Linear and Non-linear Relationships

Transcription

1 Maths Revision Yr 9 Part.qd:77_pp99_9.qd //8 6:4 PM Page 6 Answers Page a 4 5 = + Linear and Non-linear Relationships = = + a = Student Book - Series J- = = a = = + 4 = = + = Their point of intersetion Their point of intersetion is (, ) is (, ) = 5 = + Page a = = 4 = d = 4 e = 6 f = 6 a = = 8 = 6 d = e = f = a 4 a 5 d 5 6 EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK 4 Mathletis Instant Workooks Copright

2 Student Book - Series J Contents Topis Topi - Tales of values Topi - Graphing linear relationships Topi -Using the interept method to graph lines Topi 4 - Intersetion of two lines Topi 5 - Determining whether or not a point lies on a line Topi 6 - Graphing non-linear relationships Date ompleted Pratie Tests Topi - Topi test A Topi - Topi test B Author of The Topis and Topi Tests: AS Kalra Copright P Learning

3 Topi : Tales of values QUESTION Complete eah tale of values. a = = + = + d = + e = + 5 f = QUESTION Complete eah tale of values. a = p = q = d + 5 q p d d m = n 4 e s = 5t 4 f a = 4 5 n m t s a Copright P Learning

4 Topi : Graphing linear relationships QUESTION Complete the following tales of values and then graph the equation on the numer plane. a = + = = + QUESTION Complete eah tale of values and then graph the equation on the numer plane. a = = = On the same numer plane, graph the following equations first ompleting the tales of values. Find their point of intersetion. QUESTION a = = = + = + Copright P Learning

5 Topi : Using the interept method to graph lines QUESTION Find the -interept for eah equation. a + = = 4 + = 6 d = 8 e = 6 f = QUESTION Find the -interept for eah equation. a = 4 = 8 + = 6 d = e 4 = f = QUESTION Draw the graph of eah equation, given the -interept and the -interept: a -interept =, -interept = -interept =, -interept = QUESTION 4 For eah equation, find the -interept and the -interept and then draw its graph. a = = = d = 4 Copright P Learning

6 Topi 4: Intersetion of two lines QUESTION a = ; = Graph eah pair of lines on the same numer plane and find their point of intersetion. = = = ; = = = QUESTION Graph eah pair of lines on the same numer plane and find their point of intersetion. a = ; = + = = + = ; = = = Copright P Learning 4

7 Topi 5: Determining whether or not a point lies on a line QUESTION Whih of the following points lie on the line + 4 =? a (, ) (, ) ( 4, 6) d (4, ) e (4, ) f (8, ) QUESTION Whih of the following lines pass through the origin, (, )? a + = = 5 = d + = 6 e = f = 5 4 QUESTION Does the given point lie on the given line? a + = (, ) + = (, ) + = 6 (, ) d = 5 (, ) e = + 7 (4, ) f + = 5 (, ) QUESTION 4 A straight line = m + 8 passes through the point (, ). Find the value of m. QUESTION 5 If the point (, 6) is on the line a 4 9 =, what is the value of a? QUESTION 6 Find the missing oordinates to make eah of the following points satisf the equation =. a (, ) (, 4) (, ) d (5, ) e (, 5) f (, 8) Copright P Learning 5

8 Topi 6: Graphing non-linear relationships QUESTION a Complete the tale of values elow for the equation =. Draw the graph of =. What is the onavit of the paraola? _ d What is the verte of the paraola? e Whih ais is the ais of smmetr? f What is the equation of the ais of smmetr? g Does ever have a negative value? h What is the minimum value of? QUESTION a Complete the tale of values elow for the equation = d e f g Draw the graph of = 6 Does the graph ut the -ais? Does the graph ut the -ais? What is the value of when =? What is the value of when =? In whih quadrants do the ranhes of this hperola lie? QUESTION a Complete the tale of values elow for the equation =. Draw the graph of =. What is the value of when = 4 and when = 4? d What happens to the graph = as the value of inreases? e Is there an value of that would make negative? f Where does this graph ut the -ais? Copright P Learning 6

9 Topi Test PART A Time allowed: 5 minutes Total marks = 5 The straight line = passes through one of the following points. Whih one? D (, ) A (, ) B (, ) C (, ) Whih graph est represents =? Marks A B C D The equation of the line l is A = B = C = D = l 4 The graph shown ould e a part of the graph with equation A = B = C = D = 5 Whih of the following ould e the equation of the graph? A = B = C = D = 4 6 The graph of = lies entirel in A quadrant I B quadrants I & II C quadrants I & III 7 Whih of the following ould e the equation of the graph? A = B = C = D = 8 The equation of the line l is D quadrants I & IV A + 6 = B + 6 = C + 6 = 9 The equation of a linear graph with -interept 8 and gradient is A = + 8 B = 8 C = 8 D = + 8 The line = has gradient gradient gradient -interept -interept -interept A gradient -interept B C D The point (5, ) lies on whih line? A = 5 B 5 4 = 5 C 4 5 = 5 Whih one of the following points lies on the line = 4? A (, 4) B (, ) C (, 6) For the equation + = 4, find the -interept. A (4, ) B (, 4) C (, ) 4 For the equation = 6, find the -interept. D + 6 = D = 5 D (, ) D (, ) A (, ) B (, ) C (, ) D (, ) 5 The oordinates of the point of intersetion of the lines = and = 5 are A (5, ) B (5, ) C (, 5) D (, 5) l Copright P Learning Total marks ahieved for PART A 5 7

10 Topi Test PART B Time allowed: 5 minutes Total marks = 5 Question Math eah equation with a tale of values. Marks a 5 4 d e i = ii = iii = iv = 5 v = + 4 Question a On the same numer plane, draw the graphs of the following lines. i = ii = iii = iv = Write the oordinates of the point of intersetion of the lines = and =. What kind of shape is formed? d Find its perimeter. e Find its area. Question a Cop and omplete the tale of values elow for the equation =. Draw the graph of =. What is the value of when =? d Is there an value of that would make negative? e Where does this graph ut the -ais? Copright P Learning Total marks ahieved for PART B 5 8