MTN Learn - Maths Excellence

1 MTN LearnMathematicsGrade 10radio support notes Contents INTRODUCTION .. 2 GETTING THE MOST FROM MINDSET Learn XTRA RADIO REVISION .. 3 BROADAST SCHEDULE .. 4 ALGEBRAIC EXPRESSIONS .. 5 EXPONENTS .. 9 NUMBER PATTERNS .. 18 LINEAR EQUATIONS .. 23 QUADRACTIC EQUATIONS .. 27 LINEAR AND QUADRATIC EQUATIONS .. 30 LITERAL EQUATIONS .. 32 INEQUALITIES .. 34 TRIGONOMETRY .. 37 INTRODUCTION Have you heard about Mindset? Mindset Network, a South African non-profit organisation, was founded in 2002. Through our Mindset Learn programme, we develop and distribute high quality curriculum aligned educational resources for Grade 10 - 12. We make these materials available on TV (Dstv and Toptv channels 319), the Internet ( ) and as DVDs and books. At Mindset we are committed to helping South African learners succeed. This is why Mindset Learn is proud to offer Mindset Learn Xtra especially for Grade 10 12 learners. Learn Xtra offers you hundreds of hours of video and print support, live television shows between 4pm and 7pm every Monday to Thursday and a free Helpdesk where our expert teachers are on standby to help you.

2 You can find out more about Mindset Learn Xtra at Learn Xtra also offers specific exam revision support. Every year we run Winter, Spring, Exam and Supplementary Schools to help you ace your exams. And now, Mindset is proud to announce a powerful partnership with MTN and the Department of Basic Education to bring you Mindset Learn Xtra Radio Revision powered by MTN a full 3 months of radio programmes dedicated to supporting Grade 10 and 12 Mathematics, Physical Sciences and English First Additional Language. Participating Community Radio Stations Listen to any of the following community radio stations to get your daily dose of expert tuition and exam preparation. Also listen out for on air competitions in which you can stand a chance of winning great prizes. 1. KZN: a. Hindvani Radio fm (Durban) fm ( rest of KZN) b. Maputaland Radio fm 2. Limpopo: a. Sekgosese Radio fm b. Greater Tzaneen Radio fm c. Mohodi FM fm d. Moletsi fm e. Univen fm 3.

3 Eastern Cape: a. Vukani FM - fm b. Fort Hare Community Radio fm c. Mdantsane FM fm d. Nkqubela FM fm e. Graaff Reinet fm GETTING THE MOST FROM MINDSET Learn XTRA RADIO REVISION In the Grade 10 Mathematics radio programme, we will focus on questions that come from recent previous exam and test papers. This booklet contains diagrams taken from the exam and test papers so that you will be able to follow what is said during the broadcast. Before you listen to the show, read through the questions for the show and try to answer them without looking up the solutions. If you have a problem and can t answer any of the questions, don t panic. Make a note of any questions you need answered. When listening to the show, compare your approach to the teacher s. Don t just copy the answers down but take note of the method used. Make sure you keep this booklet. You can re-do the questions you did not get totally correct and mark your own work. Remember that exam preparation also requires motivation and discipline, so try to stay positive, even when the work appears to be difficult.

4 Every little bit of studying, revision and exam practice will pay off. You might benefit from working with a friend or a small study group as long as everyone is as committed as you are. Mindset believes that Mindset Learn Xtra Radio Revision will help you achieve the results you want. Contact us We want to hear from you. So let us have your specific questions or just tell us what you think through any of the following: LearnXtra @learnxtra 086 105 8262 Mindset Get the free app at BROADAST SCHEDULE Grade 10 Catch up (Term 3) 10-Sep 17:00 -18:00 10 Algebraic Expressions 11-Sep 17:00 -18:00 10 Algebraic Expressions 12-Sep 17:00 -18:00 10 Algebraic Expressions 13-Sep 17:00 -18:00 10 Exponents 15-Sep 09:00 -10:00 10 Exponents 17-Sep 17:00 -18:00 10 Numbers and Number Patterns 18-Sep 17:00 -18:00 10 Numbers and Number Patterns 19-Sep 17:00 -18:00 10 Linear Equations 20-Sep 17:00 -18:00 10 Quadratic Equations 22-Sep 09:00 -10:00 10 Linear & Quadratic Equations 24-Sep 17:00 -18:00 10 Literal Equations 25-Sep 17:00 -18:00 10 Inequalities 26-Sep 17:00 -18:00 10 Trigonometry 27-Sep 17:00 -18:00 10 Trigonometry 29-Sep 09:00 -10:00 10 Trigonometry Grade 10 Exam Revision 15-Oct 17:00 -18:00 10 Linear Functions 16-Oct 17:00 -18:00 10 Quadratic Functions 17-Oct 17:00 -18.

5 00 10 Hyperbolic Functions 18-Oct 17:00 -18:00 10 Exponential Functions 20-Oct 09:00 -10:00 10 Trig Functions 22-Oct 17:00 -18:00 10 Euclidean Geometry 25-Oct 17:00 -18:00 10 Euclidean Geometry 27-Oct 09:00 -10:00 10 Euclidean Geometry 29-Oct 17:00 -18:00 10 Finance 30-Oct 17:00 -18:00 10 Finance 2-Nov 18:00 -19:00 10 Statistics 8-Nov 17:00 -18:00 10 Analytical Geometry 9-Nov 17:00 -18:00 10 Measurement 10-Nov 09:00 -10:00 10 Probability 12-Nov 17:00 -18:00 10 Algebra 13-Nov 17:00 -18:00 10 Functions 14-Nov 17:00 -18:00 10 Finance 15-Nov 17:00 -18:00 10 Trigonometry 16-Nov 17:00 -18:00 10 Euclidean Geometry 17-Nov 17:00 -18:00 10 Maths (Helpdesk Questions) For more information, free downloads and all the schedules, visit ALGEBRAIC EXPRESSIONS STUDY NOTES Expanding When multiplying a binomial or trinomial by a single term we place the binomial or trinomial in brackets. We use the Distributive Law of multiplication to expand term by term. This means that we multiply each term inside a bracket by the term outside the brackets Simplify: 2a(a - 1) - 3(a2 - 1).

6 Solution: 2a(a - 1) - 3(a2 - 1) = 2a(a) + 2a(-1) + (-3)(a2) + (-3)(-1) = 2a2 - 2a - 3a2 + 3 = -a2 - 2a + 3 When multiplying two binomials together we apply the same Distributive Law. We multiple the two First term together, then the Outer terms(1st term of the first bracket by the 2nd term of the second bracket) then the Inner terms (2nd term of the first bracket by the 1st term of the second bracket) and then Last terms. Remember FOIL Find the product: (3x - 2)(5x + 8) Solution: (3x - 2)(5x + 8) = (3x)(5x) + (3x)(8) + (-2)(5x) + (-2)(8) = 15x2 + 24x - 10x - 16 = 15x2 + 14x - 16 Multiplying a Binomial by Trinomial Find the product: (x - 1)(x2 - 2x + 1) Solution: Step 1: Expand the bracket (x - 1)(x2 - 2x + 1) = x(x2 - 2x + 1) - 1(x2 - 2x + 1) = x3 - 2x2 + x - x2 + 2x - 1 Step 2: Simplify = x3 - 3x2 + 3x - 1 Factorising Methods of Factorising taking out a common factor difference of two squares trinomials to binomials sum and difference of cubes grouping Example: Factorise: 5(a - 2) - b(2 - a) Solution: (a-2) and (2-a) are not common factors.

7 The terms have different signs. If we take out a factor of -1 from (2-a), we can change the signs 2 - a = - (a - 2) Now we have a common factor in both terms. Be careful of the signs. 5(a - 2) - b(2 - a) = 5(a - 2) - [-b(a - 2)] = 5(a - 2) + b(a - 2) = (a - 2)(5 + b) Factorising trinomials Recognise the pattern. The process is the opposite of FOIL. The factors of the first term of a trinomial become the first terms of each of the binomials which we place in brackets. The factors of the last term of a trinomial become the second term of each of the binomials in the brackets. We select the factors so that when we expand the multiplication of inner and outer terms gives us the middle term of the trinomial. Always check that you have the correct factors by expanding the factors using FOIL. Difference and sum of two cubes You need to recognise the pattern. Notice that the product of a binomial and trinomial gives us the sum of two cubes.

8 (x + y)(x2 - xy + y2) = x(x2 - xy + y2) + y(x2 - xy + y2) = [x(x2) + x(- xy) + x(y2)] + [y(x2) + y( - xy) + y(y2)] = x3 - x2y + xy2 + x2y - xy2 + y3 = x3 + y3 Also this product gives the difference of two cubes: (x - y)(x2 + xy + y2) = x(x2 + xy + y2) - y(x2 + xy + y2) = [x(x2) + x(xy) + x(y2)] - [y(x2) + y(xy) + y(y2)] = x3 + x2y + xy2 - x2y - xy2 - y3 = x3 - y3 So to factorise the sum of cubes, we use the pattern. The terms in the first bracket are added together and the middle term in the second bracket is subtracted. x3 + y3 = (x + y)(x2 - xy + y2) For the difference of cubes, the terms in the first bracket are subtracted and the middle term in the second bracket is added. x3 - y3 = (x - y)(x2 + xy + y2) Algebraic Fractions Simplifying algebraic fractions We working with algebraic fractions in the same way we work with fractions of numbers.

9 Multiplication and division Simplify: x2 x 2 x2 + x (x 0; x 2) x2 - 4 x2 + 2x Solution: Step 1: Factorise the numerator and denominator (x+1)(x-2) x(x + 1) (x+2)(x-2) x(x +2) Step 2: Change the division sign and multiply by the reciprocal (x+1)(x-2) X x(x + 2) (x+2)(x-2) x(x +1) Step 3: Write the final answer = 1 Radio Broadcast 10 Sept 17:00 -18:00 Questions for Discussion Expand and simplify the following: (a) 22(23 )(34 )xyxy (4) (b) 2(94)(32)(32)xxx (2) (c) 22(2 )(23 )xy xxyy (3) Radio Broadcast 11 Sept 17:00 -18:00 Questions for Discussion Factorise fully: (a) 4 62153a bab (2) (b) 8888ab (4) (c) 23318xx (2) (d) 25148xx (2) (e) 3233aaa (4) Radio Broadcast 12 Sept 17:00 -18:00 Questions for Discussion Simplify: (a) 231211243xyxx (5) (b) 123234xxx (5) (c) 23482912xxxxx (4) (d) 2133 xx (4) EXPONENTS STUDY NOTES Exponential notation is a short way of writing the same number multiplied by itself many times.

10 For any real number a and natural number n, we can write a multiplied by itself n times as an. a is called the base, n is called the exponent or index. When doing calculations with exponents we use the following Law of Exponents: .mnm naaa The bases are the same so you will then add the exponents For example 44 14 xx xxx (same bases, add exponents) 3 362 .2264 (same bases, add exponents) mmnnaaa The bases are the same so you will then subtract the exponents For example 444 131xxxxxx (same base, subtract exponents) 1212 1021022242 (same base, subtract exponents) ()m nm naa With this rule, you will need to multiply the exponents For example 4 21 4 21 2 4 28(3 )(3)3 .9xxxx 1nnxx and 1nnxx With this rule, you make the exponents positive For example 2211393 221393 01a Any number raised to an exponent of 0 equals 1 For example 031 044 1 4x nnabba For example 223416439 Simplifying Exponents Change the bases to products of their prime factors and simply using the laws.