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Yr 11 MCAT Algebra Practice 5

Yr 11 MCAT Algebra Practice 5 . 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 =

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Yr 11 MCAT Algebra Practice 5

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  1. Yr 11 MCAT Algebra Practice 5 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) 3a4b + 12abc = b) 2a2 + 12a + 10 = c) a2 – 36 = 10. Simplify fully… a2 + 14a + 40 = a2 + 6a + 8 4. Simplify fully… a) (2a3)2 = b) a2 + 13a + 30 = a + 3 c) 4a2b2 x 3ab3 = d) 3a + a = 10 5 e) 13a + 5b2 – a + 4b2 = 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 = 1. Solve these equations… a) 5a4 = 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 165m2 a) Write an algebraic equation for the formula of the area being equal to 165m2. b) Solve the above equation to find the dimensions of the house. (show the steps of solving)… 3. Factorise fully a2 – 3a - 10 (1) Double (1) 4 a6 (2) _x_x_x_ = 16 a4 = 16 (3) 2a + 2b = 64 (3) - (2) - . (a + 3)(a + 10) . a + 3 a = 2 and - 2 2a = 44 sub a into (1) a = 22 = a + 10 6a – a = 1 – 26 a = –5 22 + b = 32 12 a3 b5 5a = –25 b = 10 3a + = 10 10 2a 5a = 10 a \ 2 a = 0 or a – 6 =0 a = 0 or a = 6 5a > 20 + 9b2 12a a > 4 3a + 12 < 2a + 24 3a – 2a < 24 – 12 a < 12 – 10a < 70 0 < 70 + 10a A(☐) = length x width - 70 < 10a A(☐) = a(a + 4) length = a a > - 7 - 7 < a or A(☐) = a2 + 4a width = a + 4 165 so A(☐) = a2 + 4a = 165 a3 ( ) 3 a b + 4 c 2(a2 + 6a + 5) = 2(a + 1)(a + 5) s = 3(40) - 10 = 11 110 = 11 10 a + 6 ( )( ) a - 6 a2 + 4a = 165 Exc student should see that can’t have negative length of house. a2 + 4a – 165 = 0 - 7 4a2 +15 - 11 width = 11m - 28a + 1a (a )(a ) = 0 = 4a2 – 27a - 7 (a + 4)(a + 10) . (a + 2)(a + 4) - 15 11 length = 15m so a is ___ or ___ (a + 5)(a + 5) = a2 + 5a + 5a + 25 = a + 10. a + 2 = ( )( ) a + 2 a – 5 = a2 + 10a + 25

  2. Yr 11 MCAT Algebra Practice 5 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) 3a4b + 12abc = b) 2a2 + 8a + 8 = c) a2 – 36 = 10. Simplify fully… a2 + 14a + 40 = a2 + 6a + 8 4. Simplify fully… a) (2a3)2 = b) a2 + 13a + 30 = a + 3 c) 4a2b2 x 3ab3 = d) 3a + a = 10 5 e) 13a + 5b2 – a + 4b2 = 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 = 1. Solve these equations… a) 5a4 = 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 165m2 a) Write an algebraic equation for the formula of the area being equal to 165m2. b) Solve the above equation to find the dimensions of the house. (show the steps of solving)… 3. Factorise fully a2 – 3a - 10

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