Range: The difference between largest and smallest value of the. observation is called The Range and is denoted by R ie

Size: px
Start display at page:

Download "Range: The difference between largest and smallest value of the. observation is called The Range and is denoted by R ie"

Transcription

1 TNPSC GROUP 2 APTITUDE AND MENTAL ABILITY TEST IMPORTANT FORMULAS 1 Page

2 Range: The difference between largest and smallest value of the observation is called The Range and is denoted by R ie R = Largest value Smallest value R=L-S Lorenz Curve: Lorenz curve is a graphical method of studying dispersion It was introduced by MaxOLorenz, a great Economist and a statistician, to study the distribution of wealth and income It is also used to study the variability in the distribution of profits, wages, revenue, etc Arithmetic mean or mean : WEIGHTED ARITHMETIC MEAN: - 2 Page

3 Harmonic mean (HM) : Median : The median is that value of the variate which divides the Vgroup into two equal parts, one part comprising all values greater, and the other, all values less than median Ungrouped or Raw data : Arrange the given values in the increasing or decreasing order If the number of values are odd, median is the middle value If the number of values are even, median is the mean of middle two values By formula Mode : The mode refers to that value in a distribution, which occur most frequently It is an actual value, which has the highest concentration of items in and around it Co-efficient of Range : L- LARGE NUMBER S SMALL NUMBER MENTAL ABILITY: 3 Page

4 IMPORTANT FORMULAS TOPIC WISE SIMPLIFICATION FORMULAS What is BODMAS rule? BODMAS rule defines the correct sequence in which operations are to be performed in a given mathematical expression to find its value In BODMAS, B = Bracket O = Order (Powers, Square Roots, etc) DM = Division and Multiplication (left-to-right) AS = Addition and Subtraction (left-to-right) Some Basic Formulae: (a + b)(a - b) = (a2 - b2) (a + b)2 = (a2 + b2 + 2ab) (a - b)2 = (a2 + b2-2ab) (a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca) (a3 + b3) = (a + b)(a2 - ab + b2) (a3 - b3) = (a - b)(a2 + ab + b2) (a3 + b3 + c3-3abc) = (a + b + c)(a2 + b2 + c2 - ab - bc - ac) When a + b + c = 0, then a3 + b3 + c3 = 3abc Percentage IMPORTANT FORMULAS Values to memorize for quick calculations 4 Page

5 Highest Common Factor (HCF) Lowest Common Multiple (LCM) FORMULAS Highest Common Factor (HCF) or Greatest Common Measure (GCM) or Greatest Common Divisor (GCD) The HCF of two or more than two numbers is the greatest number that divided each of them exactly There are two methods of finding the HCF of a given set of numbers: 1 Factorization Method 2 Division method Factorization Method: Express the each one of the given numbers as the product of prime factors The product of least powers of common prime factors gives HCF 2 Division Method: Suppose we have to find the HCF of two given numbers, divide the larger by the smaller one Now, divide the divisor by the remainder Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder The last divisor is required HCF Least Common Multiple (LCM) The least number which is exactly divisible by each one of the given numbers is called their LCM There are two methods of finding the LCM of a given set of numbers: 1 Factorization Method, 2 Division Method (Division Method is short cut method of LCM) 1 Factorization Method: Resolve each one of the given numbers into a product of prime factors Then, LCM is the product of highest powers of all the factors 2 Division Method : Arrange the given numbers in a row in any order Divide by a number which divided exactly at least two of the given numbers and carry forward the numbers which are not divisible Repeat the above process till no two of the numbers are divisible by the same number except 1 The product of the divisors and the undivided numbers is the required LCM of the given numbers Product of two numbers Product of two numbers = Product of their HCF and LCM Co prime numbers Two numbers are said to be co primes if their HCF is 1 HCF and LCM of Fractions 5 Page

6 Ratio and Proportion FORMULAS Ratio: The ratio of two quantities a and b in the same units, is the fraction and we write it as a : b In the ratio a : b, we call a as the first term or antecedent and b, the second term or consequenteg The ratio 5 : 9 represents 5 with antecedent = 5, consequent = 9 Rule: The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio Eg 4 : 5 = 8 : 10 = 12 : 15 Also, 4 : 6 = 2 : 3 Proportion: The equality of two ratios is called proportion If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion Here a and d are called extremes, while b and c are called mean terms Product of means = Product of extremes Thus, a : b :: c : d (b x c) = (a x d) Fourth Proportional: If a : b = c : d, then d is called the fourth proportional to a, b, c Third Proportional: a : b = b : c, then c is called the third proportion to a and b Mean Proportional: Mean proportional between a and b is Comparison of Ratios: Compounded Ratio: The compounded ratio of the ratios: (a : b), (c : d), (e : f) is (ace : bdf) Duplicate Ratios: Duplicate ratio of (a : b) is (a2 : b2) Sub-duplicate ratio of (a : b) is (a : b) Triplicate ratio of (a : b) is (a3 : b3) Sub-triplicate ratio of (a : b) is (a1/3 : b1/3) a c a+b c+d If =, then = [componendo and dividendo] b d a-b c-d Variations: We say that x is directly proportional to y, if x = ky for some constant k and we write, x y We say that x is inversely proportional to y, if xy = k for some constant k and 1 we write, x y 6 Page

7 Simple interest Compound interest IMPORTANT FORMULAS Simple Interest - Important Formulas Principal: The money borrowed or lent out for a certain period is called the principal or the sum Interest: Extra money paid for using other's money is called interest Simple Interest (SI): If the interest on a sum borrowed for certain period is reckoned uniformly, then it is called simple interest Let Principal = P, Rate = R% per annum (pa) and Time = T years Then PxRxT (i) Simple Intereest = x SI x SI x SI (ii) P = ;R= and T = RxT PxT PxR Compound Interest - Important Formulas Let Principal = P, Rate = R% per annum, Time = n years When interest is compound Annually: R n Amount = P 1 + When interest is compounded Half-yearly: (R/2) 2n Amount = P 1 + When interest is compounded Quarterly: (R/4) 4n Amount = P 1 + When interest is compounded Annually but time is in fraction, say 3 years 3 Amount = P 1 + R x 1+ R When Rates are different for different years, say R1%, R2%, R3% for 1st, 2nd and 3rd year respectively R1 R2 R3 Then, Amount = P Present worth of Rs x due n years hence is given by: x Present Worth = 1+ R 7 Page

8 Area Volume IMPORTANT FORMULAS FUNDAMENTAL CONCEPTS Results on Triangles: Sum of the angles of a triangle is 180 The sum of any two sides of a triangle is greater than the third side Pythagoras Theorem: 1 In a right-angled triangle, (Hypotenuse)2 = (Base)2 + (Height)2 2 The line joining the mid-point of a side of a triangle to the positive vertex is called the median 3 The point where the three medians of a triangle meet, is called centroid The centroid divided each of the medians in the ratio 2 : 1 4 In an isosceles triangle, the altitude from the vertex bisects the base 5 The median of a triangle divides it into two triangles of the same area The area of the triangle formed by joining the mid-points of the sides of a given triangle is one-fourth of the area of the given triangle Results on Quadrilaterals: 1 The diagonals of a parallelogram bisect each other 2 Each diagonal of a parallelogram divides it into triangles of the same area 3 The diagonals of a rectangle are equal and bisect each other 4 The diagonals of a square are equal and bisect each other at right angles 5 The diagonals of a rhombus are unequal and bisect each other at right angles 6 A parallelogram and a rectangle on the same base and between the same parallels are equal in area 7 Of all the parallelogram of given sides, the parallelogram which is a rectangle has the greatest area IMPORTANT FORMULAE 1 Area of a rectangle = (Length x Breadth) Area Area Length = and Breadth = Breadth Length 2 Perimeter of a rectangle = 2(Length + Breadth) Area of a square = (side)2 = (diagonal)2 Area of 4 walls of a room = 2 (Length + Breadth) x Height Area of a triangle = x Base x Height Area of a triangle = s(s-a)(s-b)(s-c) where a, b, c are the sides of the triangle and s = (a + b + c) 3 Area of an equilateral triangle = x (side)2 4 a Radius of incircle of an equilateral triangle of side a = 23 a Radius of circumcircle of an equilateral triangle of side a = 3 Radius of incircle of a triangle of area and semi-perimeter r = s 8 Page

9 1 Area of parallelogram = (Base x Height) 2 Area of a rhombus = 3 Area of a trapezium = 1 2 Area of a circle = R2, where R is the radius Circumference of a circle = 2 R 2 R Length of an arc =, where is the central angle R2 Area of a sector = (arc x R) = x (Product of diagonals) x (sum of parallel sides) x distance between them Circumference of a semi-circle = R R2 Area of semi-circle = 2 9 Page

10 VOLUME AND SURFACE AREA CUBOID Let length = l, breadth = b and height = h units Then Volume = (l x b x h) cubic units Surface area = 2(lb + bh + lh) sq units Diagonal = l2 + b2 + h2 units CUBE Let each edge of a cube be of length a Then, Volume = a3 cubic units Surface area = 6a2 sq units Diagonal = 3a units CYLINDER Let radius of base = r and Height (or length) = h Then, Volume = ( r2h) cubic units Curved surface area = (2 rh) sq units Total surface area = 2 r(h + r) sq units CONE Let radius of base = r and Height = h Then, Slant height, l = h2 + r2 units Volume = r2h cubic units Curved surface area = ( rl) sq units Total surface area = ( rl + r2) sq units SPHERE Let the radius of the sphere be r Then, Volume = r3 cubic units Surface area = (4 r2) sq units HEMISPHERE Let the radius of a hemisphere be r Then, Volume = r3 cubic units Curved surface area = (2 r2) sq units Total surface area = (3 r2) sq units Note: 1 litre = 0 cm3 10 P a g e

11 TIME AND WORK IMPORTANT FORMULAS If A can do a piece of work in n days, work done by A in 1 day = 1/n If A does 1/n work in a day, A can finish the work in n days If M1 men can do W1 work in D1 days working H1 hours per day and M2 men can do W2 work in D2 days working H2 hours per day (where all men work at the same rate), then M1 D1 H1 / W1 = M2 D2 H2 / W2 If A can do a piece of work in p days and B can do the same in q days, A and B together can finish it in pq / (p+q) days If A is thrice as good as B in work, then Ratio of work done by A and B = 3 : 1 Ratio of time taken to finish a work by A and B = 1 : 3 11 P a g e

12 12 P a g e

13 13 P a g e

14 14 P a g e

15 15 P a g e

16 - 16 P a g e

17 17 P a g e

18 18 P a g e

19 19 P a g e

114 Handy Formulae for Quantitative Aptitude Problems Author: Sagar Sonker Table of Contents

114 Handy Formulae for Quantitative Aptitude Problems Author: Sagar Sonker Table of Contents Table of Contents ℵ Numbers ℵ H.C.F & L.C.M of Numbers ℵ Surds & Indices ℵ Percentage ℵ Profit & Loss ℵ Ratio & Proportion ℵ Partnership ℵ Chain Rule ℵ Time & Work ℵ Pipes & Cisterns ℵ Time And Distance

More information

Quantitative Aptitude Formulae

Quantitative Aptitude Formulae Quantitative Aptitude Formulae NUMBERS: 1. Sum of first n natural numbers = n(n+1)/2 2. Sum of the squares of first n natural numbers = n (n+1) (2n+1)/6 3. Sum of the cubes of first n natural numbers =

More information

50 Keys To CAT Arithmetic, Algebra, Geometry and Modern Mathematics EASY EFFECTIVE PERSONALISED

50 Keys To CAT Arithmetic, Algebra, Geometry and Modern Mathematics EASY EFFECTIVE PERSONALISED 50 Keys To CAT Arithmetic, Algebra, Geometry and Modern Mathematics A collection of 50 very important formulae for Quantitative Ability Section of CAT from the pioneers of online CAT training EASY EFFECTIVE

More information

1 BANK EXAM TODAY CAREER TODAY

1 BANK EXAM TODAY CAREER TODAY 1 BANK EXAM TODAY CAREER TODAY OPERATIONS ON NUMBER Divisibility Rules: A number is divisible by 2 if it is an even number. A number is divisible by 3 if the sum of the digits is divisible by 3. A number

More information

Formulae Quantitative Ability

Formulae Quantitative Ability Formulae Quantitative Ability Problems on Trains: 1. km/hr to m/s conversion: a km/hr = a x 5 18 m/s. 2. m/s to km/hr conversion: a m/s = a x 18 km/hr. 5 3. Time taken by a train of length l metres to

More information

Number system. 1. When sum and difference of two numbers (X and Y) are given, then X = (sum + difference)/2 Y = (sum + difference)/2

Number system. 1. When sum and difference of two numbers (X and Y) are given, then X = (sum + difference)/2 Y = (sum + difference)/2 Number system 1. When sum and difference of two numbers (X and Y) are given, then X = (sum + difference)/2 Y = (sum + difference)/2 2. Difference between two digits of two digit number is = (Difference

More information

CBSE SAMPLE PAPER Class IX Mathematics Paper 1 (Answers)

CBSE SAMPLE PAPER Class IX Mathematics Paper 1 (Answers) CBSE SAMPLE PAPER Class IX Mathematics Paper 1 (Answers) 1. Solution: We have, 81 36 x y 5 Answers & Explanations Section A = ( 9 6 x) ( y 5 ) = ( 9 6 x + y 5 ) (9 6 x y 5 ) [ a b = (a + b)(a b)] Hence,

More information

GATE Formulas & Shortcuts for Numerical Computation

GATE Formulas & Shortcuts for Numerical Computation GATE 2017 Formulas & Shortcuts for Numerical Computation TIME AND DISTANCE -> IMPORTANT FACTS AND FORMULAE Speed = [Distance/Time], Time=[Distance/Speed], Distance = (Speed*Time) x km/hr = [x*5/18] m/sec.

More information

Free GK Alerts- JOIN OnlineGK to AREA FUNDEMENTAL CONCEPTS. 2.Sum of any two sides of a triangle is greater than the third side.

Free GK Alerts- JOIN OnlineGK to AREA FUNDEMENTAL CONCEPTS. 2.Sum of any two sides of a triangle is greater than the third side. Free GK Alerts- JOIN OnlineGK to 9870807070 24.AREA FUNDEMENTAL CONCEPTS I.RESULTS ON TRIANGLES: 1.Sum of the angles of a triangle is 180 degrees. 2.Sum of any two sides of a triangle is greater than the

More information

X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS. 1. Commutative property i ii. 2. Associative property i ii

X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS. 1. Commutative property i ii. 2. Associative property i ii X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS 1. Commutative property i ii 2. Associative property i ii 3. Distributive property i ii 4. De Morgan s laws i ii i ii 5. Cardinality of

More information

Preliminary chapter: Review of previous coursework. Objectives

Preliminary chapter: Review of previous coursework. Objectives Preliminary chapter: Review of previous coursework Objectives By the end of this chapter the student should be able to recall, from Books 1 and 2 of New General Mathematics, the facts and methods that

More information

CDS-I 2019 Elementary Mathematics (Set-C)

CDS-I 2019 Elementary Mathematics (Set-C) 1 CDS-I 019 Elementary Mathematics (Set-C) Direction: Consider the following for the next three (03) items : A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the

More information

COMMON UNITS OF PERIMITER ARE METRE

COMMON UNITS OF PERIMITER ARE METRE MENSURATION BASIC CONCEPTS: 1.1 PERIMETERS AND AREAS OF PLANE FIGURES: PERIMETER AND AREA The perimeter of a plane figure is the total length of its boundary. The area of a plane figure is the amount of

More information

Integer (positive or negative whole numbers or zero) arithmetic

Integer (positive or negative whole numbers or zero) arithmetic Integer (positive or negative whole numbers or zero) arithmetic The number line helps to visualize the process. The exercises below include the answers but see if you agree with them and if not try to

More information

Tips & tricks for Quantitative Aptitude

Tips & tricks for Quantitative Aptitude Tips & tricks for Quantitative Aptitude Quantitative Aptitude is a critical section in aptitude tests and one which all students need to master necessarily. It is critical for them in order to be clear

More information

CLASS X FORMULAE MATHS

CLASS X FORMULAE MATHS Real numbers: Euclid s division lemma Given positive integers a and b, there exist whole numbers q and r satisfying a = bq + r, 0 r < b. Euclid s division algorithm: This is based on Euclid s division

More information

INTERNATIONAL INDIAN SCHOOL, RIYADH. 11cm. Find the surface area of the cuboid (240cm 2 )

INTERNATIONAL INDIAN SCHOOL, RIYADH. 11cm. Find the surface area of the cuboid (240cm 2 ) INTERNATIONAL INDIAN SCHOOL, RIYADH CLASS: IX SUBJECT: MATHEMATICS 1. SURFACE AREAS AND VOLUMES 1. The diagonal of a cube is 12cm. Find its volume. 2. If the lateral surface area of a cube is 1600cm 2,

More information

7. Find the value of If (a+1) and (a-1) are the factors of p(a)= a 3 x+2a 2 +2a - y, find x and y

7. Find the value of If (a+1) and (a-1) are the factors of p(a)= a 3 x+2a 2 +2a - y, find x and y AJANTA PUBLIC SCHOOL ASSIGNMENT (MATHS) SESSION 2018-19 CLASS - IX 1. Are the following Statements are True or False, also give reasons? (i) zero is a rational number (ii) Zero is natural number (iii)

More information

Problem Solving Solved Contents at a Glance

Problem Solving Solved Contents at a Glance Contents at a Glance 1 Ratio 4 2 Proportion 61 3 Expressions 124 4 Equations 165 5 Perimeter 214 6 Area 251 7 Area & Coverage 292 8 Volume & Filling 336 9 Money 377 10 Planning 410 11 Number Properties

More information

AREA CALCULATION - SOLVED EXAMPLES

AREA CALCULATION - SOLVED EXAMPLES AREA CALCULATION - SOLVED EXAMPLES http://www.tutorialspoint.com/quantitative_aptitude/aptitude_area_calculation_examples.htm Copyright tutorialspoint.com Advertisements Q 1 - The difference between the

More information

27 th ARYABHATTA INTER-SCHOOL MATHEMATICS COMPETITION 2010 CLASS = VIII

27 th ARYABHATTA INTER-SCHOOL MATHEMATICS COMPETITION 2010 CLASS = VIII 7 th ARYABHATTA INTER-SCHOOL MATHEMATICS COMPETITION 00 CLASS = VIII Time Allowed: Hours Max. Marks: 00 Roll No. of the Participant: GENERAL INSTRUCTIONS :. Participant should not write his/her name on

More information

Number System. Properties of Centers of Triangle Centroid : MATHEMATICS FOR RRB ALP STAGE-II EXAM

Number System. Properties of Centers of Triangle Centroid : MATHEMATICS FOR RRB ALP STAGE-II EXAM Number System 1. L.C.M. and H.C.F. of Fractions Required number = n-digit smallest number + (L R) + k. Properties of Centers of Triangle Centroid : 2. Product of two numbers = L.C.M. of the numbers H.C.F.

More information

MockTime.com. Subject Questions Marks Time -Ve Maths hrs 1/3 CDS MATHEMATICS PRACTICE SET

MockTime.com. Subject Questions Marks Time -Ve Maths hrs 1/3 CDS MATHEMATICS PRACTICE SET 170 CDS MATHEMATICS PRACTICE SET Subject Questions Marks Time -Ve Maths 100 100 2 hrs 1/3 Q1. Which one of the following is correct? The sum of two irrational numbers (a) is always a natural or irrational

More information

Grade 8(Mathematics) EV 4( )

Grade 8(Mathematics) EV 4( ) Chapter-2 (Number system) Grade 8(Mathematics) EV 4(2016-17) Q. Find the three rational numbers between 3/5 and 3/4. Sol:- let,, be the required rational numbers. = ½ (3/5 + 3/4) = ½ ( ) = ½ 27/20 = 27/40

More information

SSC CGL PAPER 16 th August 2015 Morning Shift Part C Quantitative Aptitude

SSC CGL PAPER 16 th August 2015 Morning Shift Part C Quantitative Aptitude SSC CGL PAPER 6 th August 0 Morning Shift Part C Quantitative Aptitude 0. Let C and C be the inscribed and circumscribed circles of a triangle with sides cm, cm and cm then c. Sol. c. 9 6 radius of C =

More information

CAMBRIDGE IGCSE MATHS EXAMINATION BOARD COVERAGE

CAMBRIDGE IGCSE MATHS EXAMINATION BOARD COVERAGE CAMBRIDGE IGCSE MATHS EXAMINATION BOARD COVERAGE TIER TOPIC HEADING SUB HEADING Both Number Integers Ordering numbers Both Number Integers Rounding numbers Both Number Integers Adding and subtracting whole

More information

02)

02) GRE / GMATmath,! abscissa, scalene, intercept, markup, such that, break even. abscissa. (4, 2) 4abscissa, 2ordinate absolute value acre add adjacent angles altitude ; angle () acute angle (90 ) right angle

More information

A. 180 B. 108 C. 360 D. 540

A. 180 B. 108 C. 360 D. 540 Part I - Multiple Choice - Circle your answer: 1. Find the area of the shaded sector. Q O 8 P A. 2 π B. 4 π C. 8 π D. 16 π 2. An octagon has sides. A. five B. six C. eight D. ten 3. The sum of the interior

More information

Visit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths

Visit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths Exercise 1.1 1. Find the area of a triangle whose sides are respectively 150 cm, 10 cm and 00 cm. The triangle whose sides are a = 150 cm b = 10 cm c = 00 cm The area of a triangle = s(s a)(s b)(s c) Here

More information

MATHS X STD. Try, try and try again you will succeed atlast. P.THIRU KUMARESA KANI M.A., M.Sc.,B.Ed., (Maths)

MATHS X STD. Try, try and try again you will succeed atlast. P.THIRU KUMARESA KANI M.A., M.Sc.,B.Ed., (Maths) MATHS X STD Try, try and try again you will succeed atlast P.THIRU KUMARESA KANI M.A., M.Sc.,B.Ed., (Maths) Govt.Girls High School,Konganapuram Salem (Dt.) Cell No. 9003450850 Email : kanisivasankari@gmail.com

More information

QUESTION 1 50 FOR JSS 1

QUESTION 1 50 FOR JSS 1 QUESTION 1 5 FOR JSS 1 1. The LCM of, 3 and 4 is A. 14 B. 1 C. 1 D. 16. Estimate 578.6998 to 3 decimal places. A. 578.7 B. 578.79 C. 578.8 D. 579. 3. Express 111 two as a number in base ten. A. 15 B. 18

More information

( Bifurcated Syllabus ) ( According to Syllabus of Class X only) PART - I

( Bifurcated Syllabus ) ( According to Syllabus of Class X only) PART - I Karunamoyee, Salt Lake, Kolkata : 70009 Mathematics (COMPULSORY) (Compulsory) Full marks : NEW 90 - For SYLLABUS Regular Candidates { Time 00 ---3 Hours - For 5 Eternal Minutes Candidates ( First 5 minutes

More information

Year 9 Mastery Statements for Assessment 1. Topic Mastery Statements - I can Essential Knowledge - I know

Year 9 Mastery Statements for Assessment 1. Topic Mastery Statements - I can Essential Knowledge - I know Year 9 Mastery Statements for Assessment 1 Topic Mastery Statements - I can Essential Knowledge - I know Whole Numbers and Decimals Measures, perimeter area and volume Expressions and formulae Indices

More information

ANSWERS. CLASS: VIII TERM - 1 SUBJECT: Mathematics. Exercise: 1(A) Exercise: 1(B)

ANSWERS. CLASS: VIII TERM - 1 SUBJECT: Mathematics. Exercise: 1(A) Exercise: 1(B) ANSWERS CLASS: VIII TERM - 1 SUBJECT: Mathematics TOPIC: 1. Rational Numbers Exercise: 1(A) 1. Fill in the blanks: (i) -21/24 (ii) -4/7 < -4/11 (iii)16/19 (iv)11/13 and -11/13 (v) 0 2. Answer True or False:

More information

Angles on a Point. Always add up to 360º. a + b + c = 180º.

Angles on a Point. Always add up to 360º. a + b + c = 180º. Angles on a Point Always add up to 360º a + b + c = 180º a b c Area of a Trapezium Add the parallel sides, multiply by the perpendicular height, then divide by 2. Formula is ½(a+b)h a Perpendicular Height

More information

Mathematics Department Level 3 TJ Book 3a Pupil Learning Log. St Ninian s High School. Name Class Teacher. I understand this part of the course =

Mathematics Department Level 3 TJ Book 3a Pupil Learning Log. St Ninian s High School. Name Class Teacher. I understand this part of the course = St Ninian s High School Mathematics Department Level TJ Book a Pupil Learning Log I understand this part of the course = I am unsure of this part of the course = I do not understand this part of the course

More information

221 MATH REFRESHER session 3 SAT2015_P06.indd 221 4/23/14 11:39 AM

221 MATH REFRESHER session 3 SAT2015_P06.indd 221 4/23/14 11:39 AM Math Refresher Session 3 1 Area, Perimeter, and Volume Problems Area, Perimeter, and Volume 301. Formula Problems. Here, you are given certain data about one or more geometric figures, and you are asked

More information

CBSE CLASS-10 MARCH 2018

CBSE CLASS-10 MARCH 2018 CBSE CLASS-10 MARCH 2018 MATHEMATICS Time : 2.30 hrs QUESTION & ANSWER Marks : 80 General Instructions : i. All questions are compulsory ii. This question paper consists of 30 questions divided into four

More information

2. P = { 0,2,4,6} and { 1,2,4,5} find P Q. A. { 0,6} B. { 2,4} C. {0, 2,4} D. { 0,2,6}

2. P = { 0,2,4,6} and { 1,2,4,5} find P Q. A. { 0,6} B. { 2,4} C. {0, 2,4} D. { 0,2,6} SECTION A. 1. Express 24 as a product of prime factors. A. 2 2 x 3 3 B. 2 x 3 C. 2 2 x 3 D. 2 3 x 3 2. P = { 0,2,4,6} and { 1,2,4,5} find P Q. A. { 0,6} B. { 2,4} C. {0, 2,4} D. { 0,2,6} 3. Two sets which

More information

Aptitude & Mental Ability Tnpsc Previous Questions With Explanation - Part 2

Aptitude & Mental Ability Tnpsc Previous Questions With Explanation - Part 2 Aptitude & Mental Ability Tnpsc Previous Questions With Explanation - Part 2 Important Download Links Install Tnpsc Winmeen Mobile App Tnpsc Complete Maths Study Materials Link 1. The greatest common divisor

More information

X- MATHS IMPORTANT FORMULAS SELF EVALUVATION

X- MATHS IMPORTANT FORMULAS SELF EVALUVATION X- MATHS IMPORTANT FORMULAS SELF EVALUVATION 1. SETS AND FUNCTIONS 1. Commutative property i ii 2. Associative property i ii 3. Distributive property i ii 4. De Morgan s laws i ii i ii 5. Cardinality of

More information

DESIGN OF THE SAMPLE QUESTION PAPERS MATHEMATICS CLASS X. S.No. Learning Outcomes Marks

DESIGN OF THE SAMPLE QUESTION PAPERS MATHEMATICS CLASS X. S.No. Learning Outcomes Marks DESIGN OF THE SAMPLE QUESTION PAPERS MATHEMATICS CLASS X Time : 3 Hours Max. Marks : 100 The weightage or the distribution of marks over different dimensions of the question papers shall be as follows

More information

QUESTION 1 50 FOR JSS 3

QUESTION 1 50 FOR JSS 3 QUESTION 1 5 FOR JSS 3 1. The knowledge of probability is necessary for the following reasons except A. In predicting B. In deciding C. In selecting D. In drawing table E. In forecasting. Factorise 7a

More information

Year 1 - What I Should Know by Heart

Year 1 - What I Should Know by Heart Year 1 - What I Should Know by Heart Count in 1 s forward and backwards from 0 to 150, beginning from any number. Count in multiples of 2, 5 and 10 up to 100. Recognise odd and even numbers. Know 1 st,

More information

ANNUAL NATIONAL ASSESSMENT 2014 ASSESSMENT GUIDELINES MATHEMATICS GRADE 9

ANNUAL NATIONAL ASSESSMENT 2014 ASSESSMENT GUIDELINES MATHEMATICS GRADE 9 INTRODUCTION The 2014 cycle of Annual National Assessment (ANA 2014) will be administered in all public and designated 1 independent schools from 16 to 19 September 2014. During this period all learners

More information

12 CSEC Maths Answer Key

12 CSEC Maths Answer Key 1 CSEC Maths Answer Key 1 Computation No. Answers Further explanations 1 D In order to write a number in standard form it must be written in the form A 10 ±n, where 1 A < 10. B 3 B 4 D Therefore, to write

More information

Downloaded from

Downloaded from Triangles 1.In ABC right angled at C, AD is median. Then AB 2 = AC 2 - AD 2 AD 2 - AC 2 3AC 2-4AD 2 (D) 4AD 2-3AC 2 2.Which of the following statement is true? Any two right triangles are similar

More information

81-E If set A = { 2, 3, 4, 5 } and set B = { 4, 5 }, then which of the following is a null set? (A) A B (B) B A (C) A U B (D) A I B.

81-E If set A = { 2, 3, 4, 5 } and set B = { 4, 5 }, then which of the following is a null set? (A) A B (B) B A (C) A U B (D) A I B. 81-E 2 General Instructions : i) The question-cum-answer booklet contains two Parts, Part A & Part B. ii) iii) iv) Part A consists of 60 questions and Part B consists of 16 questions. Space has been provided

More information

CBSE CLASS-10 MARCH 2018

CBSE CLASS-10 MARCH 2018 CBSE CLASS-10 MARCH 2018 MATHEMATICS Time : 2.30 hrs QUESTION Marks : 80 General Instructions : i. All questions are compulsory ii. This question paper consists of 30 questions divided into four sections

More information

Glossary. Glossary Hawkes Learning Systems. All rights reserved.

Glossary. Glossary Hawkes Learning Systems. All rights reserved. A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Acute triangle A triangle in which all three angles are acute Addends The

More information

Mathematics Class (IX-X)

Mathematics Class (IX-X) Mathematics Class (IX-X) Objectives 1. Students of Secondary stage will be able to apply knowledge acquired at upper primary stage to learn real number system and other topics. They will be able to distinguish

More information

National 5 Course Notes. Scientific Notation (or Standard Form) This is a different way of writing very large and very small numbers in the form:-

National 5 Course Notes. Scientific Notation (or Standard Form) This is a different way of writing very large and very small numbers in the form:- National 5 Course Notes Scientific Notation (or Standard Form) This is a different way of writing very large and very small numbers in the form:- a x 10 n where a is between 1 and 10 and n is an integer

More information

COURSE STRUCTURE CLASS -IX

COURSE STRUCTURE CLASS -IX environment, observance of small family norms, removal of social barriers, elimination of gender biases; mathematical softwares. its beautiful structures and patterns, etc. COURSE STRUCTURE CLASS -IX Units

More information

VISHAL BHARTI PUBLIC SCHOOL SUBJECT-MATHEMATICS CLASS-VI ASSIGNMENT-4 REVISION (SEPTEMBER)

VISHAL BHARTI PUBLIC SCHOOL SUBJECT-MATHEMATICS CLASS-VI ASSIGNMENT-4 REVISION (SEPTEMBER) I) Chapter - Knowing Our Numbers VISHAL BHARTI PUBLIC SCHOOL SUBJECT-MATHEMATICS CLASS-VI ASSIGNMENT-4 REVISION (SEPTEMBER) Q1 Write the Roman numeral for (a) 384 (b) 999 Q2 Write the number name of 74532601

More information

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION

KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 08 (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit

More information

CHAPTER 1 BASIC ARITHMETIC

CHAPTER 1 BASIC ARITHMETIC CHAPTER 1 BASIC ARITHMETIC EXERCISE 1, Page 4 1. Evaluate 67 kg 8 kg + 4 kg without using a calculator 67 kg 8 kg + 4 kg = 67 kg + 4 kg 8 kg = 101 kg 8 kg = 19 kg. Evaluate 851 mm 7 mm without using a

More information

MOEMS What Every Young Mathlete Should Know

MOEMS What Every Young Mathlete Should Know MOEMS What Every Young Mathlete Should Know 2018-2019 I. VOCABULARY AND LANGUAGE The following explains, defines, or lists some of the words that may be used in Olympiad problems. To be accepted, an answer

More information

MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT )

MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT ) Total No. of Printed Pages 6 X/5/M 0 5 MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 80 Pass Marks : 4 ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 00

More information

Time: 3 Hrs. M.M. 90

Time: 3 Hrs. M.M. 90 Class: X Subject: Mathematics Topic: SA1 No. of Questions: 34 Time: 3 Hrs. M.M. 90 General Instructions: 1. All questions are compulsory. 2. The questions paper consists of 34 questions divided into four

More information

Mathematics Class X Past Year Paper Time: 2½ hour Total Marks: 80

Mathematics Class X Past Year Paper Time: 2½ hour Total Marks: 80 Pas Year Paper Mathematics Class X Past Year Paper - 013 Time: ½ hour Total Marks: 80 Solution SECTION A (40 marks) Sol. 1 (a) A + X B + C 6 3 4 0 X 0 4 0 0 6 6 4 4 0 X 0 8 0 0 6 4 X 0 8 4 6 X 8 0 4 10

More information

Solutions. S1. Ans.(c) Sol. Try Using option and divide With given option

Solutions. S1. Ans.(c) Sol. Try Using option and divide With given option Solutions S1. Ans.(c) Try Using option and divide 64329 With given option S2. Ans.(a) Let the fraction be x/y. According to the questions, x y of 4 7 + 4 7 = 15 14 x y 4 7 + 4 7 = 15 14 x y 4 7 = 1 2 x

More information

Section 4. Quantitative Aptitude

Section 4. Quantitative Aptitude Section 4 Quantitative Aptitude You will get 35 questions from Quantitative Aptitude in the SBI Clerical 2016 Prelims examination and 50 questions in the Mains examination. One new feature of the 2016

More information

ARITHMETIC. Averages & Percentage Interest, Profit & Loss Mixtures & Alligation Ratio & Proportion Time Speed & Distance Races & Clocks Time & Work

ARITHMETIC. Averages & Percentage Interest, Profit & Loss Mixtures & Alligation Ratio & Proportion Time Speed & Distance Races & Clocks Time & Work ARITHMETIC Averages & Percentage Interest, Profit & Loss Mixtures & Alligation Ratio & Proportion Time Speed & Distance Races & Clocks Time & Work Complied by: Er. Manit Choudhary Averages Simple Average

More information

Pre-Regional Mathematical Olympiad Solution 2017

Pre-Regional Mathematical Olympiad Solution 2017 Pre-Regional Mathematical Olympiad Solution 07 Time:.5 hours. Maximum Marks: 50 [Each Question carries 5 marks]. How many positive integers less than 000 have the property that the sum of the digits of

More information

MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT )

MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT ) Total No. of Printed Pages 6 X/3/M 0 3 MATHEMATICS ( CANDIDATES WITH PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 80 Pass Marks : 4 ( CANDIDATES WITHOUT PRACTICALS/INTERNAL ASSESSMENT ) Full Marks : 00

More information

Alg. (( Sheet 1 )) [1] Complete : 1) =.. 3) =. 4) 3 a 3 =.. 5) X 3 = 64 then X =. 6) 3 X 6 =... 7) 3

Alg. (( Sheet 1 )) [1] Complete : 1) =.. 3) =. 4) 3 a 3 =.. 5) X 3 = 64 then X =. 6) 3 X 6 =... 7) 3 Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch [1] Complete : 1) 3 216 =.. Alg. (( Sheet 1 )) 1 8 2) 3 ( ) 2 =..

More information

Important Instructions for the School Principal. (Not to be printed with the question paper)

Important Instructions for the School Principal. (Not to be printed with the question paper) Important Instructions for the School Principal (Not to be printed with the question paper) 1) This question paper is strictly meant for use in school based SA-II, March-2012 only. This question paper

More information

Senior Team Maths Challenge Regional Final 2008 Mini Relay Round

Senior Team Maths Challenge Regional Final 2008 Mini Relay Round A1 Solve the simultaneous equations: 2x 5y 2z 4 7x y 2z 13 9x 4 y 1 Write down the value of. 2 z yx 2 A2 T is the number that you will receive The expression T x 4 1 2x 2 Tx 7x 5 can be written in the

More information

( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear.

( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear. Problems 01 - POINT Page 1 ( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear. ( ) Prove that the two lines joining the mid-points of the pairs of opposite sides and the line

More information

Mathematics CLASS : X. Time: 3hrs Max. Marks: 90. 2) If a, 2 are three consecutive terms of an A.P., then the value of a.

Mathematics CLASS : X. Time: 3hrs Max. Marks: 90. 2) If a, 2 are three consecutive terms of an A.P., then the value of a. 1 SAMPLE PAPER 4 (SAII) MR AMIT. KV NANGALBHUR Mathematics CLASS : X Time: 3hrs Max. Marks: 90 General Instruction:- 1. All questions are Compulsory. The question paper consists of 34 questions divided

More information

Mathematics. GCSE subject content and assessment objectives

Mathematics. GCSE subject content and assessment objectives Mathematics GCSE subject content and assessment objectives Contents Introduction 3 Subject aims and learning outcomes 3 Subject content 4 Scope of study 4 Number 4 Algebra 6 Ratio, proportion and rates

More information

2001-CE MATH MATHEMATICS PAPER 1 Marker s Examiner s Use Only Use Only Question-Answer Book Checker s Use Only

2001-CE MATH MATHEMATICS PAPER 1 Marker s Examiner s Use Only Use Only Question-Answer Book Checker s Use Only 001-CE MATH PAPER 1 HONG KONG EXAMINATIONS AUTHORITY HONG KONG CERTIFICATE OF EDUCATION EXAMINATION 001 Candidate Number Centre Number Seat Number MATHEMATICS PAPER 1 Marker s Use Only Examiner s Use Only

More information

CHAPTER 12 HERON S FORMULA Introduction

CHAPTER 12 HERON S FORMULA Introduction CHAPTER 1 HERON S FORMULA 1.1 Introduction You have studied in earlier classes about figures of different shapes such as squares, rectangles, triangles and quadrilaterals. You have also calculated perimeters

More information

[Class-X] MATHEMATICS SESSION:

[Class-X] MATHEMATICS SESSION: [Class-X] MTHEMTICS SESSION:017-18 Time allowed: 3 hrs. Maximum Marks : 80 General Instructions : (i) ll questions are compulsory. (ii) This question paper consists of 30 questions divided into four sections,

More information

CBSE CLASS X MATH -SOLUTION Therefore, 0.6, 0.25 and 0.3 are greater than or equal to 0 and less than or equal to 1.

CBSE CLASS X MATH -SOLUTION Therefore, 0.6, 0.25 and 0.3 are greater than or equal to 0 and less than or equal to 1. CBSE CLASS X MATH -SOLUTION 011 Q1 The probability of an event is always greater than or equal to zero and less than or equal to one. Here, 3 5 = 0.6 5% = 5 100 = 0.5 Therefore, 0.6, 0.5 and 0.3 are greater

More information

Glossary. Glossary 981. Hawkes Learning Systems. All rights reserved.

Glossary. Glossary 981. Hawkes Learning Systems. All rights reserved. A Glossary Absolute value The distance a number is from 0 on a number line Acute angle An angle whose measure is between 0 and 90 Addends The numbers being added in an addition problem Addition principle

More information

Part (1) Second : Trigonometry. Tan

Part (1) Second : Trigonometry. Tan Part (1) Second : Trigonometry (1) Complete the following table : The angle Ratio 42 12 \ Sin 0.3214 Cas 0.5321 Tan 2.0625 (2) Complete the following : 1) 46 36 \ 24 \\ =. In degrees. 2) 44.125 = in degrees,

More information

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2 CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5

More information

Mathematics KSHSSA Key Stage 3 Grade Descriptors

Mathematics KSHSSA Key Stage 3 Grade Descriptors Developing Fluency, reasoning Mathematically and Problem Solving consolidate their numerical and mathematical capability from develop their mathematical knowledge, in part through key stage 2 and extend

More information

Maharashtra Board Class X Mathematics - Geometry Board Paper 2014 Solution. Time: 2 hours Total Marks: 40

Maharashtra Board Class X Mathematics - Geometry Board Paper 2014 Solution. Time: 2 hours Total Marks: 40 Maharashtra Board Class X Mathematics - Geometry Board Paper 04 Solution Time: hours Total Marks: 40 Note: - () All questions are compulsory. () Use of calculator is not allowed.. i. Ratio of the areas

More information

2. In an AP. if the common difference (d) = -4, and the seventh term (a7) is 4, then find the first term.

2. In an AP. if the common difference (d) = -4, and the seventh term (a7) is 4, then find the first term. CBSE Board Class X Set 3 Mathematics Board Question Paper 2018 Time: 3 hrs. Marks: 80 Note: Please check that this question paper contains 11 printed pages. Code number given on the right hand side of

More information

Mathematics. Sample Question Paper. Class 9th. (Detailed Solutions) 2. From the figure, ADB ACB We have [( 16) ] [( 2 ) ] 3.

Mathematics. Sample Question Paper. Class 9th. (Detailed Solutions) 2. From the figure, ADB ACB We have [( 16) ] [( 2 ) ] 3. 6 Sample Question Paper (etailed Solutions) Mathematics lass 9th. Given equation is ( k ) ( k ) y 0. t and y, ( k ) ( k ) 0 k 6k 9 0 4k 8 0 4k 8 k. From the figure, 40 [ angles in the same segment are

More information

1. SETS AND FUNCTIONS

1. SETS AND FUNCTIONS . SETS AND FUNCTIONS. For two sets A and B, A, B A if and only if B A A B A! B A + B z. If A B, then A + B is B A\ B A B\ A. For any two sets Pand Q, P + Q is " x : x! P or x! Q, " x : x! P and x b Q,

More information

Wednesday, 24 May Warm-Up Session. Non-Calculator Paper

Wednesday, 24 May Warm-Up Session. Non-Calculator Paper Wednesday, 24 May 2017 Warm-Up Session Non-Calculator Paper Non-Calculator Paper 80 marks in 90 minutes IF YOU FINISH EARLY CHECK EVERYTHING! You have made a silly mistake somewhere. Redo some questions

More information

SSC MAINS (MATHS) MOCK TEST-14 (SOLUTION)

SSC MAINS (MATHS) MOCK TEST-14 (SOLUTION) SSC MINS (MTHS) MOCK TEST- (SOLUTION). () b c a a c b b c a a c b 0 a b c a b c. (C) y hours 8 min 8 60 5 hrs. b c a a a c b b a b c 0 c hours 0 min 0 60 0 hrs. (a b c) a b c 0 V V T T /5 0 / 6 5 6 5 a

More information

Functional Skills Mathematics

Functional Skills Mathematics Functional Skills Mathematics Level 2 Learning Resource Formulae Contents Calculations Using Simple Formulae Page 3-5 Create Simple Formulae Page 6-8 Common Mathematical Page - 10 Formulae in Use West

More information

9-12 Mathematics Vertical Alignment ( )

9-12 Mathematics Vertical Alignment ( ) Algebra I Algebra II Geometry Pre- Calculus U1: translate between words and algebra -add and subtract real numbers -multiply and divide real numbers -evaluate containing exponents -evaluate containing

More information

SAMPLE QUESTION PAPER Summative Assessment II Class-X ( ) Mathematics. Time Allowed: 3 Hours Max. Marks: 90

SAMPLE QUESTION PAPER Summative Assessment II Class-X ( ) Mathematics. Time Allowed: 3 Hours Max. Marks: 90 SAMPLE QUESTION PAPER Summative Assessment II Class-X (2016 17) Mathematics Time Allowed: 3 Hours Max. Marks: 90 General Instructions: 1. All questions are compulsory. 2. The question paper consists of31

More information

presents MATH FORMULAS & FUNDAS For CAT, XAT & Other MBA Entrance Examinations Ravi Handa Version 5.0

presents MATH FORMULAS & FUNDAS For CAT, XAT & Other MBA Entrance Examinations Ravi Handa Version 5.0 presents MATH FORMULAS & FUNDAS For CAT, XAT & Other MBA Entrance Examinations Version 5.0 Ravi Handa Preface Hi, I run the website www.hanadkafunda.com In the last 8 years, I have taken classes at IMS,

More information

MATHEMATICS. (Two hours and a half) Answers to this Paper must be written on the paper provided separately.

MATHEMATICS. (Two hours and a half) Answers to this Paper must be written on the paper provided separately. CLASS IX MATHEMATICS (Two hours and a half) Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent

More information

Geometry. A. Right Triangle. Legs of a right triangle : a, b. Hypotenuse : c. Altitude : h. Medians : m a, m b, m c. Angles :,

Geometry. A. Right Triangle. Legs of a right triangle : a, b. Hypotenuse : c. Altitude : h. Medians : m a, m b, m c. Angles :, Geometry A. Right Triangle Legs of a right triangle : a, b Hypotenuse : c Altitude : h Medians : m a, m b, m c Angles :, Radius of circumscribed circle : R Radius of inscribed circle : r Area : S 1. +

More information

QUESTION BANK ON STRAIGHT LINE AND CIRCLE

QUESTION BANK ON STRAIGHT LINE AND CIRCLE QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,

More information

APTITUDE & MENTAL ABILITY SOLUTIONS

APTITUDE & MENTAL ABILITY SOLUTIONS TNPSC DEO PRELIMINARY EXAM [0.03.019] APTITUDE & MENTAL ABILITY SOLUTIONS 1. If the average of the values 9, 6, 7, 8, 5 and x is 8. Find the value of x. A. 1 B. 13 C. 10 D. 9. Find the standard deviation

More information

The Grade Descriptors below are used to assess work and student progress in Mathematics from Year 7 to

The Grade Descriptors below are used to assess work and student progress in Mathematics from Year 7 to Jersey College for Girls Assessment criteria for KS3 and KS4 Mathematics In Mathematics, students are required to become familiar, confident and competent with a range of content and procedures described

More information

Linwood High School S3 CREDIT NOTES

Linwood High School S3 CREDIT NOTES Linwood High School S3 CREDIT NOTES INDEX: page 1 Chapter 1: Calculations and the Calculator page 5 Chapter 2: Similar Shapes page 9 Chapter 3: Going Places page 11 Chapter 4: Money Matters - Saving and

More information

QUANTITATIVE APTITUDE

QUANTITATIVE APTITUDE SBI Probationery Officers QUANTITATIVE APTITUDE Mensuration (Plane Figures) Mensuration is one of the branches of mathematics. This means measurement. It is being done in our life in many situations. Here,

More information

Mathematics. Essential Learning Concepts

Mathematics. Essential Learning Concepts Mathematics Essential Learning Concepts Contents to be covered by the paper- I in G.C.E. (Ordinary Level) examination year 2016 and beyond (According to the Grade 10 and 11 Syllabi) Department of Mathematics

More information

nx + 1 = (n + 1)x 13(n + 1) and nx = (n + 1)x + 27(n + 1).

nx + 1 = (n + 1)x 13(n + 1) and nx = (n + 1)x + 27(n + 1). 1. (Answer: 630) 001 AIME SOLUTIONS Let a represent the tens digit and b the units digit of an integer with the required property. Then 10a + b must be divisible by both a and b. It follows that b must

More information

Appendices. Appendix A.1: Factoring Polynomials. Techniques for Factoring Trinomials Factorability Test for Trinomials:

Appendices. Appendix A.1: Factoring Polynomials. Techniques for Factoring Trinomials Factorability Test for Trinomials: APPENDICES Appendices Appendi A.1: Factoring Polynomials Techniques for Factoring Trinomials Techniques for Factoring Trinomials Factorability Test for Trinomials: Eample: Solution: 696 APPENDIX A.1 Factoring

More information

Solutions Math is Cool HS Championships Mental Math

Solutions Math is Cool HS Championships Mental Math Mental Math 9/11 Answer Solution 1 30 There are 5 such even numbers and the formula is n(n+1)=5(6)=30. 2 3 [ways] HHT, HTH, THH. 3 6 1x60, 2x30, 3x20, 4x15, 5x12, 6x10. 4 9 37 = 3x + 10, 27 = 3x, x = 9.

More information