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Fundamentals of Mathematics

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Arithmetic • • • •

Sum = addend + addend (or terms) Difference = minuend – subtrahend Product = multiplicand multiplier (or factors) Quotient = dividend divisor

a • Take note! is undefined 0 2 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Arithmetic • Addition – Same sign: add the numbers, copy the sign – Opposite signs: subtract the numbers, copy sign of larger number

• Subtraction – Change the operation into addition, then change the sign of the subtrahend

• Multiplication/division – Count the number of negative signs; when even = 3 positive; when odd = negative Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Properties of arithmetic • • • • •

Commutative (,) a + b = b + a Associative (,) Distributive ( over and over +) Identity element (0 for and 1 for ) Inverse elements – Additive inverses have the sum 0 – Multiplicative inverses have the product 1

• Multiplicative property of zero 4 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Properties of equality • Reflexive • Symmetric

aa

a b; then b a

• Transitive

a b and b c, then a c

• Substitution

If a b, then any expression involving a retains the same value if a is replaced by b. 5

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Order of operations: PEMDAS • Parenthesis or grouping symbols • Exponents • Multiplication and division (whichever comes first) • Addition and subtraction (whichever comes first)

http://www.mahalo.com/pemdas/

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

6 Philippines.

Laws of exponents • A power is an expression involving repeated multiplication. • base: b; power or exponent: m or n • Take note! 0

a 1 1 a a

m n

m n

b b b m n mn (b ) b m b mn 0 b ; hence b 1 n b m m m (ab) a b m m a a m b b 0 1 a 1 n a n ; since n n a a a

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Scientific notation • Write numbers as the product of a number less than 10 and a power of 10. • The sign of the exponent is positive when the original figure is less than 1 and negative when more than 1.

2

245 2.45 10 3 0.0056 5.6 10 8 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Prime, Composite or Denominate? • Prime – Numbers whose only factors are 1 and itself

• Composite – Numbers with factors other than itself and 1

• Denominate – Numbers with a unit of measurement

9 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

GCF and LCM • Greatest common factor – Useful in reducing fractions to lowest or simplest terms

• Least common multiple – Useful in operations involving dissimilar fractions

10 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Fractions • Improper fractions to mixed numbers

a remainder quotient (a b) b b

• Mixed numbers to improper fractions

a (b * c) a c b b 11 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Fractions • Equivalent fractions – Have the same value – Result from the multiplication and division of the numerators and denominators of a fraction by the same number

• Reducing to simple fractions – Determine the GCF of the numerator and denominator; divide them by the GCF 12 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Ratio and proportion • Ratios may be written as fractions or by using colons

2 is the same as 2 : 3 3 • Proportions are the equality between two ratios

2 4 is the same as 2 : 3 :: 4 : 6 3 6 13 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Sharing/dividing in a ratio When sharing/dividing any amount/quantity (e.g., n) in a ratio (e.g., a : b : c): • Add

a b c number of parts

n share per part • Divide number of parts • Multiply share per part * a share of a

or b or c

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

or b or c

Philippines.

Rules for ratio and proportion a c If , then ad bc. b d a c a b If , then b d c d. a c b d If , then . b d a c Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

15

Variation • Direct:

y kx

– Variable y varies at the same rate as variable x

• Inverse:

k y x

– As variable x increases, y decreases and vice-versa

• Joint – More than one variable is involved in a direct variation Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

16

Algebra

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Mathematical sentences • is – was – will be – has: • plus – sum – more than – greater than – farther than – years from now – increased by – exceeds by: • decreased by – minus – less than – diminished by – younger than – years ago – subtracted from: • divided by – quotient – per: 18 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Factoring polynomials • Factor out the common monomial factor • Difference of two squares 2

2

a b (a b)(a b) • Perfect square trinomial 2

2

a 2ab b (a b)

2

• FOIL method and quadratic polynomials

(a b)(c d ) ac (ad bc) bd 2 standard form : ax bx c 19 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Notes in solving word problems • Consecutive numbers: x , x 1, x 2 • Consecutive even/odd numbers: x , x 2, x 4 • Mixture (e.g., of coins, vehicles, chemicals): total amt = number of coins * denomination number of feet/wheels = animals/vehicle * # of feet/wheels of each 20 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Notes in solving word problems • Motion:

• Work:

distance speed time part of a job done by one person (in 1 day/hour) 1 number of days/hours it takes the person to complete

• Age: add when it says “# of years from now” and subtract when it says “# of years ago” 21 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Notes in solving word problems • Interest

I Prt

• Compound interest

r nt A P(1 ) n

or future value FV PV (1 r ) t • Continuous compound interest

A Pe

rt

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Notes in solving word problems • Percent change

new original % change original • Discount

Discount rate original price Discounted price original price discount • Commission

Commission rate total earnings 23 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Functions • A function is a set of ordered pairs such that for each first component, there is at most one value of the second component • Three things that specify a function: – Domain – Range – A rule which assigns to each member of the domain exactly one member of the range 24 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Functions • Domain – set of all first components in each element of the set

• Range – set of all the second components in each element of the set

• When y is a function of x, the set of values of x is the domain of the function and the set of values of y is the range of the function. 25 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Geometry

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Lines • Parallel lines do not meet. • Intersecting lines meet at one point. The sum of any 2 adjacent angles formed is 180°. • Perpendicular lines meet at one point, at 90°.

27 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Kinds of Angles • • • • •

Acute: less than 90° Right: 90° Obtuse: more than 90°, but less than 180° Straight: 180° Reflex: more than 180 degrees, less than 360°

28 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Angle relationships • Supplementary angles – Sum of measures is 180°

• Complementary angles – Sum of measures is 90°

29 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Pythagorean theorem • Applies to right triangles • Legs: a and b • Hypotenuse: c

2

2

c a b

2

30 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Polygons • Polygons are flat, closed figures consisting of line segments. • Exterior angles of a polygon add up to 360°. • The sum of the interior angles of a polygon, with the number of sides n: 180° (n 2) • The sum of the exterior angles of a simple, closed polygon is 360°. 31 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Measurements • Perimeter: sum of the length of all sides

Prectangle 2l 2w

Circumference 2r

Ptriangle a b c Psquare 4s

• Area: size covered by a surface

Asquare s

2

Acircle r

2

Arectangle lw 1 Atriangle bh 2

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

32

Measurements • Volume: the space occupied or contained by a substance or shape

Vcube s V pyramid

3

1 bh 3

4 3 Vsphere r 3 1 2 Vcone r h 3

Vrectangular prism abc or lwh 33 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Statistics, Probability and Number Series

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Measures of central tendency • Mean – Add the numbers and divide the sum by the number of values (which were added).

• Median – The middle number when numbers are written in order. (When the number of values is even, the median is the mean of the two middle values.)

• Mode – The number which occurs most often 35 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Counting techniques • If two or more actions are performed in a particular order, such that the first action produces a results, the second action produces b results, the third action produces c results, and so on, then:

a * b * c * ... total number of possible results

36 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Counting techniques: Permutation • Objects are arranged in a definite order: – n different things taken r at a time – n things taken n at a time in which q are alike, r are alike and so on – n distinct objects are arranges along a fixed circle

n! n Pr (n r )! n! n Pr (q! r!...) Pn (n 1)!

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

37

Counting techniques: Combination • Objects are not arranged in a particular order – n different things taken r at a time

n! n Cr (n r )! r!

38 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Probability Probability of an outcome number of ways an outcome can happen the total number of possible outcomes

39 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Arithmetic sequences and series • Arithmetic sequence/progression: a sequence of numbers where successive members of the sequence have a constant difference (d). • Formula for n-th term an a1 (n 1)d • Formula for sum of first n values of a sequence n(n 1)

Sn

2 40

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Geometric sequences and series • Geometric sequence/progression: a sequence of numbers where successive members of the sequence are produced by multiplying them by a constant multiplier (r, or common ratio)

a n a1 * r • Formula for n-th term • Formula for sum of first n values of a n sequence a1 (1 r )

Sn

n 1

1 r

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

41 Philippines.

References and further reading British Broadcasting Corporation. (2012). GCSE Bitesize: Maths. Retrieved 27 December 2012, from http://www.bbc.co.uk/schools/ gcsebitesize/ maths/ Fisico, M., L. Sia, J. Ho, Z. Maralit, J. Tan, . . . J. Rosello, R. Franco. (1998). 21st Century Mathematics Series. Quezon City: Phoenix Publishing House, Inc. Pierce, Rod. (2012). Math Is Fun. Retrieved 28 December 2012, from http://www.mathsisfun.com/index.htm Stapel, E. (2012). The Purplemath Forums. Retrieved 27 December 2012, from http://www.purplemath.com/ index.htm

42 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

View more...
Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Arithmetic • • • •

Sum = addend + addend (or terms) Difference = minuend – subtrahend Product = multiplicand multiplier (or factors) Quotient = dividend divisor

a • Take note! is undefined 0 2 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Arithmetic • Addition – Same sign: add the numbers, copy the sign – Opposite signs: subtract the numbers, copy sign of larger number

• Subtraction – Change the operation into addition, then change the sign of the subtrahend

• Multiplication/division – Count the number of negative signs; when even = 3 positive; when odd = negative Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Properties of arithmetic • • • • •

Commutative (,) a + b = b + a Associative (,) Distributive ( over and over +) Identity element (0 for and 1 for ) Inverse elements – Additive inverses have the sum 0 – Multiplicative inverses have the product 1

• Multiplicative property of zero 4 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Properties of equality • Reflexive • Symmetric

aa

a b; then b a

• Transitive

a b and b c, then a c

• Substitution

If a b, then any expression involving a retains the same value if a is replaced by b. 5

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Order of operations: PEMDAS • Parenthesis or grouping symbols • Exponents • Multiplication and division (whichever comes first) • Addition and subtraction (whichever comes first)

http://www.mahalo.com/pemdas/

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

6 Philippines.

Laws of exponents • A power is an expression involving repeated multiplication. • base: b; power or exponent: m or n • Take note! 0

a 1 1 a a

m n

m n

b b b m n mn (b ) b m b mn 0 b ; hence b 1 n b m m m (ab) a b m m a a m b b 0 1 a 1 n a n ; since n n a a a

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Scientific notation • Write numbers as the product of a number less than 10 and a power of 10. • The sign of the exponent is positive when the original figure is less than 1 and negative when more than 1.

2

245 2.45 10 3 0.0056 5.6 10 8 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Prime, Composite or Denominate? • Prime – Numbers whose only factors are 1 and itself

• Composite – Numbers with factors other than itself and 1

• Denominate – Numbers with a unit of measurement

9 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

GCF and LCM • Greatest common factor – Useful in reducing fractions to lowest or simplest terms

• Least common multiple – Useful in operations involving dissimilar fractions

10 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Fractions • Improper fractions to mixed numbers

a remainder quotient (a b) b b

• Mixed numbers to improper fractions

a (b * c) a c b b 11 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Fractions • Equivalent fractions – Have the same value – Result from the multiplication and division of the numerators and denominators of a fraction by the same number

• Reducing to simple fractions – Determine the GCF of the numerator and denominator; divide them by the GCF 12 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Ratio and proportion • Ratios may be written as fractions or by using colons

2 is the same as 2 : 3 3 • Proportions are the equality between two ratios

2 4 is the same as 2 : 3 :: 4 : 6 3 6 13 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Sharing/dividing in a ratio When sharing/dividing any amount/quantity (e.g., n) in a ratio (e.g., a : b : c): • Add

a b c number of parts

n share per part • Divide number of parts • Multiply share per part * a share of a

or b or c

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

or b or c

Philippines.

Rules for ratio and proportion a c If , then ad bc. b d a c a b If , then b d c d. a c b d If , then . b d a c Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

15

Variation • Direct:

y kx

– Variable y varies at the same rate as variable x

• Inverse:

k y x

– As variable x increases, y decreases and vice-versa

• Joint – More than one variable is involved in a direct variation Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

16

Algebra

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Mathematical sentences • is – was – will be – has: • plus – sum – more than – greater than – farther than – years from now – increased by – exceeds by: • decreased by – minus – less than – diminished by – younger than – years ago – subtracted from: • divided by – quotient – per: 18 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Factoring polynomials • Factor out the common monomial factor • Difference of two squares 2

2

a b (a b)(a b) • Perfect square trinomial 2

2

a 2ab b (a b)

2

• FOIL method and quadratic polynomials

(a b)(c d ) ac (ad bc) bd 2 standard form : ax bx c 19 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Notes in solving word problems • Consecutive numbers: x , x 1, x 2 • Consecutive even/odd numbers: x , x 2, x 4 • Mixture (e.g., of coins, vehicles, chemicals): total amt = number of coins * denomination number of feet/wheels = animals/vehicle * # of feet/wheels of each 20 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Notes in solving word problems • Motion:

• Work:

distance speed time part of a job done by one person (in 1 day/hour) 1 number of days/hours it takes the person to complete

• Age: add when it says “# of years from now” and subtract when it says “# of years ago” 21 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Notes in solving word problems • Interest

I Prt

• Compound interest

r nt A P(1 ) n

or future value FV PV (1 r ) t • Continuous compound interest

A Pe

rt

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Notes in solving word problems • Percent change

new original % change original • Discount

Discount rate original price Discounted price original price discount • Commission

Commission rate total earnings 23 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Functions • A function is a set of ordered pairs such that for each first component, there is at most one value of the second component • Three things that specify a function: – Domain – Range – A rule which assigns to each member of the domain exactly one member of the range 24 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Functions • Domain – set of all first components in each element of the set

• Range – set of all the second components in each element of the set

• When y is a function of x, the set of values of x is the domain of the function and the set of values of y is the range of the function. 25 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Geometry

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Lines • Parallel lines do not meet. • Intersecting lines meet at one point. The sum of any 2 adjacent angles formed is 180°. • Perpendicular lines meet at one point, at 90°.

27 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Kinds of Angles • • • • •

Acute: less than 90° Right: 90° Obtuse: more than 90°, but less than 180° Straight: 180° Reflex: more than 180 degrees, less than 360°

28 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Angle relationships • Supplementary angles – Sum of measures is 180°

• Complementary angles – Sum of measures is 90°

29 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Pythagorean theorem • Applies to right triangles • Legs: a and b • Hypotenuse: c

2

2

c a b

2

30 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Polygons • Polygons are flat, closed figures consisting of line segments. • Exterior angles of a polygon add up to 360°. • The sum of the interior angles of a polygon, with the number of sides n: 180° (n 2) • The sum of the exterior angles of a simple, closed polygon is 360°. 31 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Measurements • Perimeter: sum of the length of all sides

Prectangle 2l 2w

Circumference 2r

Ptriangle a b c Psquare 4s

• Area: size covered by a surface

Asquare s

2

Acircle r

2

Arectangle lw 1 Atriangle bh 2

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

32

Measurements • Volume: the space occupied or contained by a substance or shape

Vcube s V pyramid

3

1 bh 3

4 3 Vsphere r 3 1 2 Vcone r h 3

Vrectangular prism abc or lwh 33 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Statistics, Probability and Number Series

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Measures of central tendency • Mean – Add the numbers and divide the sum by the number of values (which were added).

• Median – The middle number when numbers are written in order. (When the number of values is even, the median is the mean of the two middle values.)

• Mode – The number which occurs most often 35 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Counting techniques • If two or more actions are performed in a particular order, such that the first action produces a results, the second action produces b results, the third action produces c results, and so on, then:

a * b * c * ... total number of possible results

36 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Counting techniques: Permutation • Objects are arranged in a definite order: – n different things taken r at a time – n things taken n at a time in which q are alike, r are alike and so on – n distinct objects are arranges along a fixed circle

n! n Pr (n r )! n! n Pr (q! r!...) Pn (n 1)!

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

37

Counting techniques: Combination • Objects are not arranged in a particular order – n different things taken r at a time

n! n Cr (n r )! r!

38 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Probability Probability of an outcome number of ways an outcome can happen the total number of possible outcomes

39 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Arithmetic sequences and series • Arithmetic sequence/progression: a sequence of numbers where successive members of the sequence have a constant difference (d). • Formula for n-th term an a1 (n 1)d • Formula for sum of first n values of a sequence n(n 1)

Sn

2 40

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

Geometric sequences and series • Geometric sequence/progression: a sequence of numbers where successive members of the sequence are produced by multiplying them by a constant multiplier (r, or common ratio)

a n a1 * r • Formula for n-th term • Formula for sum of first n values of a n sequence a1 (1 r )

Sn

n 1

1 r

Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

41 Philippines.

References and further reading British Broadcasting Corporation. (2012). GCSE Bitesize: Maths. Retrieved 27 December 2012, from http://www.bbc.co.uk/schools/ gcsebitesize/ maths/ Fisico, M., L. Sia, J. Ho, Z. Maralit, J. Tan, . . . J. Rosello, R. Franco. (1998). 21st Century Mathematics Series. Quezon City: Phoenix Publishing House, Inc. Pierce, Rod. (2012). Math Is Fun. Retrieved 28 December 2012, from http://www.mathsisfun.com/index.htm Stapel, E. (2012). The Purplemath Forums. Retrieved 27 December 2012, from http://www.purplemath.com/ index.htm

42 Exclusively for My Review Coach online LET review. Not for redistribution. © 2011 My Review Coach of

Philippines.

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