Quadratic Equations. (x + 3)(x 3) = 0. Mathletics Instant Workbooks. Copyright

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1 Quadratic Equations Student Book - Series K- ( + )( ) Mathletics Instant Wkbooks Copyright

2 Student Book - Series K Contents Topics Topic - Equations already in factised fm Date completed Topic - Equations involving the difference between two squares Topic - Equations involving a common Topic - Factising a quadratic trinomial Topic 5 - Completing the square Topic 6 - The quadratic fmula Topic 7 - Mied quadratic equations Topic 8 - Using quadratic equations to solve problems Topic 9 - Simultaneous equations resulting in a quadratic Practice Tests Topic - Topic test A Topic - Topic test B Auth of The Topics and Topic Tests: AS Kalra Mathletics Instant Wkbooks Series K Copyright P Learning

3 Topic - Equations already in factised fm QUESTION Solve the following quadratic equations that are already epressed in factised fm. a ( ) ( ) b ( ) ( + ) c ( ) ( ) d ( + 5) e ( ) f ( ) g ( ) ( 5) h ( + ) ( ) i ( + ) ( ) j ( + ) ( ) k ( ) ( + ) l ( 5) ( + 5) m ( + 6) ( ) n ( + ) ( ) o ( ) ( ) QUESTION Solve the following quadratic equations. a ( ) ( 7) b ( + ) ( 6) c ( ) ( + ) d ( + 8) e 5( ) f ( ) g ( + ) ( + ) h ( 5) i ( ) j ( + ) k ( ) l ( ) QUESTION Solve the following equations. a ( ) ( 5) b ( 8) ( + 8) c ( ) d ( ) ( + ) e ( + ) ( ) f ( ) g ( 7) ( 9) h ( + 5) ( 5 ) i ( + ) ( 5) Mathletics Instant Wkbooks Series K Copyright P Learning

4 Topic - Equations involving the difference between two squares QUESTION Solve the following quadratic equations. a b 6 c 9 d e 9 f 6 g 5 h 6 i 8 j 00 k l QUESTION Solve the following equations. a 5 b 9 6 c 6 5 d e 9 f g 9 h 8 i 9 j 5 6 k 5 0 l ( + 5) m n 7 o 5 Mathletics Instant Wkbooks Series K Copyright P Learning

5 Topic - Equations involving a common QUESTION Solve the following quadratic equations. a 5 b c d + 7 e + 5 f + 9 g = h = 9 i = j 6 k + 8 l 0 m + n 5 o = QUESTION Solve the following equations. a 6 b c 5 d 8 6 e f 6 6 g 6 + h 7 i 9 9 j 7 k 9 7 l 8 Mathletics Instant Wkbooks Series K Copyright P Learning

6 Topic - Factising a quadratic trinomial QUESTION Solve the following quadratic equations by factising. a b 5 c 5 6 d e f + 8 g h + 5 i = + 8 j + 0 = k + 5 = 6 l = 5 5 QUESTION Factise and solve the following quadratic equations. a + + b 8 + c d + 5 e f + 5 g 6 + h i j = ( + ) k 6 7 l ( + ) = 7 + ( ) = Mathletics Instant Wkbooks Series K Copyright P Learning

7 Topic 5 - Completing the square QUESTION What number must be added to make each of the following a perfect square? a + 6 b 0 c + 9 d + 8 e + 5 f + g h i 8 j 7 k l + m 6 + K = ( K) n + + K = ( + K) o + K = ( K) p K = ( + K) q + + K = ( + K) r 7 + K = ( K) QUESTION Solve the following quadratic equations by completing the square. a b c 8 + d + 9 = e f = g = h + 0 = 5 i + = j + = k + 8 l 0 = Mathletics Instant Wkbooks Series K Copyright P Learning 5

8 Topic 6 - The quadratic fmula QUESTION Solve the following equations using the quadratic fmula. Leave your answer in surd fm. a + + b c + 7 d 0 7 e f g 8 h 5 9 i j k ( + 6) = 5 l ( 8) = 5 QUESTION Use the quadratic fmula to solve. Give your answer crect to two decimal places. a b + c d e + = f 5 = 7 g = + 5 h = i ( 7) = 5 Mathletics Instant Wkbooks Series K Copyright P Learning 6

9 Topic 7 - Mied quadratic equations Solve the following quadratic equations by any suitable method. Give your answer crect to one decimal place (where appropriate). a + + b 6 5 c QUESTION d 9 5 e 7 f 6 6 g = 5 h 7 8 i + = j + 8 k 7 = l Solve the following quadratic equations. Give your answer crect to two decimal places. a ( + 5) = ( + ) ( + ) b 8 + = 5 c = 8 + QUESTION d e 7 f g + 9 h + i 8 9 Mathletics Instant Wkbooks Series K Copyright P Learning 7

10 Topic 8 - Using quadratic equations to solve problems QUESTION a In each of the following diagrams, find. All measurements are in centimetres. b ( + ) ( + ) Area = cm + 8 Area = 9 cm QUESTION a Find the number which when added to its square gives twelve. b The area of a rectangle is 5 cm and its length is cm longer than its width. Find the dimensions of the rectangle. QUESTION a When a number is subtracted from its square, the result is 0. Find the possible numbers. b The square of a number is equal to nine times the number. What are the possible numbers? c The sum of the squares of two consecutive positive integers is 5. Find the integers. Mathletics Instant Wkbooks Series K Copyright P Learning 8

11 Topic 9 - Simultaneous equations resulting in a quadratic QUESTION Solve the following simultaneous equations. a + y = b + y = 5 y = y = c y = y = + 0 d y = y = QUESTION + y = 85 Solve the following simultaneous equations. a + y = 7 b + y = + y c y = y = d y = + y = QUESTION a + y = 9 Solve simultaneously. y = 6 c y = y = b + y = 8 y = 6 + d y = y = Mathletics Instant Wkbooks Series K Copyright P Learning 9

12 Topic Test PART A Instructions This part consists of 0 multiple-choice questions Each question is wth mark Attempt ALL questions Calculats are NOT to be used Fill in only ONE CIRCLE f each question Time allowed: 5 minutes Total marks Marks ( )( ) = If + 0 then the values of are A B C D If ( ) then the values of are A B C 0 D 0 If 9 then the solution is A 0 B C ± D 9 If 8 then the solution is A 6 B ± C D 0 5 If ( 5) ( ) then the values of are A 5 B 5 C 5 D 5 6 If 5 then the values of are A ± B ± C ± 9 D ± 9 7 Which is a fact of? A B C + D + ( ) then 8 If y y + P = y + Q A P = 9, Q = B P = 9, Q = C P = 9, Q = D P = 9, Q = 9 Which one of the following is a perfect square f all values of? A + 9 B 9 C + 9 D ( ) ( ) is the same as A + 6 B C D 5 6 Mathletics Instant Wkbooks Series K Copyright P Learning Total marks achieved f PART A 0 0

13 Topic Test Instructions This part consists of 5 questions Each question is wth mark Attempt ALL questions Calculats may be used PART B Time allowed: 0 minutes Total marks = 5 Questions Answers only Marks Solve the following quadratic equations. TOPIC TEST SECTION ( 5) TOPIC TEST SECTION TOPIC TEST SECTION Quadratic ( ) ( 7) equations Instructions ( ) f SECTION You have 5 minutes to answer Section Each question is wth mark Instructions Quadratic ( + 5) f ( Quadratic SECTION ) You Attempt equations have ALL 5 questions minutes to answer Section Each Calculats question are is NOT wth to be mark used Instructions Quadratic 5 f 6 = Quadratic SECTION 0 Attempt Fill You equations in have only ALL 5 ONE questions minutes CIRCLE to answer f each Section question Calculats Each question are is NOT wth to be mark used Fill in only ONE CIRCLE f each question Instructions Attempt ALL questions Quadratic 6 7 f 8Quadratic SECTION You equations have 5 minutes to answer Section Calculats are NOT to be used If ( + ) ( ) then the values Each of question are is wth mark Fill in only ONE CIRCLE f each question Instructions 7 5f SECTION Attempt You have ALL 5 questions minutes to answer Section If A( + ) ( ) then B the values of are C D Calculats Each question are is NOT wth to be mark used Quadratic 8 If A ( 9 ) Quadratic = 50 = then 0 the B values Fill Attempt of equations in only areall ONE questions CIRCLE f each question C D If ( + ) ( ) then the values Calculats of are are NOT to be used Instructions Quadratic 9 If ( f ) Quadratic + = SECTION 7 0 then the values Fill You of equations in have only are 5 ONE minutes CIRCLE 0 to answer f each Section question 0 A B C D If ( If A + ) ( ) then the values Each of question are wth mark Quadratic Instructions B C 0 D 0 0 If What ( 9 must f = Quadratic ) = 0SECTION then the 0 be then added the solution to values Attempt You isequations 6of have to are ALL 5 questions minutes to answer Section A B make it Ca perfect square? D If If ( 0+ ) ( ) then 9 the Calculats then the solution values Each of question are are is NOT wth to be mark used Instructions is ± 9 Quadratic A f B C 0 D 0 Quadratic SECTION Fill You Attempt equations in have only ALL 5 ONE questions minutes CIRCLE to answer f each Section question If Solve ( ) + = 0 then = the 0 by values completing of are A the square. B Each Calculats question are Cis NOT wth to be mark used D If 0 8 If 9 then then the the solution solution Attempt is is ALL questions ± 9 Instructions Solve Athe following f SECTION equations B using Fill You in the have only quadratic 5 ONE minutes C CIRCLE fmula. 0 to answer f each Section question D 0 If ( 6 ) then the 8 values then solution ± Calculats of are are NOT is to be used If A( 0+ ) ( ) then B the values Each of question arec is wth ± mark D 0 9 If 5 Fill in only ONE CIRCLE f each question If 9 then the solution = 0 ) then the Attempt is ALL questions ± values of 0 0 A B C D If ( + ) ( 8 = 0 ) then then 0 A 0 B solution the values Calculats is of are are NOT to be used C ± D = 0 8 then = 0) the solution Fill then the 5 is in only ONE CIRCLE f each question If values of 5 5 ( 6 ) then the values ± of are If A( + ) ( ) then B the values of arec D 0 If 8 = 0 then the solution is 65 0 Find 5 the 5 number 5 which when 5 added to its ± square 05 gives 0. 9 If 0 5 A ( ) = 0 then ) then then B values values the values of of are of are are C D 6 ± 0 If ( + If 5 6 Solve 5 ) ( 8 ± this = 0) then the values of are then the solution 5pair of then simultaneous 5 values ± of is If A ( 9 = ) 0 then then the the solution B values of is equations: are are C ± y = 9 7 D 0 5 ± 9 5 If ( 5) ( ) then the values of are A 6 B ± C + y = 5 D 0 ± ± ± ± If A 9 then the solution B is C 0 D 0 ± 9 5 Which If If A( ( 5 5 is ) ( ) = a 5 fact 0 then of B 5? of are C 5 D 5 then ) the then values the values of are of are If 0 7 Which ± 9= 8 is 0= a fact of ±? ± ± 9 then 0 then the the solution solution is is ± 9 A B C 0 D 0 If 5 5 then the values 5 of are 5 5 A 6 0 ± 0 If 78 Which y is a yfact + P of ( y + Q 8 ± then the B solution ) then ±? is C ± D 9 If 9 then the solution is ± ± 65 If ( 5 )( 9 5 = 0 ) then then values the values of of are are If 6 8 then the solution ± is 0 A 0 8 yp = 9, yq + = P ( y + Q) P then = 9, Q = P = + 9, Q Total = marks achieved P = + 9, Q = f PART B 7 Which 5 ± is a B fact of 5 ±? C ± 5 ± 9 D 9 5 ± 9 5 If A( 6 5) ( ) then B the ± values of are C D 0 9 Which If P = one 8 = 9, Q of 0 = the then following the solution P = is 9, a perfect is Q = Quadratic square equations P f = 9, all Q values = of? 8 y y + P ( y + Q) then P = 9, Q = Which If ( 5 5 Mathletics Instant Wkbooks Series K Copyright P Learning 9 Which ) ( 5 = 0 ) is one + a 9fact then then of of the following values the 5 values is 9? of of are are 5 5 A 6 B ± C D 0 a perfect square f all values + 9 of? P = 9, Q = P = 9, Q = P = 9, Q = P = 9, Q = 8 A 5 y 0 ± y + P ( y + Q) then ( A )( B ) is the Bsame ± C 5 ± + 9 D 5 + ± 9 65 If ( 5 )( 5 = 0 ) then then values the values as 9 Which one of the following is of of are are 9 a perfect square C f all values + 9 of D? If P = 9, 5Q = then the values P ± = ± 9, of Q = are P ± = 9, A 5 B 5 C 5 9 Q = D P 5 = ± 9, 9 Q = TOPIC TEST SECTION TOPIC TEST SECTION Marks TOPIC TEST SECTION Marks TOPIC TEST SECTION TOPIC TEST SECTION Marks Marks TOPIC TEST SECTION Marks 5 Marks Marks Marks Marks

Basic Algebra. Mathletics Instant Workbooks. 7(4x - y) = Copyright

Basic Algebra. Mathletics Instant Workbooks. 7(4x - y) = Copyright Basic Algebra Student Book - Series I- 7(4 - y) = Mathletics Instant Workbooks Copyright Student Book - Series I Contents Topics Topic - Addition and subtraction of like terms Topic 2 - Multiplication