Junior Cert Maths Samples

_________________________________________ juniorcertsolutions.com ________________________________________ 2016 Question 7 – Higher Paper 1 Solution (a) 2 4 5 7 5 3 2 x x + − − = The common denominator is 6 ∴ Multiply everything by 6 ( ) 2 4 5 7 6 6 6 5 3 2 x x + −     − =         Simplify ( ) ( ) ( ) 2 2 4 3 5 7 6 5 4 8 15 21 30 4 15 30 21 8 x x x x x x + − − = ⇒ + − + = ⇒ − = − − 1 11 1 11 x x ⇒ − = ⇒ = − ( 5 marks ) (b) (i) 4, x x < ∈ ` reads x is less than 4 and x is a natural numer ∴ { } 1, 2, 3 x = Use dots to show that ( x ∈ ` ) ( 5 marks ) (ii) 4, x x < ∈ ] reads x is less than 4 and x is an integer ∴ { } 2, 1, 0,1, 2, 3 x ∈ − − … Use dots to show that ( x ∈ ] ) (iii) 4, x x < ∈ \ reads x is less than 4 and x is a real number means 4 is excluded We always use a thick line for real numbers ( 5 marks ) Comment: Very basic. This is the first algebra question. • • • • • • • • • •