1. Yr 11 MCAT Algebra Practice 5 1. Solve these equations… a) 5a 4 = 80 b) 6a + 26 = 1 + a c) a(a – 6) = 0 2. A house is build in a rectangle shape. It is four metres longer than it is wide. It has a total floor area of 165m 2 a) Write an algebraic equation for the formula of the area being equal to 165m 2. b) Solve the above equation to find the dimensions of the house. (show the steps of solving)… 3. Factorise fully a 2 – 3a - 10 4. Simplify fully… a) (2a 3 ) 2 = b) a 2 + 13a + 30 = a + 3 c) 4a 2 b 2 x 3ab 3 = d) 3a + a = 10 5 e) 13a + 5b 2 – a + 4b 2 = 5. The formula for the size of a persons shoe is given by… s = 3c – 10 11 where c is the centimetre length of their foot. What size shoe does a person with a 40cm foot have? 6. Expand and simplify… a) (4a + 1)(a – 7) = b) (a + 5) 2 = 7. Simultaneously solve for both a and b… a + b = 32 4a + 2b = 108 8. Solve these inequations… a) 5a + 1 > 21 b) 3(a + 4) < 2(a + 12) c) -10a – 3 < 67 9. Factorise… a) 3a 4 b + 12abc = b) 2a 2 + 12a + 10 = c) a 2 – 36 = 10. Simplify fully… a 2 + 14a + 40 = a 2 + 6a + 8 a 4 = 16 _x_x_x_ = 16 a = 2 and - 2 6a – a = 1 – 26 5a = –25 a = –5 a = 0 or a – 6 =0 a = 0 ora = 6 A( ☐ ) = length x width length = a width = a + 4 A( ☐ ) = a(a + 4) A( ☐ ) = a 2 + 4a A( ☐ ) = 165so a 2 + 4a = 165 a 2 + 4a – 165 = 0 (a )(a ) = 0 +15- 11 so a is ___ or ___ - 1511 Exc student should see that can’t have negative length of house. width = 11m length = 15m = ( )( )a a – 5 + 2 4 a6a6 (a + 3)(a + 10). a + 3 = a + 10 12 a3a3 b5b5 3a + = 10 10 2a 5a = 10 a \ 2 12a + 9b 2 s = 3(40) - 10 = 11 110 = 11 10 4a 2 - 28a + 1a - 7 = 4a 2 – 27a - 7 (a + 5)(a + 5) = a 2 + 5a + 25 = a 2 + 10a+ 25 (1) (2) Double (1) 2a + 2b = 64 (3) (3) - (2) -. 2a =44 a = 22 sub a into (1) 22 + b = 32 b = 10 5a > 20 a > 4 3a + 12 < 2a + 24 3a – 2a < 24 – 12 a < 12 – 10a < 70 0 < 70 + 10a - 70 < 10a - 7 < aor a > - 7 ( ) 3ab a3a3 + 4c 2(a 2 + 6a + 5) = 2(a + 1)(a + 5) ( )( ) a a + 6 - 6 (a + 4)(a + 10). (a + 2)(a + 4) = a + 10. a + 2

2. Yr 11 MCAT Algebra Practice 5 1. Solve these equations… a) 5a 4 = 80 b) 6a + 26 = 1 + a c) a(a – 6) = 0 2. A house is build in a rectangle shape. It is four metres longer than it is wide. It has a total floor area of 165m 2 a) Write an algebraic equation for the formula of the area being equal to 165m 2. b) Solve the above equation to find the dimensions of the house. (show the steps of solving)… 3. Factorise fully a 2 – 3a - 10 4. Simplify fully… a) (2a 3 ) 2 = b) a 2 + 13a + 30 = a + 3 c) 4a 2 b 2 x 3ab 3 = d) 3a + a = 10 5 e) 13a + 5b 2 – a + 4b 2 = 5. The formula for the size of a persons shoe is given by… s = 3c – 10 11 where c is the centimetre length of their foot. What size shoe does a person with a 40cm foot have? 6. Expand and simplify… a) (4a + 1)(a – 7) = b) (a + 5) 2 = 7. Simultaneously solve for both a and b… a + b = 32 4a + 2b = 108 8. Solve these inequations… a) 5a + 1 > 21 b) 3(a + 4) < 2(a + 12) c) -10a – 3 < 67 9. Factorise… a) 3a 4 b + 12abc = b) 2a 2 + 8a + 8 = c) a 2 – 36 = 10. Simplify fully… a 2 + 14a + 40 = a 2 + 6a + 8