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XT – MATHS Grade 11 – Equations

XT – MATHS Grade 11 – Equations

XT – MATHS Grade 11 –

XT - MATHS Grade 11Subject: Equations 1: Basic, Formula, InequalitiesTotal Marks: 64Date: 2010/06/291. TRUE 2Explanation:2x− 3 x− 10 =0Then ...( x− 5)( x+ 2) =0∴ x= 5 or x= −22. FALSE 3Explanation:For quadratic inequalities, we must use a number line to determine whether the interval(s) we are lookingfor lies between or beyond the critical values.x 2 ≤ 9x 2 - 9 ≤ 0(x - 3)(x + 3) ≤ 0If we substitute a number less than -3 into the given inequality, the product of the two brackets will bepositive.If we substitute a number between -3 and 3 into the given inequality, the product of the two brackets willbe negative.If we substitute a number greater than 3 into the given inequality, the product of the two brackets willagain be positive.The product of the two brackets must be negative or zero; hence the solution is -3 ≤ x ≤ 3.3. A 4Explanation:2x 2 + x - 1 < 0(2x - 1)(x + 1) < 0If we substitute a number less than -1 into the given inequality, the product of the two brackets will bepositive.If we substitute a number between -1 and ½ into the given inequality, the product of the two brackets willbe negative.If we substitute a number greater than ½ into the given inequality, the product of the two brackets willagain be positive.The product of the two brackets must be negative; hence the solution is -1 < x < ½.4. A 5Explanation:p is a root, therefore: x = pThe roots of this equation are …x− ( − 2 q) ± (2 q) −4(1)( q)=2(1)2=2q ± 4q −4q22Therefore …Page 1

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