Everything Maths Grade 11

Surds 3 3.1 Introduction EMBF In the previous chapteron exponents, we sawthat rational exponentsare directly related to surds. W ...

3.2 CHAPTER 3. SURDS 3. √ a^2 b^3 × √ b^5 c^4 = √ a^2 b^8 c^4 = ab^4 c^2 Surd Law 2: n � a b = √na √n b EMBI If we look atn �a b ...

CHAPTER 3. SURDS 3.2 Like and Unlike Surds EMBK Two surdsm √ a andn √ b are called like surds if m = n, otherwise they are calle ...

3.2 CHAPTER 3. SURDS Simplest Surd Form EMBL In most cases, when working with surds, answers are given in simplest surd form. Fo ...

CHAPTER 3. SURDS 3.2 QUESTION Simplify: √ 147 + √ 108 SOLUTION Step 1 : Simplify each square root by converting each number to a ...

3.2 CHAPTER 3. SURDS or similarly c √ a− √ b = √ a + √ b √ a + √ b × c √ a− √ b (3.10) = c √ a + c √ b a− b Example 4: Rationali ...

CHAPTER 3. SURDS 3.2 5 x− 16 √ y− 10 × √ y + 10 √ y + 10 Step 2 : Multiply out the numerators and denominators 5 x √ y− 16 √ y + ...

3.2 CHAPTER 3. SURDS Expand: ( √ x− √ 2)( √ x + √ 2) Rationalise the denominator: 10 √ x−^1 x Write as a single fraction: 3 2 ...

CHAPTER 3. SURDS 3.2 The use of a calculator is not permissible in this question. Simplify completely by showing all your steps ...

Error Margins 4 5.1 Introduction EMBN When rounding off, wethrow away some of thedigits of a number. Thismeans that we are makin ...

CHAPTER 4. ERROR MARGINS 4.2 Example 1: Simplification and Accuracy QUESTION Calculate^3 √ 54 +^3 √ 16. Write the answer to thre ...

4.2 CHAPTER 4. ERROR MARGINS √ x + 1 + 1 3 � (2x + 2)− (x + 1) = √ x + 1 + 1 3 √ 2 x + 2− x− 1 = √ x + 1 + 1 3 √ x + 1 = 4 3 √ x ...

CHAPTER 4. ERROR MARGINS 4.2 (e) √ 4 + √ 20 √ 18 to six decimal places (f) √ 3 + √ 5 √ 6 to one decimal place Calculate: (a) √ ...

Quadratic Sequences 5 5.1 Introduction EMBP In Grade 10 you learnedabout arithmetic sequences, where the difference between cons ...

CHAPTER 5. QUADRATIC SEQUENCES 5.2 1. 3; 6; 10; 15; 21;... 2. 4; 9; 16; 25; 36;... 3. 7; 17; 31; 49; 71;... 4. 2; 10; 26; 50; 82 ...

5.2 CHAPTER 5. QUADRATIC SEQUENCES Step 2 : Find the second differences between the terms 7 11 15 +4 +4 So the second difference ...

CHAPTER 5. QUADRATIC SEQUENCES 5.2 QUESTION The following sequenceis quadratic: 8;22;42;68;... Find the rule. SOLUTION Step 1 : ...

5.2 CHAPTER 5. QUADRATIC SEQUENCES where a, b and c are some constants to be determined. Tn = an^2 + bn + c T 1 = a(1)^2 + b(1) ...

CHAPTER 5. QUADRATIC SEQUENCES 5.2 SOLUTION Step 1 : The next number in thesequence The numbers go up in multiples of 6 1 + 6(1) ...

5.2 CHAPTER 5. QUADRATIC SEQUENCES Extension: Plotting a graph of terms of a quadratic sequence Plotting Tnvs. n for a quadratic ...