Math L2 Module 5

Mathematics NQF Level 2 Downloaded from hlayiso.com *see terms and conditions Mathematics NQF Level 2

Solving algebraic equations and inequalities Module 5 Downloaded from hlayiso.com Mathematics NQF Level 2

Learning activity 5.1 Downloaded from hlayiso.com Mathematics NQF Level 2

1. Solve the following equations: 1.7 a 3 2 4  a 3    4  2 4  4  a 3  8 a  8  3  11 Downloaded from hlayiso.com Learning activity 5.1

1. Solve the following equations: 1.14 x3 x2  4 3 2 6  x  3 6  x  2  6(4) 3 2 2( x  3)  3( x  2)  24 2 x  6  3 x  6  24 Downloaded from hlayiso.com Learning activity 5.1

1. Solve the following equations: 1.14 (continued) 5 x  24  12 5 x  36 36 x  5 1 7 5 Downloaded from hlayiso.com Learning activity 5.1

3. Two buns and a cup of coffee cost R14,30. If the coffee costs R6,20, calculate the price of a bun. Let the price of a bun be x. 2 x  y  14, 30 2 x  6, 20  14,30 2 x  14, 30  6, 20 2 x  8,1  x  4, 05 The price of a bun is  R4,05 R4,05. Downloaded from hlayiso.com Learning activity 5.1

Learning activity 5.2 Downloaded from hlayiso.com Mathematics NQF Level 2

2. Draw the graph of y = x2 − x − 12. x −3 −2 −1 0 1 2 3 4 y 0 −6 −10 −12 −12 −10 −6 0 f ( 3)  ( 3) 2  ( 3)  12  9  3  12  0 f ( 2)  ( 2) 2  ( 2)  12  4  2  12  6 f ( 1)  ( 1) 2  ( 1)  12  2  12  10 f (0)  12 f (1)  1  1  12  12 f (2)  (2) 2  (2)  12  4  2  12  10 f (3)  (3) 2  (3)  12  9  3  12  6 f (4)  (4) 2  (4)  12  16  4  12  0 Downloaded from hlayiso.com Learning activity 5.2

2. Draw the graph of y = x2 − x − 12. Figure 5.1 Downloaded from hlayiso.com Learning activity 5.2

Learning activity 5.3 Downloaded from hlayiso.com Mathematics NQF Level 2

Solve for x: 10. 25  5x1 125 52 x1  5 53 2 3 x 1 5 5 x  1  1  x  2 Downloaded from hlayiso.com Learning activity 5.3

Solve for x: x 3 16. (3k )  27 k x 3 3 (3k )  3 k x 3 (3k )  (3k ) x  3 Downloaded from hlayiso.com Learning activity 5.3

Learning activity 5.4 Downloaded from hlayiso.com Mathematics NQF Level 2

Solve for x and illustrate your answer on a number line. Also give the solution in interval notation and set-builder notation. 4. x2  2x 1 4 x  2  4(2 x  1) x  2  8x  4 x  2  x  8x  4  x Downloaded from hlayiso.com Learning activity 5.4

Solve for x and illustrate your answer on a number line. Also give the solution in interval notation and set-builder notation. 4. 2  7 x  4 2  4  7 x  4  4 2  7x 2 x 7 Downloaded from hlayiso.com Learning activity 5.4

Solve for x and illustrate your answer on a number line. Also give the solution in interval notation and set-builder notation. 4. 2 Interval notation: (¥; ] 7 2 Set-builder notation: {x | x  ; x  } 7 Downloaded from hlayiso.com Learning activity 5.4

Learning activity 5.5 Downloaded from hlayiso.com Mathematics NQF Level 2

• Unit 2.2 Click above to play this video. Downloaded from hlayiso.com Learning activity 5.5

• Unit 2.2 Click above to play this video. Downloaded from hlayiso.com Learning activity 5.5

Summative assessment Module 5 Downloaded from hlayiso.com Mathematics NQF Level 2

1. Calculate the price of one saw blade if you buy four, pay with R50 and get R4,50 change. Let the price of a saw blade be b. 4b  4,5  50 4b  45,5  b  R11,38 Downloaded from hlayiso.com Summative assessment – Module 5

2. Solve the following equations: a4 2.1  2a  3 2 a  4  4a  6 (  2) a  4 a  6  4 3a  2 2 a  3 Downloaded from hlayiso.com Summative assessment – Module 5

2. Solve the following equations: 2.2 2 x2  4 x  6 2 x  2x  3  0 ( x  3)( x  1)  0  x  3 or x  1 Downloaded from hlayiso.com Summative assessment – Module 5

2. Solve the following equations: 2.3 2(3) x 2  54 x 2 (3)  27 x 2 3 3 3 x23 x 1 Downloaded from hlayiso.com Summative assessment – Module 5

3. Solve the following equations simultaneously (algebraically and graphically): 3.1 Algebraically y  2x 1 ...① y  3 x  1 ...② ①  ② : 0  5x  0 x  0 Substitute into ①:  0; 1 y  1 Downloaded from hlayiso.com Summative assessment – Module 5

3. Solve the following equations simultaneously (algebraically and graphically): 3.1 Graphically y  2 x  1: y  3 x  1: x-intercept  y  0 x -intercept  y  0 0  2x 1 1  3x 1 1 x   x  2 3 y -intercept  1 y -intercept  1 Downloaded from hlayiso.com Summative assessment – Module 5

3. Solve the following equations simultaneously (algebraically and graphically): 3.1  0; 1 Figure 5.9 Downloaded from hlayiso.com Summative assessment – Module 5

3. Solve the following equations simultaneously (algebraically and graphically): 3.2 Algebraically y  1  3x ... (1) y  x 1 ... (2) (2)  3: 3 y  3 x  3 ... (3) (1)  (3) : y  3y  1 3x  3x  3 4y  4  y 1 Downloaded from hlayiso.com Summative assessment – Module 5

3. Solve the following equations simultaneously (algebraically and graphically): 3.2 Algebraically (continued) Substitute into (2) : y  x 1 1  x 1 x  0   0; 1 Downloaded from hlayiso.com Summative assessment – Module 5

3. Solve the following equations simultaneously (algebraically and graphically): 3.2 Graphically y  1  3x : y  x  1: x -intercept  y  0 x -intercept  y  0 0  1  3x 1  x 1 x   x  1 3 y -intercept  1 y -intercept  1 Downloaded from hlayiso.com Summative assessment – Module 5

3. Solve the following equations simultaneously (algebraically and graphically): 3.2 Figure 5.10  0; 1 Downloaded from hlayiso.com Summative assessment – Module 5

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 5

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 5

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 5

Click above to play this video. Downloaded from hlayiso.com Summative assessment – Module 5

4. Solve the following inequalities. Show the answers on a number line: 4.1 3 x  4  2( x  1) 3x  4  2 x  2 3x  2 x  2  4 3x  2 x  6 x  6 Downloaded from hlayiso.com Summative assessment – Module 5

4. Solve the following inequalities. Show the answers on a number line: 4.2 5  1  x  7 5  1   x  7  1 6   x  6 6  x  6 Downloaded from hlayiso.com Summative assessment – Module 5

Downloaded from hlayiso.com Mathematics NQF Level 2