1. Yr 11 MCAT Algebra Practice 6 (all previous year’s NCEA questions) 1. Factorise completely… a) a 2 – 7a + 6 b) 2a 2 – 4a – 16 c) c 2 – 5c - 24 2. Josh estimates the area of a circle by using the formula A = 3r 2 What is the area if r = 5cm? 3. Simplify Fully… a) 3a 2 – 15ab = 6a 2 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) 3a 4 x 2a 3 = b) (2a 2 ) 3 = c) a 2 + 5a + 6 = a + 3 d) 9a 5 = 12a 3 e) 4(a 2 ) n x 3a 4 = 12a 16 what is the value of n? 8. Solve the equation to find the values of a… a 2 + 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. = ( )( )aa- 1- 6 = 2( ) a 2 – 2a - 8 = 2( )( ) aa- 4+ 2 = ( )( )cc- 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 ___ 1/21/2 - 3 6a – 2a = 9 + 2 4a = 11 a = 11 / 4 P ≥ 2M andM = 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 6 a7a7 8 a6a6 ( )( ) = a + 3 a a + 3 + 2 a + 2 3a 4 n = 6 ( )( ) = 0aa- 9+ 1 a is ___ or ___ 9- 1 x by four 12p + 4m = 159.2 _____________ minus these - _____________ 10p = 119.5 p = 11.95 sub back in 2(19.5) + 4m = 39.70 4m = 15.80 m = 3.95 5a +5+2a-6=7a-6 6a 2 +15a -2a-5 =6a 2 +13a-5 (a – 2)(a – 2) =a 2 -4a+4 simultaneous eqn’s E = J + 4E x J = 725 sub J + 4 for E (J+4) x J = 725 J 2 + 4J = 725 J 2 + 4J – 725 = 0 ( )( ) = 0J J -25 +29 J is ___ or ___ -29 25 can’t be -ve

2. Yr 11 MCAT Algebra Practice 6 (all previous year’s NCEA questions) 1. Factorise completely… a) a 2 – 7a + 6 b) 2a 2 – 4a – 16 c) c 2 – 5c - 24 2. Josh estimates the area of a circle by using the formula A = 3r 2 What is the area if r = 5cm? 3. Simplify Fully… a) 3a 2 – 15ab = 6a 2 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) 3a 4 x 2a 3 = b) (2a 2 ) 3 = c) a 2 + 5a + 6 = a + 3 d) 9a 5 = 12a 3 e) 4(a 2 ) n x 3a 4 = 12a 16 what is the value of n? 8. Solve the equation to find the values of a… a 2 + 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.