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Yr 11 MCAT Algebra Practice 6 (all previous year’s NCEA questions) 8. Solve the equation to find the values of a… 5. Solve the following… a2 + 8a – 9 = 0 0 or ___ -4 a) 3a(a + 4) = 0 a is ___ 1. Factorise completely… a) a2 – 7a + 6 = ( a - 1 )( a - 6) b) 2 2a2 – 4a – 16 = 2(a – 2a - 8 ) c) c2 – 5c - 24 b) (2a – 1)(a + 3) = 0 a is = 2( a - 4 )(a + 2 ) c) 6a – 2 = 2a + 9 = ( c - 8 )( c + 3 ) 6a – 2a = 9 + 2 2. Josh estimates the area of a circle by using the formula A = 3(5)2 = 3(25) = 75 3. Simplify Fully… b) _ + 5a _ = 8a a + a = 3a 15 15 15 5 3 4. Make b the subject of this formula… P = 2b + 2h 2b + 2h = P 2b = P – 2h b = (P – 2h) 2 4a = 11 a = 11/4 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… What is the area if r = 5cm? 3a2 – 15ab = 3a(a – 5b) = a – 5b 3a(2a) 2a 6a2 -3 or ___ 6. Peter has more than twice as many A = 3r2 a) 1/ 2 ___ . ( a - 9 )( a + 1 ) = 0 9 or ___ -1 a is ___ 9. Simultaneously Solve to find values of p and m… 12p + 4m = 159.2 2p + 4m = 39.70 minus these - _____________ _____________ 3p + m == 119.5 39.80 x by four 10p p = 11.95 sub back in 2(19.5) + 4m = 39.70 4m = 15.80 m = 3.95 P ≥ 2M and M = 97 – P 10. Expand and simplify… substitute 97 - P for M P ≥ 2(97 – P) a) 5(a+1) + 2(a-3) = 5a +5 +2a -6 =7a-6 P ≥ 194 – 2P P ≥ 64 2/3 = 2P + P ≥ 194 Peter would have b) (3a-1)(2a+5) 2 6a +15a-2a-5 =6a2 +13a-5 3P ≥ 194 at least 65 cd’s c) (a – 2)2 = (a – 2)(a – 2) 7. Simplify Fully… =a2 -4a +4 a) 3a4 x 2a3 = 6 a7 b) (2a2)3 = 8a6 c) d) 11. James is 5 years old, Emma is 4 years older. a2 + 5a + 6 = (a + 3 )(a + 2 ) = a + 2 How many years will it be from now unit James and Emma’s ages a+3 a+3 multiply to 725? Show equations and working. simultaneous eqn’s 9a5 = 3a E = J + 4 E x J = 725 4 12a3 sub J + 4 for E (J+4) x J = 725 e) 4(a2)n x 3a4 = 12a16 what is the value of n? n = 6 J2 + 4J = 725 + 4J – 725 = 0 (J-25 )(J+29) = 0 can’t be -ve J is ___ -29 or ___ 25 J2 Yr 11 MCAT Algebra Practice 6 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? (all previous year’s NCEA questions) 8. Solve the equation to find the values of a… 5. Solve the following… a2 + 8a – 9 = 0 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… b) 3a2 – 15ab = 6a2 a + a = 5 3 4. Make b the subject of this formula… P = 2b + 2h 2p + 4m = 39.70 3p + m = 39.80 10. Expand and simplify… a) 5(a+1) + 2(a-3) = 3. Simplify Fully… a) 9. Simultaneously Solve to find values of p and m… b) (3a-1)(2a+5) = 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? 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.