HO1 - Basics of Algebra PDF

## Chapter 1: Starting Algebra ### Exercise 1A 1. Put each of the following expressions into a simpler form. - 3 - 5 + 4 - b + b + 7 - c + 2c - 3d + 2d - 12 - 2e - 7 + 5e + 8 - 4f + 7 - 3f - 7 - 6 - g - 4 + g - 3h + 4 - h - 3 - 2h - 1 - 4i + 2i - 7i + 1 - 2x...

## Chapter 1: Starting Algebra ### Exercise 1A 1. Put each of the following expressions into a simpler form. - 3 - 5 + 4 - b + b + 7 - c + 2c - 3d + 2d - 12 - 2e - 7 + 5e + 8 - 4f + 7 - 3f - 7 - 6 - g - 4 + g - 3h + 4 - h - 3 - 2h - 1 - 4i + 2i - 7i + 1 - 2xg + 5xg - 3xf - 2xf - 2xx - 3xx + 2xx - 4y - 2xy - 4z - 2z - 3 - 2u - 1 - uxu 2. Simplify the following expressions. - a + 2b + 3a + 4b - c - 2d + 2c - 5d - x × 2 - 3xy - y + 2x - 2x - y - y - y + 4x + 3y - 2u - v + 3w - u + v + w - 3l - 2m + 4l - 3n 3. Simplify the following. - 2xxy + 3xx y - 2xy + 4yx - ab + 2bxb - 2ba + 3ab - 2px3p + 4p² - 4qx4q - 3a²b + bx2a 4. Express the following in a simpler form - 4g - 2 + g × g - 2g + 4 - 2g - h² + h + 3h² - 2h - 2j² - 3j - 6j + 9 - 2k² + h² - 3h - 2k² + h - 31² + 111 + 30 - 12 + 21 - 9 - m² - m - 2 - m² + 2m - 1 5. Simplify the following. - pxpxp - 2qxqxq - 3r × 2rxr - 2s²xs - 2px3p² - 4p³ - 3xx² + 2xxx - 4t²x3t - 3x²y² - 4yxy² - 3zx4z² - 2z²x6z 6. Not all the following expressions can be simplified. Simplify those which can be simplified. - 4a - 2axb - 4bxa - 2axb - a + b + 2ab - a² - bab + 2a²b - a² - aab + 2a²b - x³ - 3xx² + 2x²xx ### Exercise 1B 1. If a = 3, b = 5, c = 6 and d = 2, find the values of the following expressions. - a + b - b - c - a - c - d - ab - a + bc - ad - bc - a² - bd - ad - c² - cd - b² - a³ - a² + b² - c² - d² - ab + bc + cd - da - a³ - b³ + c³ - d³ 2. If x = -2, y = 3 and z = -4, find the values of the following expressions. - x + y - x - y + z - 4x - 3y + 2z - -2x + y + 5z - xy - 2xz + yz - yz + zx + xy - x² + y² - y² - z² - x² - y² - 2xy - x³ + y³ + z³ - x³ - y³ + z³ ### Test Exercise 1 1. Simplify, where possible, the following expressions. - a + b + c - a + 2b - b + 2a - x - 2z - y + 2z - 2lm + l - m - abc - b² - axb + c - a + bxc - 2pxp - qx3q² - pqx2pq - 4xx4x - 2xy x 4xy² 2. If x = 2, y = -3 and z = 4 find the values of the following expressions. - x + y - 2x - 3y - 4z - z - x + y - z - x -y - x - 2z - x² + z² - y² + z² - 2xy - 2xy - yz - 3zx3z - 2yzx8yz - 2xy x 4 xy² 3. A rectangular shaped room is to have wallpaper on the walls and ceiling. The length, breadth and height of the room are *x* metres, *y* metres and *z* metres respectively. The area *A* m² to be papered, neglecting doors and windows, is given by A = xy + 2xz + 2yz. If x = 4.6, y = 3.2 and z = 2.8, calculate the area to be papered, giving your answer correct to the nearest square metre (you will need a calculator). ### Answers #### 1. Starting Algebra ##### Exercise 1A (page 5) 1. - a) 2 - b) 2b + 7 - c) 3c - d) 5d - 12 - e) 7e + 1 - f) f - g) 2 - h) 0 - i) 1 - i - j) 7g - k) f - l) x - m) 2y - n) 2z - 3 - o) 2u - 1 - u² 2. - a) 4a + 6b - b) 3c - 7d - c) 4x - 4y - d) 6x - e) u + 4w - f) 7l - 2m - 3n 3. - a) 5xy - b) 6xy - c) 2ab + b² - d) 10p² - e) 16q² - f) 8ab 4. - a) 2 + g² - b) 4h² - h - c) 2j² - 9j + 9 - d) h² - 2h - e) 21² + 131 + 21 - f) m - 3 5. - a) p³ - b) 2q³ - c) 6r³ - d) 2s³ - e) 12t³ - f) 2p³ - g) 5x² - h) 6y² - 4y³ - i) 0 6. - a) 4a - 2ab - b) 2ab - c) a + b + 2ab - d) a² - ab² + 2a²b - e) a² + a²b - f) 0 ##### Exercise 1B (page 7) 1. - a) 8 - b) -1 - c) -5 - d) 15 - e) 33 - f) -24 - g) -1 - h) -30 - i) -40 - j) -6 - k) 51 - l) 110 2. - a) 1 - b) -9 - c) -25 - d) -13 - e) -6 - f) 4 - g) -10 - h) 13 - i) -7 - j) 7 - k) -45 - l) -99 ##### Test exercise 1 (page 8) 1. - a) a + b + c - b) 3a + b - c) x - y - d) 2lm + l - m - e) abc - b² - f) ab + c - g) a + bc - h) 2p² - i) 3q³ - j) 2p² - q - k) 16x² - l) 8x²y³ 2. - a) -1 - b) -13 - c) -1 - d) -5 - e) -6 - f) 8 - g) 9 - h) -12 - i) -15 - j) 24 - k) -192 - l) 96 3. 58 m²