3-Let - General Education - Mathematics 53-81

GENERAL EDUCATION

MATHEMATICS

MATHEMATICS

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MATHEMATICS 1 – FUNDAMENTALS OF MATH 1.1 Use of four fundamental operations in problem solving involving: 1.1. Operations with whole numbers, decimals, fractions, and integers 1.2 Prime, composite, denominate numbers 1.3 Prime factorization 1.4 LCM, GCF 1.5 Divisibility rules 1.6 Ratio and proportion 1.7 Percentage, Base and Rate 1.8 Measurement and units of measure 1.8.1 Perimeter 1.8.2 Area 1.8.3 Volume 1.8.4 Capacity 1.8.5Weight 1.9 Convertunits in the matrix system 1% MATHEMATICS 2 – PLANE GEOMETRY 2.1 Show mastery of basic terms and concepts in plane trigonometry 2.1.1 lines and curves, perpendicular and parallel lines 2.1.2 angles, angle property 2.1.3 special triangles and quadrilaterals 2.1.4 polygons 2.2 Solve problems involving basic terms and concepts in plane trigonometry MATHEMATICS 3 – ELEMENTARY ALGEBRA 3.1 Show mastery of basic terms and concepts in Elementary Algebra 3.1.1 Algebraic expression 3.1.2 Polynomials 3.1.3 Linear equations 3.1.4 Linear inequalities 3.2 Solve problems, evaluate and manipulate symbolic and numerical problems in elementary algebra by applying fundamental rules, principles and processes MATHEMATICS 4 – STATISTICS AND PROBABILITY 4.1 Show mastery and knowledge of basic terms and concepts in statistics and probability 4.1.1 Counting techniques 4.1.2 Probability of an event 4.1.3 Measures of central tendency 4.1.4 Measures of variability 4.2 Solve, evaluate, manipulate symbolic and numerical problems in statistics and probability by applying fundamental rules

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LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS)

NOTES Read, analyze and reflect on these NOTES. 1. When evaluating mathematical expressions, always be guided by the order of operations: a. Simplify all operations inside parenthesis. b. Simplify all exponents c. Perform all multiplications and divisions, working from left to right. d. Perform all additions and subtractions, working from left to right. Remember the mnemonic P-E-M-D-A-S ( Parenthesis-Exponents- Multiplications/DivisionsSubtractions-Additions). 2. Numbers may be classified as prime, composite and natural denominate: a. A prime numbers is a positive numberwhich may only divided by 1or itself. b. A composite number is a positive number which has a positive divisor other 1 or itself. All even numbers are composite exceptthe number 2. c. A natural number like 0 or 1 is neither prime nor composite. d. A denominate number is a number with an attached unit of measurement. 3. Prime factorization is the process of finding which prime numbers tou need to multiply together to get the original number. There are 2 methods of Prime factorization. a. In the factor tree method, we use a pictorial method of finding factors, where the number to be factorized is placed at the top and all its factors branch out one by one till we get all prime factors, just like a tree.

24 12

3

2

4 2

2

3 × 2 × 2 × 2 = 24 b. In the continuous divivision method, we rperform repeated divisionsusing prime factors as divisor until the last dividend becomes 1. 2 2 2 3

24 12 6 3 1

4. The least common multiple (LCM) is the smalles multiple that 2 numbers have in common. The greatest common factor (GCF) is the larges multiple that can exactly divide 2 numbers. To obtain the LCM or the GCF, prform prime factorization of the 2 numbers and compare their prime factors. a. For LCM, after you list down the 2 factors, mark similar prime factors as one pair. After you have done so, multiply together the pairedand unpaired prime factors.

GENERAL EDUCATION

MATHEMATICS

24 = 2

2

2

2

36 = 2

2

2

2

LCM = ⏟ 2x2x3

x

paired factors

2⏟ 𝑥3

55

= 72

𝑢𝑛𝑝𝑎𝑖𝑟𝑒𝑑 𝑓𝑎𝑐𝑡𝑜𝑟𝑠

b. For GCF, after you list down the prime factors, mark similar prime factors as one pair. After you have done so, multiply together the paired prime factors ONLY.

24 = 2

2

2

2

36 = 2

2

2

2

GCF = ⏟ 2x2x3

x = 12

paired factors

1. Please be guided by the divisibility rules. Divisor 2 3 4 5 6

8

9 10

Divisibility condition The last digit is even (0, 2, 4, 6, or 8). Sum of the digits is clearly divisible by 3. The last two digits are divisible by 4. Thelast digit is 0 or 5. It is divisible by 2 or by 3. by 3 and the last digit is even, hence the Subtracttwo times the last digit from the rest. The result should be divisible by 7 The last three digits are divisible by 8. Ad four times the hundreds digit to twice the tens digit to the ones digit. The result should be divisible by 8. Sum of the digits is divisible by 9. The last digit 0.

Examples 1294: 4 is even. 405 => 4 + 0 + 5 = 9 40832: 32 is divisible by 4. 495: the last digit is 5. 1,458: 1 + 4 + 5 + 8 = 18, so it is divisible number is divided by 6. 483: 48 – (3 × 2) = 42: 42 is divisible by 7. 34152: 152 is divisible by 8. 34152: (4 × 1) + (2 × 5) + 2 = 16 2,880: 2 + 8 + 8 + 0 = 18 130: the las digit is 0.

2. Recall the concepts of ratio and proportion. a. A ratio is an expression of the relative size of two quantities; it is usually expressed as the quotient of one number divided by the other. The ratio of 1 to 2 is written as 1:2 or 1/2. b. A proportion is a statement of equality between two ratios. The ratio of 1:2 to 3:6 forms of the proportion 1:2 = 3:6 or ½ = 3/6. 3. Recall the concept of percentage, base and rate. a. The percentage is the fraction of the original number that is obtained by multiplying the rate and the base. In problems, it is the number that comes before the word is. b. The base is the number or quantity which represents the original number. It also represents the total. It is obtained by dividing the percentage by the rate. In problems, , it is the number that comes after the word of. c. The rate is the number represents the percent. It is obtained by dividing the percentage by the base. In problems, is the number that is attached to the word percent or to a % sign. d. To facilitate recall of the formulate for percentage, base and rate, draw a PBR triangle.

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LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS)

P B

R

4. Measurment is the oprocess or result of determining the magnitude of a quantity. a. Perimeter is the total distance around any 2 dimensional shape. The formulae for for perimeter as follows: i. perimeter of triangle = a + b + c, whare a, b and c represens the lengths of the three sides of the triangle

a

b

c ii. perimeter of a rectangle = 2l = 2w, where l and w represens the length and the width respectively

w l iii. perimeter of a square = 4s, where s represents the length of one side of a square

s

iv. perimeter of circle = 2 r, where represents the constant equal to 3.1416 and r represents the radius of the circle r

b. Area iWs the total amount of space that a 2 dimensional object occupies. It is measuresd in square units (ie, square meters, square centimeters). i. area of a triangle = ½ × b × h, where b represents the base and h represents the perpendicular height.

h b

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ii. area of a rectangle = 1 × w, where l and w represens the length and the width respectively

w l iii. area of a square = s², where s represents the length of one side of a square

s

iv. area of a circle = πr², where π represents the constant equal to 3.1416 and r represents the radius of a circle r

v. area of an isosceles trapezoid = x (b1 + b2) x h, where b1 and b2 represent the length of the 2 parallel bases and h is the perpendicular height b1 h b2 c. volume is the total amount of space occupied by a three dimensional object. It is measured in cubic units (ie, cubic meters, cubic centimeters). i. volume of a cube = s3, where s is length of 1 side of the cube.

s

ii. volume of a rectangular prism = 1 × w × h, where l is the length, w is the width and h is the height. h l

w

iii. volume of a cylinder = πr2h, where π represents the constant equal to 3.1416, r represents the radius of the circular base and h represents the height of the cylinder. r h

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LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS) iv. volume of a cone = (1/3) x πr2h, where π represents the constant equal to 3.1416, r represents the radius of the circular base and h represents the height of the cone

h s

v. volume of a pyramid = (1/3) x B x h, where B is the area of the base and h is the height

vi. volume of sphere = (4/3) x represents the radius

π 3

r , where π represents the constant equal to 3.1416, r

d. Capacity is the total amount of fluid that a 3-dimensional container can hold. It is used hand in hand with volume and is calculated using the same formulae. e. Weight is a measure of the amount of gravitational pull exerted on a mass. Beyond the realm of physics, weight and mass are used interchangeably. Conventional units include kilograms and pounds. 5. The standard system of measurement in the present day is the metric or SI system. The alternative system used in European countries is the English system. a. Convertion of units in the SI system requires awareness of various key prefixes signifying powers of ten.

Name Symbol Factoer

deca Da 101

hecto H 102

kilo k 103

SI Prefixes for Multiples mega giga tera M G T 106 109 1012

Name Symbol Factor

deci d 10-1

centi C 10-2

milli m 10-3

SI Prefixes for Fractions micro nano pico μ n p 10-6 10-9 10-12

peta P 1015

exa E 1018

zetta Z 1021

yotta Y 1024

femto f 10-15

atto a 10-18

zepto z 10-21

yocto y 10-24

Dimensional analysis is done to determine equivalent SI units using different prefixes. For example, to convert 8 kilometers into centimeters. 8 km (

10𝑚3 ) 1 𝑘𝑚

3

(11𝑐𝑚 ) = 8 x 103-(-2)cm = 8 × 105 cm 𝑘𝑚

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b. Conversion of units from English system to the SI system requires memorization of convertion factors. 1 kilogram 2.54 centimeters 12 inches 1 meter 3 feet 1 mile 1 kilometer

= = = = = = =

2.2 pounds 1(lbs) 1 inch 1 foot 3.28 feet 1 yard 5,280 feet 0.62 mile

6. Recall the following concepts in plane trigonometry. a. A line is a series of points that extends in two opposite directions without end. Two points are needed to define a line. It has no fixed length or width. It is considered infinitely long. i. The point of intersection is the point where two lines meet or come together. ii. Perpendicular lines from right angles to the point of their intersection. They will never intersect with each other. b. A curve line is a line that representsa mathematical equation. IT may two-dimensional or threedimensional. c. An angle is the figure formed by two rays sharing a common endpoint, called the vertexof the angle. Angles are measured in degrees (0). i. A right angle is an angle whose measure is exactly 90 degrees. ii. An acute angle is an angle whose measure is lees than 90 degrees. iii. An obtuse angle is an angle whose measure is more than 90 degrees but less than 180 degrees. iv. A straight angle is an angle whose measure is is exactly 180 degrees. v. A reflex angle is an angle whose measure is more than 180 degrees but less than 360 degrees. vi. Two angles are complementary if their sum is 90 degrees. vii. Two angles are supplementary if their sum is 180 degrees. d. A triangle is a plane geometric figure with three verticesand three sides. The sum of three internal angles of a triangle is always equal to 180 degrees. i. Triangles may be classified on the length of sides: 1. An equilateral triangle has three sides of equal length. It is also called equiangular triangles because all three angles measure exactly 60 degrees. 2. An isosceles triangle has two sides of equal length. the two angles opposite the two equal sides are also equal in measure. 3. A scalene triangle has three sides of unequal length. All three angles are also of unequal measure. ii. Triangles may also be classified based on the measure of internal angles: 1. A right triangle has exactly one right angle among its internal angles. 2. An acute triangle is composed of three acute internal angles. 3. An obtuse triangle has exactly one obtuse angle among its internal angles. ii. Special triangles have properties that aloow us to compute algebraically the lengths of their corresponding sides. 1. The dimension of the right triangle follow the Pythagorean theorem. c a b

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LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS) a. The side opposite the right angle is called the hypotenuse (c). b. The two other sides are called the legs (a, b). c. For any right triangle, a2 +b2 = c2. For a 45-45-90 right triangle: 450 𝑎√2

450

a. The length of the hypotenuse is equal to the length of one the legs multiplied by √2. 3. For a 30-60-90 right triangle: a. The length of the hypotenuse is two time the length of the shorter leg. b. The length of the longer leg is equal to the length of the shorter leg multiplied by √3.

4. For equilateral triangle:

a. The height is defined by the following formula: height = a2

√3 2

The area is defined by the following formula: area = a2

√3 4

5. Heron’s theorem may be used to calculate the area of any triangle given the length of the three sides. a. First, calculate the semiperimeter: s=

𝑎+𝑏+𝑐 2

b. Use the semiperimeter to calculate the area using Heron’s theorem: area = √𝑠 (𝑠 − 𝑎)(𝑠 − 𝑐)

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c. A quadrilateral is a plane geometric figure with exactly four sides and four vertices. The sum of the measures of the interior angles of a quadrilateral is exactly 360o. i. A parallelogram is a quadrilateral with two pairs of parallel sides. 1. The opposite angles of a parallelogram are equal in measure. 2. The adjacent angles of a parallelogram are supplementary. 3. The diagonals of a parallelogram bisect each other. ii. A rectangle is aquadrilateral with four right internal angles. 1. The diagonals are equal in length and bisect each other. 2. The length of each diagonal is equal to √𝑙 2 + 𝑤 2 iii. A square is a quadrilateralwith four equal sides and four right internal angles. 1. The diagonals of a square bisect each other and meet at 90 degrees. 2. The diagonals of a square bisect its angles. 3. The diagonals of a square are perpendicular. iv. A rhombus is a quadrilateral with four equal sides. 1. Oppositeangles of a rhombus are equal sides. 2. The two diagonals of a rhombus are perpendicular. d. A polygon is a plane geometric figure bounded by a closed path or circuit, composed of a finite sequence of straight line segments. i. The segments are called its sides, and the points where two edges meet are the polygon’s vertices. ii. Polygons are named based on the number of sides: # of sides 3 4 5 6 7 8 9 10 11

Name of polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Undecagon

# of sides 12 13 14 15 16 17 18 19 20

Name of polygon Dodecagon Triskaidecagon Tetradecagon Pentadecagon Hexadecagon Heptadecagon Octadecagon Nonadecagon Icosagon

iii. A regular polygon has equal length of all sides and equal measure of all interior angles. iv. The sum of all the interior angle of a regular polygon is equal to (n – 2) × 180. v. The measure of eac interior angle of a regular polygon is equal to (n−2 x 180 𝑛

7. Recall the following basic concepts in Elementary algebra: a. An algebraic expression is a mathematical expression made up of the signs and symbols of algebra. These symbols include the Arabic numerals, literal numbers, the signs of operation, and so forth. b. The components of algebraic expression are called terms. Based on the number of terms, special designation is given to algebraic expressions: i. An expression containing only one term (ie, 2x) is called a monomial. ii. A binomial contains two terms (ie, 2x + 1). iii. A trinomial consist of three terms (ie, 2x2 + 3x + 4). iv. Any expressions containing two or more terms may also be called by the general name, polynomial.

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LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS) 8. A ppolynomial expression is a monomial or a sum of monomials. a. The degree of a polynomial expression with one variable is the value of the largest exponent of the variable that appears in any term. For example, the degree of the binomial x2 + 4 is 2. b. A functional relationship between quantities that can be described by an equation where y equals a polynomial expression of x is a polynomial function. i. A linear function is a polynomial function with a degree equal to 1 (ie, y = 5x + 3). 1. The graph of a linear function is a straight line. ii. A Quadratic function is a polynomial function with a degree equal to 2 (ie, y = 5x2 + 3x + 3). 1. The graph of a quadratic function is a parabola. iii. A cubic function is a polynomial function with a degree equal to 3 (ie, y = 5x3 + 3x2 + x + 3). 1. The graph of a cubic function is a curve. 9. Recall the principles in evaluation of polynomial expressions. a. Group like terms using cummutative and associative properties. b. Combine like terms using distributive property. c. Simplifying powers can also help you multiply monomials. i. multiplying powers with like bases: am x an = am+n. ii. Raising apower to a power: (am)n = amn. iii. Raising a product to a power: (ab)n = an x bn. iv. Zero power: ao = 1. v. Negative power a-n =

1 𝑎𝑛

vi. Dividing powers with like bases:

𝑎𝑚 𝑎𝑛

= a(m-n).

𝑎 𝑛

𝑎𝑛

𝑏

𝑏𝑛

vii. Raising a quotient to a power: ( ) =

10. Factoring a polynonmial means writing it as a product of 2 or more monomials. a. Common monomial factor: i. Consider the trinomial 2x3 – 10x2 + 6x. The common monomial factor is 2x. So using the distributive property in reverse, we factor this expression as: 2x (x2 + 5x + 3). b. Grouping: i. Consider x3 – x2 + x – 1 = 0. x3 – x2 + x – 1 =0 3 2 (x – x ) + (x – 1) =0 x2 (x- 1) + (x – 1) =0 (x – 1) (x2 +1) =0 c. square of a binomial (perfect square trinomial): i. (a +b)2 = a2 + 2ab + b2. ii. (a +b)2 = a2 - 2ab + b2. d. Difference of two squares: ii. (a = b) (a – b) = a2 - b2. e. Completing the square: i. Consider x2 + 6x + 5 = 0. (x2 + 6x + 5 + 4) – 4 (x2 + 6x + 9) – 4 (X + 3)2 – 4 (x + 3 + 2) (x + 3 + 2) (x + 1) (x + 5)

=0 =0 =0 =0 =0

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63

f. Sum of two cubes: i. (a+b)3 = (a + b) (a2 _ a + b2). g. Difference of two cubes: i. (a - b)3 = (a - b) (a2 + ab + b2) 15. A linear equation is an algebraic equation in which each term is either a constant or a product of a constant and (the first power of) a single variable. These may be expressed in the following forms: a. Standard form: Ax + By + C = 0, where, i. the x-intercept is (-C/A, 0). ii. the y-intercept is (0, -C/B). iii. the slope of a line is –A/B. b. Slope intercept form: y = mx + b, where, m is the slope and (0, b) is the y-intercept. y2-y1 𝑦 −𝑥

c. Two point form: y-y1 = 𝑦2 − 𝑥1 (x-x1) where, where (x1, y1) and (x2, y2)are two different poits on 2

1

the line. d. Point slope form: y – y1 = m (x – x1), where m is the slope of the line and (x1, y1) is any point on the line. 𝑥

𝑦

e. Intercept form: 𝑎 + 𝑏 = 1, where (a, 0) is the x-intercept and (0, b) is the y-intercept. 16. A linear inequality is an inequality which involves a linear function. The solution to a linear inequality is obtained by shading the corresponding half-space in the Cartesian plane after graphing the expression as a linear equation. 17. Recall the various counting techniques: a. Fundamental Principle of Counting: In a sequence of events, the total possible number of ways all events can performed is the product of the possible number of ways each individual event can be perform. b. Factorial: n! = (n – 1) (n - 2) … (3) (2) (1); for example, 5! = 5 x 4 x 3 x 2 x 1. c. Permutation: A permutation is an arrangement of objects without repetation where order is important. A permutation of n objects, arranged in groups of size r, without repetition, and order 𝑛! being important is: nPr = (𝑛−𝑟)! d. Combination: A combination is an arranement of objects without repetation where order is not important. A combination of n objects, arrangedin groups of size r, without repetation, and order 𝑛! not being important is: nCr = (𝑛−𝑟)! 𝑟!

18. Probability is a measure of certainty or uncertainty that an event will happen. It arranges from 0 to 1. a. The probability of an impossible event (an event that wil never occur) is 0. b. The probability of an certain event (an event that will surely happen) is 1. c. The probability (P) of an event (E) is expressed mathematically as: (𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑎𝑛𝑡𝑒𝑑 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠) P(E) = (𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑠𝑜𝑐𝑚𝑒𝑠)

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LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS) 19. Measures of central tendency are numerical descriptive measures which indicate or locate the center of distribution or data set. a. The mean of a set of values or measurements in the sum of all the measurements divided by the number of measurements in the set. b. The meadian is the middle value of a given set of measurements, provided that the values or measurements are arranged in an array. An array is an arrangement of values in increasing or decreasing values. c. The mode is the value occurs most frequently in a set of measurements or values. d. Measures of variability are measures of the average distance of each observation from the center of distribution. They measure homogeneity or heterogeity of a particular group. a. The range is the difference between the highest and the lowest values. This is the simpliest and most unreliable measure of variability since it uses only two values in the distribution. b. the mean obsolute deviation is the average of summation of the absolute deviation of each observation from the mean. The formula for the mean absolute deviataion is: ∑ 𝑥−𝑥̅

mean absolute deviation = 𝑛 where, x is a value or score from the raw data, 𝑥̅ is the mean and n is the total number of cases. c. Variance (s2) is the average of the squared deviation from the mean . The formula for ∑(𝑥 −𝑥̅ ) 2

finding the variance is shown below: s2 = 𝑛 where, x is a value or score from the raw data, 𝑥̅ is the mean and n is the total number of cases. d. The standard deviation is the square root of the average deviation from the mean. It is mathematically equal to the square root of the variance. ∑(𝑥 −𝑥̅ ) 2

s=√

𝑛

where, x is a value or score from the raw data, x is the mean and n is the total number of cases.

GENERAL EDUCATION

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PRACTICE TEST: Test your mastery of competencies. Choose the letter that correspond to the best answer. I Math 1-Fundamentals of math 1. Use of four fundamental operations in problem solving involving: 1.1 Operation with whole numbers, decimals, Fractions, and integers 1.2 Prime, composite, denominate numbers 1.3 Prime factorization 1.4 LCM, GCM 1.5 Divisibilty rules 1. Evalute the following expression: 5 + 3 (42 + 7) – 7 (2 + 32 x 8)0 A. 0 C. 72 B. 152 D. -444

2. Evaluate the following mathematical expression: A. 16 B. 24

3+4 (5−2 x 6)+12 (2+4)+1 1+(3 x 6)−

80 5

C. 36 D. 12

3. Which among the following is NOT a prime number? A. 31 C. 51 B. 41 D. 61 4. How many prime numbersare there between 1 and 100? A. 23 C. 25 B. 24 D. 26 5. What is the largest prime number less than 100? A. 91 C. 95 B. 93 D. 97 6. What are the prime factors of 128? A. 1 x 2 x 8 B. 2 x 2 x 2 x 2 x 2 x 2 x 2

C. 2 x 2 x 2 x 4 x 4 D.2 x 3 x 2 x 2 x 2 x 2 x 2 x 2

7. What are the prime factors of 153? A. 3 x 3 17 B. 3 x 3 x 7 x 9

C. 153 x 1 D. 3 x 7 x 13

8. What are the prime factors of 273? A. 3 x 3 x 7 x 7 B. 3 x 17 x 11

C. 3 x 6 x 9 x 11 D. 3 x 7 x 13

9. What is the least common multiple of 24 and 80? A. 360 C. 240 B. 80 D. 480

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LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS)

10. One trip around a running track is 440 yards. One jogger can complete one lap in 8 minutes, the other can complete it in 6 minutes. How long will it take for both joggers to arrive at their starting point together if they start at the same time and maintain their jogging pace? A. 12 minutes C. 36 minutes B. 24 minutes D. 48 minutes 11. Josefa is making bead necklaces. She has 90 green beeds and 180 blue beads. What is the greatest number of identical necklaces she can make if she wants to use all of this beads? A. 12 C. 16 B. 15 D. 18 12. Lisa bought a big bag of candy at a warehouse store. There are 102 pieces of candy in a bag. Lisa needs to divide the candy up into smaller bags. She wants to put the same number of pices in each small bag. How many small bags could lacey use? A. 17 C.19 B. 18 D. 20 13. A dish company needs to ship an order of 117 glass bowls. The company will put the bowl into several boxes. Each box contains the same number of bowls. How many boxes could the company use for the order? A. 11 C. 13 B. 12 D. 17 14. The number, 212115273999132, is NOT divisible by which of the following factors? A. 2 C. 4 B. 3 d. 8 15. When 2,000 pounds of paper are recycled, 17 trees are saved. How many trees are saved if 5,000 pounds of paper is recycled? A. 41 C. 45 B. 42.5 D. 63 16. A recipe calls for 2 eggs for every 5 cups of flour. A local chief will use 35 cups of flour, how many eggs must be have? A. 12 C. 14 B. 13 D. 16 17. Five out of every seven households have cable TV. If 42,000 households in a certain city hyave a TV, how many do not have cable TV? A. 12,000 C. 30,000 B. 21,000 D. 32,000 18. Our school has 8 male teachers who comprise 25% of all our teachers. How many teachers do we have? A. 24 C. 32 B. 28 D. 40 19. Miss Santiago’s class has 20 boys and 15 girls in her English class. What percent of the students are girls? A. 28% C. 44% B. 43% D. 50%

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20. Jerome answered 80% of the 50 items correctly in math test. How many items did he answer correctly? A. 40 C. 45 B. 44 D. 50 21. A business man had incurred the following expenses in his trips to the Visayanislands: P5100.00, P4600.00, P3800.00, and P3200.00. What was his total for his trip? A. P16000 C. P17000 B. 16700 D. P17500 22. Ms. Tonelada weighed 60 kg. She lost 4 kg on her first week of exercise, gained 2 kg on her second week, lost 6kg on her 3rd week and and remained her weight on 4th week. What was her weight on the 4th week? A. 52 kg C. 68 kg B. 58 kg D. 72 kg 23. A group of young people from four countries gathered together for an international conference: 40 from Manila, 60 from Japan, 35 from Thailand and 45 from Singapore. The participants will form discussiongroups with equal number of members from each country in each group. What is the greatest number of discussion groups that can be formed? A. 5 C. 20 B. 15 D. 25 24. During summer, a lady visits Baguio 6 days, and his best friend every 4 days. If they visited Baguio last April 11, what does the earliest date did both of them visit Baguio again A. April 21 C. May 5 B. April 23 D. May 11 25. A recipe calls a ¾ of sugar. How much sugar should be used if only ½ of the quantities given in the recipe is to be prepared? A.

3

C.

4 2

B.

1 2

D.

3

3 8

26. In a bundle of new 100 bils, The bills are consecutively numbered RTC3432260 to RTC3432280. How much is the total amount of the bills? A. 3200 C. 3400 B. 3300 D. 3500 27. The sum of three consecutive integers is 96. What are the integers? A. 31, 32, 33 C. 30, 32, 34 B. 32, 33, 34 D. 33, 34, 35 28. A farmer can plow

2 3

of a hectare in 1 hr. At this rate, in how many hours will 5 farmers plow the same

fields? A. B.

1

5 10 3

C.

15 2

D. 10

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LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS)

29. If the exchange rate of the US dollars to pesos is $1 = Php47.90 what is the value of Php1 in American cents? A. 02 C. 2 B. 479 D. 4.79 30. In a card game, a player got the following scores: 35, -60, -40, 80, -100, 25, -25. Whatis his final score? A. -115 C. 85 B. -85 D. 115 31. The first 5 numbers in a sequence are 2, 3, 5, 8, and 12. What is the 7th number in the sequence? A. 15 C. 23 B. 19 D. 25 32. A teacher wants to group his pupils into groups of 3 or 5 or 6. However, if she found out that if she do that there will always be 1 pupil left. What is the least possible number of pupils in the class? A. 81 C. 21 b. 31 d. 11 33. Twelve pesos more than twice Mico’s allowance is at most 600 pesos. What is her maximum allowance? A. 300 pesos C. 588 pesos B. 634 pesos D. 294 pesos 34. What integer should be added to 11 to get the sum of at least 37? A. At least 15 C. At least 26 B. At least 25 D. At least 32 35. What are the largest two consecutive odd integers whose sum is at most 60? A. 25, 27 C. 29, 31 B. 27, 29 D. 31, 33 36. Two numbers are in ratio of 3:4. If there sum is 84, what is the smallest number? A. 24 C. 48 B. 36 D. 54 37. The numerator of a fraction is 3 less than the denominator. If the numerator and denominator are each increased by 1, the value of the fraction becomes ¾. What is the original fraction? A. 7/12 C. 8/11 B. 8/12 D. 6/13 38. Mr. Lucido deposited 225 pesos in the bank. If his deposit consisted of 29 bills, consisting of 5 peso and 10 peso bills, how many 10 peso bills did he deposit? A. 13 C. 15 B. 14 D. 16 39. Brenda has saved 300 coins, consisting of 25 centavo and 10 centavo coins.if the total value of her savingsis 4 pesos, how many 10 centavocoins did she save? A. 100 C. 300 B. 200 D. 400

GENERAL EDUCATION

MATHEMATICS

69

40. Julia can finish a project in 10 hours while Elenita can do the same project in 8 hours. How will it take them to finish the project together? A. 3.44 hours C. 4.44 hours B.4.00 hours D. 18 hours 41. If a liter of chemical X is 95% pure, how many liters of water must be added to make a 50% solution? A. 0.80% L C. 0.94% L B. 0.90 L D. 0.09 L 42. Arthur has blended coffee worth 95 pesos per kilogram with coffee worth 115 pesos per kilogram to make 50 kilograms of coffee that will be sold at 107 pesos per kilogram. How many kilograms of each kind did he blend? A. 20 kilos of 95/kg and 30 kilos of 115kg B. 30 kilos of 95/kg and 30 kilos of 115kg C. 30 kilos of 95/kg and 50 kilos of 115kg D. 60 kilos of 95/kg and 30 kilos of 115kg 43. A Victory liner bus traveling at a rate 70 km/h leaves the station after a freight truck has left and overtakes it in 5 hours. At what ratewas the freight truck traveling? A. 20km/h C. 40km/h B. 30 km/h D. 50 km/h 44. Don Antonio invested part of 30,000 pesos at 5% interest and the remaining interest at 6% interest at BPI. If his investment yields annual income of 1,620 pesos, how much did he invest at 6% interest? A. 12,000 pesos C. 16,000 pesos B. 14, 000 pesos D. 18,000 pesos 45. The units digit of a two-digit number exceeds the tens digit by 2. Find the number if it 4 times the sum of its digits. A. 24 C. 48 B. 42 D. 82 46. Using t6he integers 4, 7, 9, 8 and 5, how many two digit numberscan be formed if repletion is NOT allowed. A. 20 C. 25 B. 23 D. 28 47. In how many ways can 5 boys be seated in a row of 5 seats? A. 72 C. 102 B. 9 D. 120 48. In how many ways can a term of 10 basketball players be chosen from 12 players? A. 62 C. 66 B. 64 D. 72 MATH 1-1.6

Ratio and proportion

49. If a picture frame is 27 cm long and 18 cm wide, what is the ratio of its length to its width? A. 3:2 C. 3:5 B. 2:3 D.5:3

70

LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS)

50. Five bananas weigh as much as 3 star apples. Inthis rate, how many star apples will weigh as much as 45 bananas? A. 27 C. 33 B. 30 D. 36 51. It takes 20 men to build a building for 60 days. Assuming that all men work at this rate, how many men will be needed to build the same building in 15 days? A. 5 C. 100 B. 80 D. 120 52. The ratio of the numbers of carabaos, goats and cows in a farm is 5:1:2. If there are 48 animals of these kinds in his backyard, how many of them are goats? A. 2 C. 6 B. 4 D. 8 53. The ratio of the numbers of red, green and blue balls in a box is 2:5:6. How many green marbles are there if there are 52 marbles in all? A. 4 C. 20 B. 8 D. 24 54. In a university, the ration of the female professors to the male professors 8:5. If there are 75 male professors, how many are female professors? A. 120 C. 225 B. 180 D. 375/8 55. A meter stick is cut into 2 at the 25 cm mark. What is the ratio of the smaller piece to the larger pice? A. 1:3 C.3:4 B. 2:5 D. 4:5 MATH 1-1.7 Percentage, Base and Rate 56. In asurvey to determine the reaction of people about having a new GSIS card, 80% of the 2,400 people voted in favor of the new card. How many of the voters did not vote for the new card? A. 1920 C. 800 B. 1600 D. 480 57. Lulu spends 15% of her monthly income for house rental, 10% for electric bill and 25% for food and other miscellaneous expenses, she still has P6,000 left. How much does she earn every month? A. P15,000.00 C. P9,000.00 B. P12,000.00 D. P8,000.00 58. If 500 or 25% of a graduating class are girls, how many are graduating? A. 2,000 C. 10,000 B. 5,000 D. 20,000 59. At 25% discount, Ms. Barat paid P150.75 for a bag. What was the original price of the bag? A. P37.69 C. P201.00 B. P150.75 D. P603.00

GENERAL EDUCATION

MATHEMATICS

71

60. A man accepts a position at P14,250 basic salary with an agreement that he will receive a 2% increase every year for 3 years. What will his salary be at the end of 3 years? A. P14,950.00 C. P15,122.21 B. P15,105.00 D. P16,500.00 61. A man invested Php 100000. He put part of it in a bank at 5% interest. On the other hand, he invested the remainder in bonds with a 9% yearly return. How much did he put in a bank if his yearly income from the two investments was Php 7,400? A. Php40,000.00 C. Php60,000.00 B. Php50,000.00 D. Php 70,000.00 MATH 1-1.8

Measurement and units of measure

62. Max is planning to take a leisurely stroll around their rectangular patio, which measures 27.7 m long and 21.5 m wide. Howfar does Max have to walk? A. 96.4 m C. 98.4 m B. 120.4 m D. 88.4 m 63. Which among the following has the largest perimeter? A. Square pizza with perimeter of 80 cm B. Circular pizza with radius of 13 cm C. Rectangular pizza with dimension 10 cm x 14 cm D. Circular pizza with radius 8.5 cm 64. You own a small rectangular box measuring 3 cm x 2 cm. If the dimensions of this box are increased by 10%, what is the area of resulting box? A. 6.26 cm2 C. 7.12 cm2 2 B. 6.22 cm D. 7.26 cm2 65. What is the area of the rhombus whose diagonals measures10 m and 12 m respectively? A. 120 m2 C. 60 m2 2 B. 100 m D. 360 m2 66. Find the volume of a toy ball whose radius is 2 cm. A. 33. 49 cm3 C. 51.76 cm3 B. 48.56 cm3 D. 50.24 cm3 67. A tin can has a radius of 6 cm and a height of 20 cm. What is the volumeof milk that this container can hold? A. 3, 00cm3 C. 1,689 cm3 B. 2,261 cm3 D. 2,200 cm3 68. The total surface area of a cubic box is 600 cm2. What is the length one side of this box? A. 6 cm C. 9 cm B. 8 cm D. 10 cm 69. After a stone is dropped into a cylindrical container filled with 100 cm3 of water, the water rises and the new reading is 106.5 cm3. What is the volume of the stone? A. 6.5 cm3 C. 60.5 cm3 B. 60.65 cm3 D. 10.65 cm3

72

LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS)

70. Which of the following length is the longest? A. 555 cm B. 5.5 m

C. .005 km D. 5555 mm

71. One-fifth of the width and one-fourth of the length of a rectangular cardboardis cut off. What part of the original cardboard is the area of the remained piece? A. 30% of the original area C. 50% of the original area B. 40% of the original area D. 60% of the original area 72. If the area of a triangle is 1 sq unit and its height is unit, what is the length of its base? A. 1 unit C. 3 units B. 2 units D. 4 units 73. What is the radius of a circle whose area is 25 cm2? A. 25 cm C. 5 cm B. 25 cm D. 5 cm 74. Refer to the figure. Given: m 2 = 55o and m 3 = 80. What is m 4? 3

4

1

2

A. 90o B. 105o

5

C. 115o D. 135o

75. Mrs. Dina Ta Tandadivided her lot among her 4 children. The first got 3 1

2

1 2

1 3

ha, the second 3 ha, the

third 34 ha and the fourth 35 ha. How big is Ms. Tanda’s lot? 5 A. 1214 ha B. 13 ha

29

C. 1360

ha

D. 14 ha

76. An elevator can carry a maximm load of 605 kg. How many passengers of weight50.5 kg each can the elevator hold? A. 12 C. 11 B. 11.9 D. 10 77. A room is 30 ft. long, 25 ft wide and 14 ft high. If 42 ballons are inside the room, how many cubic feet of space does this allow for each balloon? A. 25 C. 250 B. 69 D. 690 78. What is the volume of air in an atmospheric balloon with a diameter of 24 cm? A. 144 cm3 C. 570 cm3 3 B. 240 cm D.2304 cm3 \

GENERAL EDUCATION

MATHEMATICS

73

79. A photograph measuring 7 ½ cm by 5 cm is enlarged so that the longer side is 24 cm. What is the length (in cm) of the shorter side? A. 36 C. 6 B. 16 D. 1.6 80. How many cm are there in 2 m and 550 mm? A. 75 B. 255

C. 2055 D. 2550

81. How much liquid containing 6% boric acid should be mixed with 2 quarts of a liquid that is 15% boric acid in order to obtain a solution that is 12% boric acid? A. 1 quart C. 3 quarts B. 2 quarts D. 5 quarts 82. A defective ruler was found found 11.5 in long. Using this ruler, Samuel was found to be 4 ft tall. What is Samul’s actual height? A. 4 ft 2 in C. 3 ft 11.5 in B. 4 ft 4 in D. 3 ft 10 in MATH 1-1.9

Convert units in the metric system

83. How many grams are there in 1 petagram? A.5 B.5,000

C.1015 D.5 x 1015

84. If an apple weighs about 170grams, about how many apples are in 3.5 kilogram bags of apple? A. 20 C. 22 B. 21 D. 23 85. A new supercomputer measures 462 lbs in weight. How much does it weigh in grams? A. 21 g C. 21,000 g B. 2,100 g D. 210,000 g 86. How many liters are there in 353 quarts? A. 353 L B. 334 L

C. 326 L D. 324 L

87. Paul and his son participated in a marathon. Paul traveled 3 km 50 m while his son ran 502 m 36 cm. What is the total distance that the father and tandem covered? A. 3,760 m C. 3,552 m B. 5,452 m D. 3550 m 88. A slow moving snail traveled 4,800 mm. How far did it travel in kilometers? A. 0.0048 km C. 0.48 km B. 4.8 km D. 0.048 km 89. For the fruit punch, 3050mL of fruit juice is needed. How much fruit juice is needed in dekaliters? A. 0.305 daL C. 5.03 daL B. 3.05 daL D. 0.053 daL 90. The measure of an angle is 25 more than its supplement. What is the measure of the larger angle? A. 102.5 degrees C. 90 degrees B. 77.5 degrees D. 110 degrees

74

LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS)

2. PLANE GEOMETRY 2.1 Show mastery of basic terms and concepts in Plane Geometry 2.2 Solve problems involving basic terms and concepts in Plane Geometry 91. If the measure of angle is twice the measure of its complement, what is the measure of the angle? A. 30 degrees C. 90 degrees B. 60 degrees D. 120 degrees 92. Which among the following statements is ALWAYS TRUE? A. The supplement of an angle is acute. B. The supplement of an angle is obtuse. C. The supplement of any acute angle is acute. D. Two supplementary angles are congruent. 93. Which among the following statements is ALWAYS TRUE? A. Two adjacent right angles are supplementary. B. Complements of congruent angles are congruent. C. Two intersecting lines form two pairs of vertical angles. D. Angles that form a linear pair are complementary. 94. What is the measure of an angle if the measure of its supplements is 39 degrees more than twice the measure of its complement? A. 29 degrees C. 49 degrees B. 39 degrees D. 59 degrees 95. Consider the triangle illustrated below. Find the measure of angle x. 3x - 5

3x – 15

5x + 5

A. 57 degrees B. 47 degrees

C. 55 degrees D. 22 degrees

96. Consider the triangle illustrated below. Find the value of x.

68 x

A. 55 B. 35

125

C. 60 D. 25

97. Two angles of a triangle measure 4 cm and 7 cm. What is the range of values for the possible lengths of the third side? A. 4 < x < 7 C. 7 < x < 11 B. 3 < x < 11 D. 11 < x < 15 98. Which of the following statements is TRUE? A. Arectangle is a square. B. A parallelogram is a trapezoid. C. A rhombus is a rectangle. D. A square is a rhombus.

GENERAL EDUCATION

MATHEMATICS

75

99. Consider the quadrilateral below. Find the value of x.

A. 22 B. 56

C. 112 D. 54

100.

If the sum of the interior angles of a regular polygon is 1980 degrees, how many sides does it have? A. 11 C. 13 B. 12 D. 14

101.

What is the sum of the measures of the interior angles of an icosagon? A. 3100 C. 3240 B. 3140 D. 2850

102.

What is the measure of an interior angle of a dodecagon? A. 120 degrees C. 140 degrees B. 130 degrees D. 150 degrees

103.

How many unique diagonals can be drawn in the pentagon? A. 5 C. 7 B. 6 D. 10

104.

Nine unique diagonals can be drawn in a regular polygon.How many sides does it have?? A.9 C.7 B.8 D.6

105.

A triangle has a perimeter of 50.If 2 of its sides are equal and the third side is 5 more than the equal sides , What is the length of the third side? A. 5 C. 15 B. 10 D. 20

106.

A rectangle is4times as long as it is wide. If the length is increased by 4 inches and the width is decreased by by 1 inche, the area will be 60 square inches. What were the dimensions of the original rectangle? A. 2 x 32 C. 3 x 14 B. 4 x 16 D 5 x 12

107.

In a quadrilateral two angles are equal. The third angle is equal to the sum of the two equal angles. The fourth angle is 60o lees than twice the sum of the other three angles. Find the measures of the angles in the quadrilateral. A. 25o, 35o, 90o and 220o C. 35o, 35o, 70o and 220o o o o B. 25 , 45o, 70 and 70 D. 35o, 35o, 70o and 210o

108.

If one side of a square is doubled in length and the adjacent side is decreased by two centimeters, the area of the resulting rectangle is 96 square centimeters larger than that of the original square. Find the dimensions of the rectangle. A. 17 x 24 C. 10 X 24 B. 24 x 24 D. 6 x 16

76

LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS)

109.

The smallest angle of a triangle is two-third the size of the middle angle, and the middle angleis three-sevenths of the largest angle. Find all three angle measures. A. 30o, 60o, 90o C. 35o, 45o, 110o o o o B. 45 , 45 , 90 D. 30o, 445o, 105o

110.

If the height of a triangle is 5 inches less than the length of its base, and if the area of the triangle is 52 square inches, find the base and the height. A. Base = 13, height = 8 C.Base = 11, height = 7 B. Base = 12, height = 9 D. Base = 13, height = 4

111.

A wood frame for pouring concrete has an interior perimeter of 14 meters. Its length is 1 meter greater than its width. The frame is to be braced with twelve-gauge steel croos wires. Assuming an extra half meter of wire is used at either end of a cross-wire for anchoring, what length of wire should be cut for its brace? A. 6 m C. 8 m B. 7 m D. 12 m

112.

Find the largest possible rectangular area you can enclose, assuming you have 128 meters of fencing. A. 256 m2 C. 1024 m2 B. 512 m2 D. 2048 m2

113.

In a photograph, Bianca is 9 cm tall and his brother Tristan is 10 cm tall. Bianca’s actual height is 153 cm. What is Tristan’s actual height? A. 148 cm C. 168 cm B. 156 cm D. 170 cm

114.

The measures of the angles of a triangle are in a ratio of 2:3:4. Find the measure of the middle angle. A. 30o C. 60o o B. 40 D. 80o

115.

The graph shows the number of socks, belts, handkerchiefs, neckties sold by a store in one week.

Number of items

150 100

50

0 Items Sold by Store

The names of the items are missing on the graph. Socks were the most often sold, and fewer neckties than any other item were sold. More belts than handkerchiefs were sold. How many belts were sold? A. 80 C. 120 B. 90 D. 140

GENERAL EDUCATION

MATHEMATICS

77

116. An empty box weighs 1.3 kilos. A Math book weighs 1.5 kilos. Which expression gives the weight of the box when filled with the y Math books? A. 1.3y + 1.5 C. 1.3 + 1.5y B. 1.5y - 1.3 D. 1.3y + 1.5y

2.2

Solve problems involving basic terms and concepts in plane geometry

117. A builbing 25 m tall casts a shadow 10 m long. How long is the shadow of a 5-foot girl beside the buiding? A. 2 ft C. 10 ft B. 2.5 ft D. 250 ft

standing

118. What is the maximum number of books, each 1.4 cm thick that can be put vertically in a shelf which is 64 cm long? A. 44 C. 46 B. 45 D. 64 ELEMENTARY ALGEBRA 3.1 Show astery of basic terms and concepts in 3.1.1 Polynomials 3.1.2 Linear equation 3.1.3Linear inequalities 3.2 Solve, evaluate, and manipulate symbolic and numerical problems in eelementary algebra by applying fundamental rules, principles and processes 119.

Factor completely the expression: a2x – 5by – 5a2y + b2x. A. (a2 + b2)(x – 5y) C. (a + b)(a – b)(x – 5y) 2 2 B. (a + b )(x + 4y + 3) D. (a2 + b2)(x2 – 5y2)

120.

Which among the following is NOT a perfect square trinomial? A. x2 + 8x + 16 C. 49x2 + 70x + 36 2 B. 9x + 12x + 4 D. x2 + 6x + 9

121.

Factor completely the expression: 27a3 – 54a2b + 36ab2 – 8b3. A. (3a – 3b)3 C. (4a – 3b)3 3 B. (a – 3b) D. (3a – 2b)3

122.

What is the greatest monomial factor of the expression: -13abc – 39bc +26ab? A. 3b B. -13b

123.

Which factoring technique will best help you to factor the expression: x2 + 6x – 7 = 0? A. Difference of two cubes B. Common monomial factor

124.

C. 13abc D. 26b

C. Grouping D. Completing the square

Find the general equation of the line which passes through the points: (2, -1) and (-3, 5). A. 6x + 5y – 7 = 0 B. 5x – 6y – 7 = 7

C. 6x + 7y – 5 = 0 D. 6x + 6x – 5 = 0

78

LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS) 123.

What is the equation of the line with x-intercept of 4 and y-intercept of 3? A. 3x + 4y = -12 C. 6x – 8y = 12 B.3x – 4y = 12 D. 4x – 3y = 12

124.

Find the equation of the line with a slope of 4 and passing through the point (-5, 3). A. x – 4y = -23 C. 4x – y = -23 B. 4x - 4y = 23 D. x – y = -4

125.

Find the slope of the line describe by the following table of values: x -2 0 2 4 y -7 -4 -1 2 A.1.50 C. 2.50 B. 0.66 D. 3.50

126.

What is the equation of the line whose slope is -2 and whose y-intercept is 3? A. 2x + 3y = 6 C. 2x +2y = 4 B. x + 2y = 3 D. 2x + y = 3

129.

The length of rectangle is 18 cm. What are the possible widths that will give a perimeter less than 150 cm? A. 3 < width < 54 C. 18 < width < 36 B. 0 < width < 57 D. 12 < width < 57

130.

What is the simplest form of the expression? A. -2x + 4y – 17 B. 2x + 4y + 17

131.

If x = 1 and y = -2, what is the value of the expression A. − 15

B. 2 132.

C. 2x + 4y – 17 D. 2x + 4y

9 2

C. − D.

-

𝑥2 2𝑦𝑥

4x +

3𝑥 𝑦2

?

7 2 17 4

If -3x < 6, which of the following statement is TRUE? A. x < - 2 C. x > 2 B. x < 2 D. x > -2

4. STATISTICS AND PROBABILITY 4.1 Show mastery and knowledge of basic terms and concepts in statistics and probability 4.2 Solve, evaluate, and manipulate symbolic and numerical problems in statistics and probability by applying fundamental rules, principles and processes. 133.

If a die is rolled, what is the probability of getting a number divisable by 2? A. 1/6 C.1/4 B.1⁄2 D. 1/3

134.

Which among the measures of central tendency is NOT influenced by outliers? A. mean C. median B. weightend mean D. mode

GENERAL EDUCATION

MATHEMATICS

135.

Monica obtained the following results from her mathematics exams: 80, 82, 83, 91. What score must she get on the next exam so that her average score is 85? A. 92 C. 89 B. 93 D. 8

136.

In the Filipino test, eight students obtained the following scors: 10, 15, 12, 18, 16, 24, 12, 14. What is the median score? A.14 C. 15 B. 14.5 D. 15

137.

The following table summarizes the scores of Section A on the recent periodic test in social studies. What is the median score interval? Score 16-23 24-31 32-39 40-47 48-45 56-62

Frequency 2 4 6 12 10 8

A. 24-31 B. 32-39

C. 40-47 D. 48-55

138.

The following measurements were obtained from the caliper: 20, 15, 20, 14, 18, 15, 6. What is the mode? A. 15 C. 14 B. 20 D. 15 and 20

139.

The following are Joselito’s grades for the 3rd quarter. Find his general weighted average. Subject Math English Science Filipino HEKASI A. 87.08 B. 89.50

Units 3 2 3 2 2

Grade 89 84 90 86 84 C. 86.36 D. 87.45

For the numbers 96-100, consider the following situation.The grades in math of the students in section B are as follows: 70, 95, 60, 80, 100. 140.

What is the mean absolute deviation of their group? A. 11.7 C. 14.6 B. 13.2 D. 15.9

141.

What is the population variance of their group? A. 224 C. 264 B. 250 D. 280

79

80

LET Comprehensive Reviewer Based on NCBTS and Table of Specifications (TOS) 142.

What is the population standard deviation of their group? A. 16.73 C. 1.58 B. 1.41 D. 14.97

143.

What is the range of their group? A. 60-95 B. 70-100

C. 60-100 D. 80-95

144.

What can you infer from the measures of variability obtained from this population? A.The population is very homogeneous. B. The measures are very unstable. C. The grades are very scattered. D.The range of scores is a very reliable measure of variability.

145.

What measure of central tendency can best describe the size of t-shirts commonly used by teen-agers A. mean C. mode B. median D. both A and C

146.

The following aree the results of the recent achievement test in mathematics of four divisions. Division I II III IV Which division performed best? A. I B. II

Mean 34 34 23 20

Standard deviation 4.5 3.0 1.0 2.0

C. III D. IV

147.

What is the probability of getting a multiple of 3 when a die is tossed? A. 1/6 C. 1/3 B. 1/4 D. 1/2

148.

In how many ways can a 5 basketball players be choosen from a group of 9 players? A. 126 C. 15,120 B. 212 D. 362,880

GENERAL EDUCATION

MATHEMATICS

ANSWER KEY: MATHEMATICS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

B A C C D B A D C B D A C D B C C C B A B A A B D B A A A B C B D C C B C D B C B A D A A A D C A A B C C

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 105

A A D B A C C A C B D C A B D A D D C D D D C C D B B A D C A D B C A A A B C D B A D B D B C C D A D D B

106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

B C C D A A C D C C C A B A C D B D A C A D B C C D B C C B C D A B A C C C C B C A

81