngest among the three brothers Then, 5x = 20 000 and x = 4 000 Thus, 12x => 12 (4 000) = 48 000 and 7x => 7(4 000) = 28 000 Hence, the difference between the shares of two brothers is P48 000 - P28 000 = P20 000

The ratio of the girls to boys in the class of Mr. Fernandez is 7:3. If there are 21 girls in the class, how many students are there in the class of Mr. Fernandez? a. 9 b. 12 c. 27 d. 30

Answer: D Solution: Let x := number of boys 7:3 = 21:x 7x = (3)(21) 7x = 63 X = 9, number of boys. Thus, there are 21+9 = 30 students in total.

What method of dispersion greatly affected by extremes scores? a. Mean b. Standard deviation c. Variance d. Range

Answer: D Solution: Mean is most commonly used and affected by extremes scores under measure of central tendency while range is for measure of dispersion or variability.

In Math test, the following sample scores are drawn: 31, 26, 24, 31, 28, 25, and 24. What is the mode? a. 24 b. 26 c. 31 d. 24 and 31

Answer: D Solution: Mode is the most frequent data. There are two 31 and 24. Thus, modes are 24 and 31. We call this mode as bimodal.

Which of the following is perpendicular to x - 2y = 1? a. 2x - 4y = 1 b. 2x - 4y = 2 c. x + 2y = 5 d. 2x + y = 8

Answer: D Solution: Perpendicular means, slopes of two equations are negative reciprocal of each other. 2x + y = 8 has slope of -2 while x - 2y = 1 has a slope of 1/2.

A sala set that originally cost Php 29 599.00 is now sold at Php 25 159.15. What is the percentage discount decrease in the price of sala set? a. 45% b. 35% c. 25% d. 15%

Answer: D Solution: Php 25 159.15 ÷ Php 29 599.00 = 0.85. Thus, discount percentage is 0.15 = 15%.

Find the mean absolute deviation given the Science grades of five students: 78, 92, 68, 83, and 99. a. 8.5 b. 9.5 c. 10.5 d. 11.5

Answer: D Solution: Since MEAN = 84, we get the MAD by adding all the difference of mean to each data then divide it to (n - 1). So |78 - 84| = 6, |92 - 84| = 8, |68 - 84| = 16, |83 - 84| = 1 and |99 - 84| 15. Then MAD = (6 + 8 + 16 + 1 + 15)/(5 - 1) = 46 / 4 = 11.5

Which one of the statements is ALWAYS TRUE? a. The complement of an angle is obtuse. b. The supplement of an angle is acute. c. Two supplementary angles are congruent. d. The complement of any angle is acute.

Answer: D Solution: Since the sum of the complementary angle is 900 , it only implies that the two angles are both acute.

Find the remainder when x3 - x 2 + 3x - 4 is divided by x + 2. a. 12 b. -12 c. 22 d. -22

Answer: D Solution: Substitute x = -2 to x3 - x 2 + 3x - 4. We get: (-2)3 - (-2)2 + 3(-2) - 4 = -22

If the difference between a number and ten is tripled, the result is five more than twice the number. What is the number? a. 20 b. 25 c. 30 d. 35

Answer: D Solution: The equation would be: 3(x - 10) = 5 + 2x 3x - 30 = 5 + 2x X = 35, the number.

Which of the following must be subtracted to 887, 513 to make it divisible by 6. a. 5 b. 11 c. 17 d. All of the above

Answer: D Solution: The number must be even and the sum of digits must be divisible by 3 so that it will be divisible by 6.

. If 3 kgs of mangoes cost as much as 8 kgs of apples, how many kilograms of mangoes would cost as much as 60 kgs of apples? a. 2.5 kgs b. 7.5 kgs c. 12.5 kgs d. 22.5 kgs

Answer: D Solution: The proportion of mangoes to apples is given by 3:8 = x:60, where x = corresponding kgs of mangoes. Then, we get 8x = 3(60) 8x = 180 x = 22.5 kgs of mangoes.

What must be added to m2 - 16m to make it a perfect square trinomial? a. -16 b. -64 c. 16 d. 64

Answer: D Solution: This is completing the square, get the half of the linear term and square it. In this problem, half of -16 is -8 and its square is (-8)2 = 64.

Find the length of the hypotenuse whose legs are 6 cm and 15 cm respectively. a. 18 cm b. 21 cm c. 2√61 cm d. √261 cm

Answer: D Solution: Using Pythagorean theorem, we get: c 2 = 62 + 152 c 2 = 36 + 225 c 2 = 261 and c = √261 cm

A cube has an edge of 8 dm. Which of the following is the volume of the cube? a. 24 cu dm. b. 64 cu dm. c. 144 cu dm. d. 512 cu dm.

Answer: D Solution: Using V = s3 , we get: V = (8dm)3 = 512 dm3

Find the distance between point A(-3, -4) and B(5, 2). a. 7 units b. 8 units c. 9 units d. 10 units

Answer: D Solution: Using distance formula between two points. d = √(𝑥1 − 𝑥2) 2 + 𝑦 − 𝑦) 2 We get: d = √[2 − (−4)] 2 + [5 − (−3)] 2 d = √6 2 + 8 2 d = √100 = 10

Which of the following is the solution set of -5a < 20? a. {a|a ∈ 𝑅} b. {a|a = -4} c. {a|a < -4} d. {a|a > -4}

Answer: D Solution: When we divide or multiply negative sign in an inequality, the symbol will be changed to its opposite.

What is the sum of the prime numbers between 100 and 110? a. 420 b. 311 c. 204 d. 210

Answer: A Solution: The prime numbers between 100 - 110 are 101, 103, 107, and 109.

Given the numbers 12, -15, 0, -29, 7. Which of the following is arranged in descending order? a. 0, 7, 12, -15, -29 b. -29, -15, 12, 7, 0 c. 12, 7, 0 -15, -29 d. 12, 7, 0, -29, -15

Answer: C Solution: Draw a number line. A number is less than to the number on its right side.

Find the area and perimeter of a trapezoid if height is 4 cm and bases are 12 cm and 18 cm. a. A = 60 sqm and P = 40 cm b. A = 60 sqm and P = 38 cm c. A = 40 sqm and P = 40 cm d. A = 40 sqm and P = 38 cm

Answer: A Solution: To get perimeter, find the value of c. c 2 = 32 + 42 c 2 = 9 + 16 c 2 = 25 and c = 5 Hence P = 12cm + 18cm + 5cm + 5cm = 40cm To find area, use A = (b1 + b2)h/2 A = (12 + 18)(4)/2 A = 30(4)/2 A = 120/2 and A = 60 sqm

How many prime numbers are there between 25 and 95? a. 14 b. 15 c. 16 d. 17

Answer: Solution: Listing Method

Find the difference of mean and median of the above sample scores. a. 1 b. 2 c. 3 d. 4

Answer: Solution: MEAN = (31 + 26 + 24 + 31 + 28 + 25 + 24)/7 = 27 while median is 26. Thus, difference is 27 - 26 = 1

In how many ways can you arrange the word MATHEMATICS? a. 11P2 b. 11C2 c. 11!/2! d. 11!/2!2!2!

Answer: Solution: Since there are 11 letters and number of letter M = 2, T = 2, and A =2, we can compute the probability as; 11!/2!2!2!

How many 4-digit numbers can be formed using 0, 1, 2, 3, 4, 5, and 6 without repetition? a. 200 b. 240 c. 300 d. 320

Answer: Solution: Since there are 6 numbers and first digit can't be 0, then we have to compute it as: 5 x 5 x 4 x 3 = 300, representing the possible numbers in each digit.

Which of the following is the 10th term of the sequence: 4, 17, 30, ... a. 160 b. 173 c. 186 d. 199

Answer: Solution: Using an = a1 + (n - 1)d a1 = 4, d = 13, n = 10, and a10 = ? a10 = 4 + (10 - 1)13 a10 = 4 + (9)13 a10 = 4 + 117 = 121

Which one of the statements is TRUE? a. A square is a rhombus. b. A rhombus is a rectangle. c. A parallelogram is a trapezoid. d. A rectangle is a square.

Answer: A Solution: A square is a rhombus as well as rectangle. However, rectangle is sometimes a square or a rhombus.

Which of the following is the translation of "nine less than a number"? a. n - 9 b. 9 - n c. 9 < n d. n < 9

Answer: A Solution: "Less than" is translated as "-" and the positions of the terms must interchanged, While "is less than" is translated as <

If 90 is the LCM of 15 and W, then what is the value of W? a. 18 b. 12 c. 24 d. 30

Answer: A Solution: 15 = (3)(5) while 18 = (2)(3)(3). The LCM of 15 and 18 is 90 = (2)(3)(3)(5). Thus W = 18.

Find the discriminant of x2 - 5x - 6 = 0. a. 1 b. -1 c. -49 d. 49

Answer: A Solution: Discriminant can be solved using b2 - 4ac. If it is less than 0, then nature of the roots is imaginary/unreal. If the discriminant is greater than 0, then the nature of roots is real and unequal. Lastly, if discriminant is zero, the nature of roots is real and equal.

What percent of Php 2500.00 is Php 125.00? a. 5% b. 10% c. 15% d. 20%

Answer: A Solution: P = 125, B = 2 500, and R = ?. Using R = P/B, we get: 125 ÷ 2 500 = 0.05 = 5%

Which of the equations is parallel to x - 2y = 1 a. 2x - 4y = 1 b. 2x - 4y = 2 c. x + 2y = 5 d. 2x - y = 8

Answer: A Solution: Parallel means, equations have the same slope with different y-intercepts. Letter B has same slope with x - 2y, however, it is not parallel, instead coincide since slope and y-intercepts are equal.

Which of the following is divisible by 2, 3, 5, and 8? a. 240 b. 420 c. 80 d. 40

Answer: A Solution: Since 240 = (2)(2)(2)(2)(3)(5), thus it shows that 240 can have a factor of 2, 3, 5, and 8.

A store gives 30% discount on all items. How much would Juan pay if he bought an item worth Php 1799.00? a. Php 1259.30 b. Php 1529.30 c. Php 539.70 d. Php 593.70

Answer: A Solution: Since Juan has 30% discounts, thus he will only pay 70% on all items. Then, (Php 1799.00)(70%) = Php 1259.30

A ball is drawn at random from a box containing 5 blue balls, 2 white balls and 8 green balls. Find the possibility that the ball drawn is NOT blue? a. 2/3 b. 1/2 c. 1/3 d. 1/6

Answer: A Solution: Since there are 15 balls and 10 not blue balls, thus probability is 10/15 = 2/3.

From a deck of cards, in how many ways can you draw two ace cards? a. 12 b. 14 c. 16 d. 18

Answer: A Solution: Since there are 4 ace cards, thus the probability can be computed as 4 x 3 = 12.

Refer to the given figure (81-85 on the given material) Using given on number 16, what is the length of LM? a. 22 b. 24 c. 26 d. 28

Answer: A Solution: Since x = 6 and LM = 5x - 8, then we get LM = 5(6) - 8 = 30 - 8 = 22

The number of hours spent by John for review in English, Math, and Science is in the ratio of 2: 5: 3. If John reviewed for a total of 150 hours in a week, how many hours did he spend reviewing for English and Science? a. 15 b. 25 c. 75 d. 120

Answer: C Solution: Let x := common ratio of number of hours spent for review 2x := total hours spent in English 5x := total hours spent in Math 3x := total hours spent in Science Then, 2x + 5x + 3x = 150, 10x = 150, and x = 15 hours Hence, 2x + 3x => 2(15) + 3(15) = 30 + 45 = 75 total number of hours spent in English and Science for review.

In Math test, the following sample scores are drawn: 31, 26, 24, 31, 28, 25, and 24. What is the median? a. 24 b. 25 c. 26 d. 28

Answer: C Solution: Median is the middle value of the data. If there are two middle values, then median would be the average of the two middle values.

400 is 60% of what number? a. 240 b. 600 c. 666.6 6 d. 6 000

Answer: C Solution: P = 400, R = 0.6, and B = ?. Using B = P/R, we get: 400 ÷ 0.6 = 666.66

If there are 30% or 450 male students in a school, how many students are there? a. 1 050 b. 1 200 c. 1 500 d. 1 800

Answer: C Solution: P = 450, R = 0.30, and B = ?. Using B = P/R, we get: 450 ÷ 0.30 = 1 500

Refer to the given figure (81-85 on the given material) If LQ = 3(x - 3) and MU = 2x + 11, what is the length of LQ? a. 31 b. 41 c. 51 d. 61

Answer: C Solution: Since LQ = MU, we get: 3(x - 3) = 2x + 11 LQ = 3(20 - 3) 3x - 9 = 2x + 11 LQ = 3(17) = 51 3x - 2x = 11 + 9 X = 20

What is the area of a circle whose diameter is 20 units? a. 20π units b. 100π units c. 100π sq. units d. 400π sq. units

Answer: C Solution: Since d = 2r and d = 20, the r = 10 units. Using A = πr2 we get: A = π(10 units)2 = 100π sq. units

Given the problem above, what is the possibility that the ball drawn is green? a. 2/3 b. 7/ 15 c. 8/15 d. 1/3

Answer: C Solution: Since there are 14 balls and there are 8 green balls, thus probability is 8/15

A rectangular garden has a length of 12 meters and a diagonal of 13 meters. What is its perimeter? a. 25 meters b. 27 meters c. 34 meters d. 36 meters

Answer: C Solution: Solve for the width using Pythagorean theorem. w2 = 132 - 122 P = 2l + 2w w2 = 169 - 144 P =2(12) + 2(5) w2 = 25 P = 24 + 10 w = 5 meters P = 34 meters

What is the remainder when x2 - 5x + 9 is divided by x - 1? a. 1 b. -1 c. 5 d. -5

Answer: C Solution: Substitute x = 1 to x2 - 5x + 9. We get: (1)2 - 5(1) + 9 = 1 - 5 + 9 = 5

Which of the following is the supplement of 1120 a. 120 b. 220 c. 680 d. 860

Answer: C Solution: The sum of the supplementary angles is always equal to 1800 .

Which of the following can be the sides of a triangle? a. 2, 2, 4 b. 2, 3, 6 c. 3, 4, 5 d. 4, 3, 1

Answer: C Solution: The sum of the two sides must be greater than to the third side.

What is the slope of the equation 3x - 5y = 6 a. 5/3 b. -5/3 c. 3/5 d. -3/5

Answer: C Solution: Transform the equation into y = mx + b, m is the slope. 3x - 5y = 6 -5y = -3x + 6 : Divide both sides by -5. Y = (3x - 6)/5 : m = 3/5

In an isosceles triangle, the hypotenuse is 12cm long. What is the measure of its leg? a. 6 cm b. 8 cm c. 6√2 cm d. 6√3 cm

Answer: C Solution: Using a2 + b2 = c2 and a = b, we get: a 2 + a2 = c2 2a2 = 144 a 2 = 72 and a =6√2 cm

If the dimensions of a rectangular pyramid are 5 cm, 10 cm, and 12 cm respectively. Find its volume? a. 600 cm3 b. 300 cm3 c. 200 cm3 d. 100 cm3

Answer: C Solution: V = Bh/3, then we get: V =(5)(10)(12)/3 = 200 cm3

Find the volume of a cylinder whose radius is 0.2 meters and height of 50 centimeters? a. 200π cm3 b. 2000π cm3 c. 20000π cm3 d. 200000π cm3

Answer: C Solution: V = πr2h = π(20cm)2 (50 cm)

Evaluate the expression: 3 - 5(20 + 4) - 4[5 +9(3)]. a. -5 b. 245 c. -245 d. -251

Answer: C Solution: 3 - 5(24) - 4[5 + 27] = 3 - 120 - 4[32] = 3 - 120 - 128 = 3 - 248= -245

Find two numbers such that the GCF is 12 and the LCM is 180. a. 15 and 36 b. 15 and 24 c. 24 and 60 d. 36 and 60

Answer: D Solution: 36 = (2)(2)(3)(3) GCF = (2)(2)(3) = 12 60 = (2)(2)(3)(5) LCM = (2)(2)(3)(3)(5) = 180

What is the expansion of (2x - 3)3? a. 8x3 + 36X2 + 54X + 27 b. 8x3 + 36x2 + 54x - 27 c. 8x3 - 36x2 - 54x - 27 d. 8x3 - 36x2 + 54x - 27

Answer: D Solution: (2x)3 - 3(2x)2 (3) + 3(2x)(3)2 - (3)3 = 8x3 - 36x2 + 54x - 27

Find the integral solutions given the inequality -15 < 2x - 9 < 7 a. X = {-3, -2, -1, ... , 6, 7} b. X = {-3, -2, -1, ... , 7, 8} c. X = {-2, -1, 0, ... , 7 8} d. X = {-2, -1, 0, ... , 6, 7}

Answer: D Solution: -15 < 2x - 9 < 7 -6 < 2x < 16 -15 + 9 < 2x < 7 + 9 -3 < x < 8

What is the range of the above scores? a. 5 b. 6 c. 7 d. 8

Answer: D Solution: 31 - 24 = 7. Range is determined by getting the difference of highest value and lowest value.

What must be replaced to k so that 44k285 is divisible 7? a. 2 b. 3 c. 5 d. 6

Answer: D Solution: 446285 when divided by 7 has no remainder. Thus, k = 6

What must be added to 492, 277 to make it divisible by 6 and 9? a. 5 b. 23 c. 15 d. 5 and 23

Answer: D Solution: 492 277 + 5 = 492 282 which can be divided by 6 and 9. 492 277 + 23 = 492 300 which is also divisible by 6 and 9.

Solve for the area of the composite figure at the right. a. 52 sq mm b. 96 sq mm c. 156 sq mm d. 168 sq mm

Answer: D Solution: A = 18(6) + 10(6) A = 108 + 60 A = 168 sq mm

Which of the following is arranged in ascending order? −5/8 , −6/5 , −7/12 , −3/11 ? a. −3/11 , −6/5 , −7/12 , −5/8 b. −5/8 , −7/12 , −6/5 , −3/11 c. −6/5 , −7/12 , −5/8 , −3/11 d. −6/5 , −5/8 , −7/12 , −3/11

Answer: D Solution: Convert all fractions to decimals to arrange it easily.

What must be the smallest positive integer multiplied to 1240 to make it a perfect square number? a. 55 b. 155 c. 210 d. 310

Answer: D Solution: Do the prime factorization of 1240. Thus, the factors are 2 x 2 x 2 x 5 x 31. To make it a perfect square number we need factors of 2, 5, and 31.