Year 11 mcat 90127 revision page 6
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This document contains 11 math problems involving algebra concepts such as factorizing, solving equations, expanding expressions, and finding simultaneous solutions. The key details are: 1) Factorize quadratics and solve equations for variables. 2) Find the area of a circle given the radius. 3) Simplify algebraic expressions and set up equations to solve word problems. 4) Solve simultaneous equations to find values of variables. 5) Expand expressions and set up and solve equations to solve word problems involving ages multiplying to a given value in the future.
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E-learning to solve Logarithms Concept in Mathematics
Year 11 mcat 90127 revision page 6
- 1. Yr 11 MCAT Algebra Practice 6 (all previous year’s NCEA questions) 1. Factorise completely… a) a2 – 7a + 6 b) 2a2 – 4a – 16 c) c2 – 5c - 24 2. Josh estimates the area of a circle by using the formula A = 3r2 What is the area if r = 5cm? 3. Simplify Fully… a) 3a2 – 15ab = 6a2 b) a + a = 5 3 4. Make b the subject of this formula… P = 2b + 2h 5. Solve the following… a) 3a(a + 4) = 0 b) (2a – 1)(a + 3) = 0 c) 6a – 2 = 2a + 9 6. Peter has more than twice as many cd’s as Mary. Together they have 97 cd’s. What is the least number of cd’s Peter has. Write equations and solve, showing working… 7. Simplify Fully… a) 3a4 x 2a3 = b) (2a2 )3 = c) a2 + 5a + 6 = a + 3 d) 9a5 = 12a3 e) 4(a2 )n x 3a4 = 12a16 what is the value of n? 8. Solve the equation to find the values of a… a2 + 8a – 9 = 0 9. Simultaneously Solve to find values of p and m… 2p + 4m = 39.70 3p + m = 39.80 10. Expand and simplify… a) 5(a+1) + 2(a-3) = b) (3a-1)(2a+5) = c) (a – 2)2 = 11. James is 5 years old, Emma is 4 years older. How many years will it be from now unit James and Emma’s ages multiply to 725? Show equations and working. = ( )( )a a- 1 - 6 = 2( )a2 – 2a - 8 = 2( )( )a a- 4 + 2 = ( )( )c c- 8 + 3 A = 3(5)2 = 3(25) = 75 3a(a – 5b) = 3a(2a) a – 5b . 2a _ + _ = 15 15 3a 5a 8a 15 2b + 2h = P 2b = P – 2h b = (P – 2h) 2 a is ___ or ___0 - 4 a is ___ or ___ 1 /2 - 3 6a – 2a = 9 + 2 4a = 11 a = 11 /4 P ≥ 2M and M = 97 – P substitute 97 - P for M P ≥ 2(97 – P) P ≥ 194 – 2P 2P + P ≥ 194 3P ≥ 194 P ≥ 64 2 /3 Peter would have at least 65 cd’s 6a7 8a6 ( )( ) = a + 3 a a+ 3 + 2 a + 2 3a 4 n = 6 ( )( ) = 0a a- 9 + 1 a is ___ or ___9 - 1 x by four 12p + 4m = 159.2 _____________ minus these - _____________ 10p = 119.5 p = 11.95sub back in 2(19.5) + 4m = 39.70 4m = 15.80 m = 3.95 5a +5 +2a -6 =7a-6 6a2 +15a-2a-5 =6a2 +13a-5 (a – 2)(a – 2) =a2 -4a +4 simultaneous eqn’s E = J + 4 E x J = 725 sub J + 4 for E (J+4) x J = 725 J2 + 4J = 725 J2 + 4J – 725 = 0 ( )( ) = 0J J-25 +29 J is ___ or ___-29 25can’t be -ve
- 2. Yr 11 MCAT Algebra Practice 6 (all previous year’s NCEA questions) 1. Factorise completely… a) a2 – 7a + 6 b) 2a2 – 4a – 16 c) c2 – 5c - 24 2. Josh estimates the area of a circle by using the formula A = 3r2 What is the area if r = 5cm? 3. Simplify Fully… a) 3a2 – 15ab = 6a2 b) a + a = 5 3 4. Make b the subject of this formula… P = 2b + 2h 5. Solve the following… a) 3a(a + 4) = 0 b) (2a – 1)(a + 3) = 0 c) 6a – 2 = 2a + 9 6. Peter has twice as many cd’s as Mary. Together they have 97 cd’s. What is the least number of cd’s Peter has. Write equations and solve, showing working… 7. Simplify Fully… a) 3a4 x 2a3 = b) (2a2 )3 = c) a2 + 5a + 6 = a + 3 d) 9a5 = 12a3 e) 4(a2 )n x 3a4 = 12a16 what is the value of n? 8. Solve the equation to find the values of a… a2 + 8a – 9 = 0 9. Simultaneously Solve to find values of p and m… 2p + 4m = 39.70 3p + m = 39.80 10. Expand and simplify… a) 5(a+1) + 2(a-3) = b) (3a-1)(2a+5) = c) (a – 2)2 = 11. James is 5 years old, Emma is 4 years older. How many years will it be from now unit James and Emma’s ages multiply to 725? Show equations and working.