Yr 11 MCAT Algebra Practice 6 (all previous year’s NCEA questions)

1. Yr 11 MCAT Algebra Practice 6 (all previous year’s NCEA questions) 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. 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? 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 = ( )( ) a - 1 a - 6 0 - 4 a is ___ or ___ ( )( ) = 0 a - 9 a + 1 = 2( ) a2 – 2a - 8 1/2 9 - 1 - 3 a is ___ or ___ a is ___ or ___ = 2( )( ) a - 4 a + 2 4a = 11 = ( )( ) c - 8 c + 3 12p + 4m = 159.2 a = 11/4 6a – 2a = 9 + 2 minus these - _____________ _____________ x by four 10p = 119.5 sub back in p = 11.95 2(19.5) + 4m = 39.70 4m = 15.80 m = 3.95 P ≥ 2M and M = 97 – P A = 3(5)2 = 3(25) = 75 substitute 97 - P for M P ≥ 2(97 – P) 5a +5 +2a -6 =7a-6 P ≥ 194 – 2P P ≥ 64 2/3 3a(a – 5b) = 3a(2a) a – 5b . 2a 2P + P ≥ 194 Peter would have at least 65 cd’s 6a2 +15a =6a2 -2a -5 +13a -5 3P ≥ 194 (a – 2)(a – 2) -4a +4 =a2 5a 8a 15 3a _ + _ = 15 15 a7 6 8 a6 a + 3 ( )( ) = a + 3 a a + 2 + 2 simultaneous eqn’s 3a 4 E = J + 4 E x J = 725 (J+4) x J = 725 sub J + 4 for E 2b + 2h = P J2 + 4J = 725 2b = P – 2h J2 + 4J – 725 = 0 J +29 -25 ( )( ) = 0 J b = (P – 2h) 2 n = 6 can’t be -ve -29 J is ___ or ___ 25

2. Yr 11 MCAT Algebra Practice 6 (all previous year’s NCEA questions) 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. 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? 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