Evaluation. Simplification + 3 KU. Factorisation. a 9b Evaluate 30 3p 2 q where p = 1 and q = 6 2 KU. 2. Simplify 4(3x 2 KU
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1 . Algebra 1 Basic algebraic operations Evaluation... 1 Simplification, removing brackets, FOIL, squares... 1 Factorisation, common factor, difference of two squares, quadratic (trinomial)... 1 Solving linear equations... Simultaneous Equations... Functions, evaluating, finding values... Quadratic equations using factorisation, using the formula... Inequalities solving... 4 Changing the subject of the formula... 5 Algebraic Fractions simplifying, common denominator... 6 Algebraic fraction equations solving... 6 Indices... 7 Surds... 8 Evaluation 1. Evaluate 0 p q where p = 1 and q = 6 KU Simplification. Simplify 4( ) 5(4 + 1) Remove the brackets and collect like terms ( a b)( a 5b) KU KU 4. Remove the brackets and simplify your answer ( )( ) ( ) 5. Remove the brackets and simplify ( y 4) KU 6. Multiply out the brackets and simplify. ( )( 4 1) + Factorisation 7. Factorise 8. Factorise 6 9 KU 4a 9b KU 9. a) Factorise the epression y b) Hence simplify 9 y y 1 KU KU 10. a) Factorise a 9b 1 KU a 9b b) Hence simplify KU a + 6b 11. a) Factorise 9 1 KU 4(5 + ) b) Epress in its simplest form KU Epress 9 16 in its simplest form - 1 -
2 1. i) Factorise completely 6 1 KU 6 ii) Epress in its simplest form. KU Factorise 1 10 KU Solve Linear Equations 15. Solve the equation ( ) 5 1+ = Solve the equation 5 + a = a 15 Simultaneous Equations 17. Solve algebraically, the system of equations a + 4b = 7 a 5b = Solve the system of equations 5a + b = 9 7a b = 5 Functions 1.. f ( ) =, evaluate f (-) KU h( t) 15t t = Find h(-) KU. Given that f ( ) = evaluate f ( ) 4. f ( ) = 9 6 (a) Evaluate f (-) 1 KU (b) Given that f (t) = 11, find t KU 5. The function f () is given by the formula f ( ) = 7, where is a real number. (a) Find the value of f ( ). KU (b) Find the values of a for which f ( a ) = f ( ) = find ( 1 ) f KU 7. ( ) f = a) Find f(4) 1 KU - -
3 b) Given that f ( ) = 7, find. 8. f ( ) = Find the eact value of f() Give your answer as a fraction with a rational denominator. KU 9. f ( ) = Find the eact value of f(1), giving your answer as a surd, in its simplest form. KU Quadratic Equations 1. Solve algebraically, the equation. Solve algebraically, the equation. Solve algebraically, the equation = 7 6y y 0 = KU = 4. Solve for : 5. Solve the equation 6. Solve the equation = = p p 10 0 = where p is a real number. 7. Two functions are given below: f ( ) = + 1 g( ) = 5 + Find the values of for which f() = g() 8. Find the two roots of the equation 4 = 0 (Answer correct to 1 decimal place). 9. Solve the equation + 6 = 0 Give your answers correct to significant figures. 4 KU 5 KU - -
4 Inequalities 1. Solve the inequality 8 > ( + 5). Solve algebraically the inequality y < 4 ( y + ). Solve the inequality ( 6) < 4. Solve algebraically the inequality 6 < 5(1 ) 5. Solve algebraically, the inequality Solve the inequality 5( ) 4(1 ) where is a positive integer. 5 KU 7. An inequality, like , can be solved by then ii) i) solving and solving looking carefully at the two sets of answers to decide on the correct solution to the original inequality. a) Solve KU b) Write down the set of all possible solutions where is an INTEGER. 1 KU - 4 -
5 Changing the subject of the formula 1. Y ( v w) = Change the subject of the formula to v. 5. P 1 ( m s) = Change the subject of the formula to m KU 6. L = 8 + Change the subject of the formula to Y. Y k m 4. Change the subject of the formula to k. d = KU t 5. Q p T = + Change the subject of the formula to T. KU 6. M = R t Change the subject of the formula to R. 7. Change the subject of the formula to b. = 4 A b c 8. a) Change the subject of the formula Q = s + t, to s b) Find the value of s when Q =.5 and t =. KU 9. The frequency, F hertz of the sound you hear as you drive past a factory siren at a speed of v metres per second is given by the formula F f 1 v = s where f is the true frequency of the sound emitted by the siren and s is the speed of sound. Change the subject of the above formula to v
6 Algebraic Fractions 1. Epress as a single fraction in its simplest form 1 1, 0 KU. Epress as a single fraction in its simplest form +, 0. Epress as a single fraction in its simplest form 5, 0 or ( ) Fraction Equations 1. Solve the equation. Solve the equation + 1 = = 1, where is a real number.. Solve algebraically the equation ( 5 + ) = 4 4. Solve the equation 1 + = 4 4 KU 5. Solve this equation for : 1 = 4 KU 4 6. Solve algebraically, the equation 7. Solve algebraically, the equation ( 1) + = 4 ( 1 ) m m = 5-6 -
7 Indices 1. Evaluate 7 KU Epress in its simplest form ( ) y y KU. Simplify 7 a ( a + 5) KU 4. Epress y 4y 6y 5 1 in its simplest form. 5. Epress 4 y y y in its simplest form. KU 6. Epress b 1 b b in its simplest form. KU 7. Remove the brackets and simplify 8. Remove the brackets and simplify b b + b a a + a KU - 7 -
8 Surds 1. Epress 50 as a surd in its simplest form. 1 KU. Simplify 7 KU. Simplify 48 KU 4. Epress as a surd in its simplest form. KU 5. Epress as a surd in its simplest form 6. Epress + 8 as a surd in its simplest form. 7. Multiply out the brackets ( 6 ) Epress your answer as a surd in its simplest form. KU 8. f ( ) = Find the eact value of f(1), giving your answer as a surd, in its simplest form. KU 9. Epress 5 as a fraction with a rational denominator. KU 10. Simplify 4 Epress your answer as a fraction with a rational denominator 11. f ( ) = Find the eact value of f() Give your answer as a fraction with a rational denominator. KU 1. A function f is given by f ( ) = 4 Find the value of ( ) f KU - 8 -
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