Yr 11 MCAT Algebra Practice 5 1 Solve

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

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

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