hsn.uk.net Page Circles Paper1SectionA Each correct answer in this section is worth two marks.
|
|
|
- Mitchell Higgins
- 6 years ago
- Views:
Transcription
1 2.4 Circles Paper1SectionA Each correct answer in this section is worth two marks. 1.Thepoint (2, 3)liesonthecircle with equation x 2 +y 2 +6x 2y +c =0. Whatisthevalueofc? A. 31 B. 13 C The point P(2, 3) lies on the circle with centre C as shown.the gradient of CP is 2.What is the equation of thetangentatp? C y O P(2, 3) x D. 9 A. y +3 = 2(x 2) B. y 3 = 2(x +2) C. y +3 = 1 2 (x 2) D. y 3 = 1 2 (x +2) 2.Acirclehascentre (2,4)andpasses through ( 1, 1). Whatistheequationofthecircle? A. (x 2) 2 + (y 4) 2 = 18 4.ThepointP( 2,4)liesonthecircle with equation x 2 +y 2 2x +2y 32 =0. Whatisthegradientofthetangent tothecircleatp? A. 1 3 B. (x 2) 2 + (y 4) 2 =18 C. (x +2) 2 + (y +4) 2 =18 D. (x +2) 2 + (y +4) 2 =26 hsn.uk.net Page 1 B. 3 5 C. 1 D. 3 Questions marked c SQA
2 5.Acirclehasequation (x +1) 2 + (y 2) 2 =29. Whatisthegradientofthetangent tothecircleatthepoint (1, 3)? A. 2 5 B. 0 C. 5 2 D Acirclehasequation x 2 +y 2 2x 4y +1 =0. Here are two statements about the circle: I.Thecirclehascentre ( 2, 4). II.Thecirclehasradius1. Which of the following is true? A. neither statement is correct B. only statement I is correct C. only statement II is correct D. both statements are correct 6.Thelinewithequationy =2x intersects the circle with equation x 2 +y 2 =5atthepointsJandK. Whatarethex-coordinatesofJand K? A. x J =1,x K = 1 B. x J =2,x K = 2 C. x J =1,x K = 2 D. x J = 1,x K =2 7.Acirclehasequation x 2 +y 2 +8x +6y 75 =0. Whatistheradiusofthecircle? A. 5 B Acirclehasequation x 2 +y 2 4x +6y +4 =0. Here are two statements about the circle: I.Thecirclehascentre ( 2,3). II.Thecirclehasradius3units. Which of the following is true? A. neither statement is correct B. only statement I is correct C. 75 C. only statement II is correct D. 175 hsn.uk.net Page 2 D. both statements are correct Questions marked c SQA
3 10. A circle has equation x 2 +y 2 ax +2by +c =0.The centreofthecircleis ( 1,4). Whatarethevaluesofaandb? a b A. 2 4 B. 1 2 C. 2 4 D A circle has equation (x 3) 2 + (y +4) 2 =20. Findthegradientofthetangentto thecircleatthepoint (1,0). A. 2 B. 1 2 C Theequationofthecircleshownin the diagram is x 2 +y 2 6x 10y +9 =0.The x-axisandthelinelareparallel tangents to the circle. y O Whatistheequationoflinel? A. y =5 B. y =10 C. y =18 D. y =20 l x D Acirclehascentre (2, 1),andhas they-axisasatangent. Whatistheequationofthecircle? A. (x +2) 2 + (y 1) 2 =4 B. (x 2) 2 + (y +1) 2 =4 C. (x +2) 2 + (y 1) 2 =1 D. (x 2) 2 + (y +1) 2 =1 14.Whatisthelargestrangeofvalues ofkforwhichtheequation x 2 +y 2 6x +4y +k =0represents acircle? A. k <52 B. k <13 C. k > 13 D. Allrealk hsn.uk.net Page 3 Questions marked c SQA
4 [ENDOFPAPER1SECTIONA] Paper1SectionB 15. The diagram below shows the graph of the cubic with equation y =x 3 3x 2 +5x +4andacirclewith centre C. AtthepointPthelinelisatangentto boththecurveandthecircle. (a)thetangentline l hasgradient 2. Find the coordinates of P. Q 5 (b) The circle has equation l O x x 2 +y 2 14x 8y +c =0. 2 Determine the value of c. (c)the line PQ is a diameter of the circle. Determine the coordinates ofq. 2 y y =x 3 3x 2 +5x +4 P C 16.Acirclehasequationx 2 +y 2 ax +2by +c =0,wherea,bandcareconstants. (a)giventhatthecentreofthecircleis ( 1,4),determinethevaluesofaandb. 2 (b)giventhatthepoint (5,4)liesonthecircle,determinethevalueofc AcirclehasP(0,1)andQ( 10,9)asendpointsofitsdiameter. Find the equation of this circle Findtheequationofthecirclecentredat (1, 3)andpassingthrough (7,5). Determine whether or not the point (8, 4) lies within this circle CirclePhasequationx 2 +y 2 8x 10y +9 =0. CircleQhascentre ( 2, 1) andradius2 2. (a) (i)showthattheradiusofcirclepis4 2. (ii)henceshowthatcirclespandqtouch. 4 (b)findtheequationofthetangenttothecircleqatthepoint ( 4,1). 3 (c)thetangentin(b)intersectscirclepintwopoints.findthex-coordinatesof thepointsofintersection,expressingyouanswersintheforma ±b 3. 3 hsn.uk.net Page 4 Questions marked c SQA
5 20. ThepointP(2,3)liesonthecircle (x +1) 2 + (y 1) 2 =13.Findtheequationof thetangentatp Acirclehasequationx 2 +y 2 8x +6y +15 =0. FindtheequationofthetangenttothecircleatthepointA(1, 2) (a)find the equation of the line which passes through ( 1, 4) and is perpendiculartothelinewithequationx +3y =2. 3 (b)showthatthelinedoesnotintersectthecirclewithequation (x 2) 2 + (y +3) 2 = Forwhichvaluesofkisthelinewithequationy= 3 4 x +katangenttothecircle withequationx 2 +y 2 =16? The points A and B have coordinates (6, 8) and (18, 8) respectively. (a)findtheequationofl,theperpendicularbisectorofab. 4 (b)showthatlisatangenttothecirclewithequationx 2 +y 2 2x +4y 20 =0 and find the coordinates of the point of contact Forwhichvaluesofkdoestheequationx 2 +y 2 +10x 14y +k =0representa circle? 3 26.Findtherangeofvaluesofkforwhichtheequationx 2 +y 2 kx (k+1)y+ 5 4 =0 represents a circle Forwhatrangeofvaluesofkdoestheequationx 2 +y 2 +4kx 2ky k 2 =0 represent a circle? 5 28.Thecirclewithcentre (8,a)passesthroughthepoints (3,3)and (5,1). Findthevalueofaandhencefindtheequationofthecircle. 5 hsn.uk.net Page 5 Questions marked c SQA
6 29. (a)findtheradiusandequationofthecirclecentredattheoriginandpassing through the point (3, 4). 2 (b) Determine whether the point (8, 5) lies inside, outside or on this circle Findtherangeofvaluesofkforwhich2x 2 +2y 2 6x +4y +k =0representsa circle. 4 [ENDOFPAPER1SECTIONB] hsn.uk.net Page 6 Questions marked c SQA
7 Paper 2 1. Find the equation of the tangent at the point (3, 4) on the circle x 2 +y 2 +2x 4y 15 = Triangle ABC has vertices A(2, 2), B(12, 2) and C(8, 6). (a)writedowntheequationofl 1, the perpendicular bisector of AB. 1 A(2, 2) B(12, 2) (b)find the equation of l 2, the perpendicular bisector of AC. O x 4 (c) Find the point of intersection of linesl 1 andl 2. 1 (d)hencefindtheequationofthe circle passing through A, B and C. 2 y C(8, 6) 3. (a) Find the equation of AB, the perpendicular bisector of the line y Q(1, 9) joing the points P( 3,1) and Q(1,9). A 4 (b)cisthecentreofacirclepassing throughpandq.giventhatqcis parallel to the y-axis, determine the C equation of the circle. 3 (c)thetangentsatpandqintersectat T. Write down (i)theequationofthetangentatq P( 3, 1) (ii) the coordinates of T. 2 O B x hsn.uk.net Page 7 Questions marked c SQA
8 4. 5. FindtheequationofthecirclewhichhasP( 2, 1)andQ(4,5)astheendpoints of a diameter Theliney = 1isatangenttoacirclewhichpassesthrough (0,0)and (6,0). Find the equation of this circle hsn.uk.net Page 8 Questions marked c SQA
9 8. 9. hsn.uk.net Page 9 Questions marked c SQA
10 Thecirclewithequationx 2 +y 2 10x +9 =0isshownbelow. y x 2 +y 2 10x +9 =0 O A x ThepointAliesonthecircumferenceofthecircleandthex-axis. FindtheequationofthetangenttothecircleatA. 5 hsn.uk.net Page 10 Questions marked c SQA
11 13. Find the equation of the tangent at the point (3, 1) on the circle x 2 +y 2 4x +6y 4 = Agardenisbeingdesignedsothattherearethree areas for planting around a triangular decked area. A diagram of the garden, relative to a set of coordinate axes is shown to the right. The points P, Q and R lie on the circle with equation x 2 +y 2 = 4. The triangle PQR is equilateral, and the line PR is parallel to the x-axis. (a)findtheequationofthelinethroughpand Q. 4 (b) (i)findthecoordinatesofthepointp. (ii) Hence calculate the shaded area. 7 P y O Q x 2 +y 2 =4 R x 16.Thelinewithequationy +x =5meetsthecirclewithequation x 2 +y 2 8x +2y 3 =0atthepointsPandQ. (a)findthecoordinatesofpandq. 4 (b)findtheequationofthecirclewhichhaspqasitsdiameter. 3 hsn.uk.net Page 11 Questions marked c SQA
12 Thecirclewithequation (x 8) 2 + (y 4) 2 =16 isshowninthediagram. ThelineOAisanon-horizontaltangenttothe circle. (a)giventhatoahasgradientm,writedown the equation of OA. 1 (b) Hence or otherwise determine the value O ofm. x 7 y A hsn.uk.net Page 12 Questions marked c SQA
13 19. (a) (i)showthatthelinewithequationy=3 xisatangenttothecirclewith equationx 2 +y 2 +14x +4y 19 =0. (ii) Find the coordinates of the points of contact, P. 5 (b)relativetoasuitablesetofcoordinateaxes,thediagrambelowshowsthe circlefrom(a)andasecondsmallercirclewithcentrec. P C Theliney =3 xisacommontangentatthepointp. Theradiusofthelargercircleisthreetimestheradiusofthesmallercircle. Find the equation of the smaller circle Findthevaluesofkforwhichthelinex +y =kisatangenttothe circlex 2 +y 2 4x +2 = Findthepossiblevaluesofkforwhichthelinex y =kisatangenttothecircle x 2 +y 2 =18. 5 hsn.uk.net Page 13 Questions marked c SQA
14 22.The larger circle shown in the diagram has equation y B x 2 +y 2 10x 4y +12 =0. Thesmallercirclehascentre (10, 13 4 )andradius Thelinethrough AandBpassesthrough the centre of both circles. Point A has coordinates (1, 1). (a) Show that the circles touch externally. 4 (b) (i)findtheequationofthetangenttothelargercircleata. (ii)hencestatethegradientofthetangenttothesmallercircleatb. 4 O A x 23. (a)showthatthepointp(5,10)liesoncirclec 1 withequation (x +1) 2 + (y 2) 2 = (b)pqisadiameterofthiscircleas y showninthediagram. Findthe equationofthetangentatq. P(5, 10) 5 O x Q (c)twocircles,c 2 andc 3,touchcircleC 1 atq. TheradiusofeachofthesecirclesistwicetheradiusofcircleC 1. FindtheequationsofcirclesC 2 andc hsn.uk.net Page 14 Questions marked c SQA
15 25. Explainwhytheequationx 2 +y 2 +2x +3y +5 =0doesnotrepresentacircle Forwhatrangeofvaluesofcdoestheequationx 2 +y 2 6x +4y+c =0represent acircle? hsn.uk.net Page 15 Questions marked c SQA
16 hsn.uk.net Page 16 Questions marked c SQA
17 hsn.uk.net Page 17 Questions marked c SQA
18 33. hsn.uk.net Page 18 Questions marked c SQA
19 34.Showthattheequationx 2 +y 2 +kx 4y 2 =0representsacircleforallvalues ofk CircleC 1 hasequation (x +1) 2 + (y 1) 2 =121. AcircleC 2 withequationx 2 +y 2 4x +6y +p =0isdrawninsideC 1. The circles have no points of contact. Whatistherangeofvaluesofp? 9 [ENDOFPAPER2] hsn.uk.net Page 19 Questions marked c SQA
Circle. Paper 1 Section A. Each correct answer in this section is worth two marks. 5. A circle has equation. 4. The point P( 2, 4) lies on the circle
PSf Circle Paper 1 Section A Each correct answer in this section is worth two marks. 1. A circle has equation ( 3) 2 + ( + 4) 2 = 20. Find the gradient of the tangent to the circle at the point (1, 0).
Circles. hsn.uk.net. Contents. Circles 1
hsn.uk.net Circles Contents Circles 1 1 Representing a Circle A 1 Testing a Point A 3 The General Equation of a Circle A 4 Intersection of a Line and a Circle A 4 5 Tangents to Circles A 5 6 Equations
hsn.uk.net Page 1 Circle Find the equation of the tangent at the point (3, 4) on the circle x 2 +y 2 +2x 4y 15 =0. 4 Higher Mathematics
Circle 1. Find the equation of the tangent at the point (3, 4) on the circle x 2 +y 2 +2x 4y 15 =0. 4 4 C CN G2,G5,G9 1996P1Q4 hsn.uk.net Page 1 2. (a) Find the equation of AB, the perpendicular bisector
NAME: Date: HOMEWORK: C1. Question Obtained. Total/100 A 80 B 70 C 60 D 50 E 40 U 39
NAME: Date: HOMEWORK: C1 Question Obtained 1 2 3 4 5 6 7 8 9 10 Total/100 A 80 B 70 C 60 D 50 E 40 U 39 1. Figure 2 y A(1, 7) B(20, 7) D(8, 2) O x C(p, q) The points A(1, 7), B(20, 7) and C(p, q) form
y hsn.uk.net Straight Line Paper 1 Section A Each correct answer in this section is worth two marks.
Straight Line Paper 1 Section Each correct answer in this section is worth two marks. 1. The line with equation = a + 4 is perpendicular to the line with equation 3 + + 1 = 0. What is the value of a?.
5 Find an equation of the circle in which AB is a diameter in each case. a A (1, 2) B (3, 2) b A ( 7, 2) B (1, 8) c A (1, 1) B (4, 0)
C2 CRDINATE GEMETRY Worksheet A 1 Write down an equation of the circle with the given centre and radius in each case. a centre (0, 0) radius 5 b centre (1, 3) radius 2 c centre (4, 6) radius 1 1 d centre
Circles, Mixed Exercise 6
Circles, Mixed Exercise 6 a QR is the diameter of the circle so the centre, C, is the midpoint of QR ( 5) 0 Midpoint = +, + = (, 6) C(, 6) b Radius = of diameter = of QR = of ( x x ) + ( y y ) = of ( 5
Edexcel New GCE A Level Maths workbook Circle.
Edexcel New GCE A Level Maths workbook Circle. Edited by: K V Kumaran kumarmaths.weebly.com 1 Finding the Midpoint of a Line To work out the midpoint of line we need to find the halfway point Midpoint
Recurrence Relations. Each correct answer in this section is worth two marks.
Recurrence Relations Paper1SectionA Each correct answer in this section is worth two marks. 1.Asequenceisdefinedbytherecurrencerelationu n+1 =2u n +3andu 0 =1. Whatisthevalueofu 2? A. 7 B. 10 C. 13 D.
1.4 Recurrence Relations
Paper1SectionA 1.4 Recurrence Relations Each correct answer in this section is worth two marks. 1.Asequenceisdefinedbytherecurrencerelationu n+1 =au n +b,whereaandb are constants. Giventhatu 0 =4andu 1
Integration Past Papers Unit 2 Outcome 2
Integration Past Papers Unit 2 utcome 2 Multiple Choice Questions Each correct answer in this section is worth two marks.. Evaluate A. 2 B. 7 6 C. 2 D. 2 4 /2 d. 2. The diagram shows the area bounded b
Additional Mathematics Lines and circles
Additional Mathematics Lines and circles Topic assessment 1 The points A and B have coordinates ( ) and (4 respectively. Calculate (i) The gradient of the line AB [1] The length of the line AB [] (iii)
Vectors. Paper 1 Section A. Each correct answer in this section is worth two marks. 4. The point B has coordinates
PSf Vectors Paper Section A Each correct answer in this section is worth two marks.. A vector v is given b 2. 6 What is the length, in units, of v? A. 7 B. 5. 2 D. 49 4. The point B has coordinates (,
DISCRIMINANT EXAM QUESTIONS
DISCRIMINANT EXAM QUESTIONS Question 1 (**) Show by using the discriminant that the graph of the curve with equation y = x 4x + 10, does not cross the x axis. proof Question (**) Show that the quadratic
Core Mathematics 2 Coordinate Geometry
Core Mathematics 2 Coordinate Geometry Edited by: K V Kumaran Email: kvkumaran@gmail.com Core Mathematics 2 Coordinate Geometry 1 Coordinate geometry in the (x, y) plane Coordinate geometry of the circle
Prelim practice. Part Marks Level Calc. Content Answer U1 OC1 3 C CR G2 1992P1Q13
Prelim practice 1. Part Marks Level Calc. Content Answer U1 OC1 3 C CR G2 1992P1Q13 2. Find the equation of the perpendicular bisector of the line joining A(2, 1) and B(8,3). 4 Part Marks Level Calc. Content
1 k. cos tan? Higher Maths Non Calculator Practice Practice Paper A. 1. A sequence is defined by the recurrence relation u 2u 1, u 3.
Higher Maths Non Calculator Practice Practice Paper A. A sequence is defined b the recurrence relation u u, u. n n What is the value of u?. The line with equation k 9 is parallel to the line with gradient
National Quali cations
H 2018 X747/76/11 National Quali cations Mathematics Paper 1 (Non-Calculator) THURSDAY, 3 MAY 9:00 AM 10:10 AM Total marks 60 Attempt ALL questions. You may NOT use a calculator. Full credit will be given
The gradient of the radius from the centre of the circle ( 1, 6) to (2, 3) is: ( 6)
Circles 6E a (x + ) + (y + 6) = r, (, ) Substitute x = and y = into the equation (x + ) + (y + 6) = r + + + 6 = r ( ) ( ) 9 + 8 = r r = 90 = 0 b The line has equation x + y = 0 y = x + y = x + The gradient
S56 (5.3) Recurrence Relations.notebook September 09, 2015
Daily Practice 31.8.2015 Q1. Write down the equation of a circle with centre (-1, 4) and radius 5 Q2. Given the circle with equation (x 4) 2 + (y + 5) 2 = 40. Find the equation of the tangent to this circle
3.1 Vectors. Each correct answer in this section is worth two marks.
3.1 Vectors Paper1SectionA Each correct answer in this section is worth two marks. 3 1.Avectorvisgivenby 2. 6 Whatisthelength,inunits,of3v? A. 7 B. 15 C. 21 D. 49 Key Outcome Grade Facility Disc. Calculator
Exam Revision. y B A E. Find the coordinates of E, the point of intersection of the diagonals. 3
Eam Revision 1. quadrilateral has vertices ( 1, 8), B(7, 12), C(8, 5) and D(2, 3) as shown in the diagram. y B E C O D (a) Find the equation of diagonal BD. 2 (b)theequationofdiagonalcis +3y =23. Find
CBSE X Mathematics 2012 Solution (SET 1) Section B
CBSE X Mathematics 01 Solution (SET 1) Section B Q11. Find the value(s) of k so that the quadratic equation x kx + k = 0 has equal roots. Given equation is x kx k 0 For the given equation to have equal
National Quali cations
H 2017 X747/76/11 FRIDAY, 5 MAY 9:00 AM 10:10 AM National Quali cations Mathematics Paper 1 (Non-Calculator) Total marks 60 Attempt ALL questions. You may NOT use a calculator. Full credit will be given
Recognise the Equation of a Circle. Solve Problems about Circles Centred at O. Co-Ordinate Geometry of the Circle - Outcomes
1 Co-Ordinate Geometry of the Circle - Outcomes Recognise the equation of a circle. Solve problems about circles centred at the origin. Solve problems about circles not centred at the origin. Determine
Ch 10 Review. Multiple Choice Identify the choice that best completes the statement or answers the question.
Ch 10 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In the diagram shown, the measure of ADC is a. 55 b. 70 c. 90 d. 180 2. What is the measure
Review exercise 2. 1 The equation of the line is: = 5 a The gradient of l1 is 3. y y x x. So the gradient of l2 is. The equation of line l2 is: y =
Review exercise The equation of the line is: y y x x y y x x y 8 x+ 6 8 + y 8 x+ 6 y x x + y 0 y ( ) ( x 9) y+ ( x 9) y+ x 9 x y 0 a, b, c Using points A and B: y y x x y y x x y x 0 k 0 y x k ky k x a
Old Past Papers- Differentiation. Part Marks Level Calc. Content Answer U1 OC3 4 C NC G2,C4 (2,4) 2002P1Q4. 1 dy dx
Old Past Papers- Differentiation 1. Findthecoordinatesofthepointonthecurve=2 2 7 +10wherethetangent tothecurvemakesanangleof45 withthepositivedirectionofthe-ais. 4 4 C NC G2,C4 (2,4) 2002P1Q4 1 sp: knowtodiff.,anddifferentiate
Higher Mathematics. Exam Revision. Questions marked [SQA] c SQA All others c Higher Still Notes. hsn.uk.net Page 1
![Higher Mathematics. Exam Revision. Questions marked [SQA] c SQA All others c Higher Still Notes. hsn.uk.net Page 1](/thumbs/87/95881312.jpg "Higher Mathematics. Exam Revision. Questions marked [SQA] c SQA All others c Higher Still Notes. hsn.uk.net Page 1")
Exam Revision hsn.uk.net Page 1 1. A quadrilateral has vertices A( 1, 8), B(7, 12), C(8, 5) and D(2, 3) as shown in the diagram. y B A E C O x D (a) Find the equation of diagonal BD. 2 (b)theequationofdiagonalacisx
National Quali cations
H 08 X747/76/ National Quali cations Mathematics Paper (Non-Calculator) THURSDAY, MAY 9:00 AM 0:0 AM Total marks 60 Attempt ALL questions. You may NOT use a calculator. Full credit will be given only to
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca Euclid Contest. Wednesday, April 15, 2015
The CENTRE for EDUCATION in MATHEMATICS and COMPUTING cemc.uwaterloo.ca 015 Euclid Contest Wednesday, April 15, 015 (in North America and South America) Thursday, April 16, 015 (outside of North America
Circles - Edexcel Past Exam Questions. (a) the coordinates of A, (b) the radius of C,
- Edecel Past Eam Questions 1. The circle C, with centre at the point A, has equation 2 + 2 10 + 9 = 0. Find (a) the coordinates of A, (b) the radius of C, (2) (2) (c) the coordinates of the points at
CIRCLES, CHORDS AND TANGENTS
NAME SCHOOL INDEX NUMBER DATE CIRCLES, CHORDS AND TANGENTS KCSE 1989 2012 Form 3 Mathematics Working Space 1. 1989 Q24 P2 The figure below represents the cross section of a metal bar. C A 4cm M 4cm B The
2. (i) Find the equation of the circle which passes through ( 7, 1) and has centre ( 4, 3).
Circle 1. (i) Find the equation of the circle with centre ( 7, 3) and of radius 10. (ii) Find the centre of the circle 2x 2 + 2y 2 + 6x + 8y 1 = 0 (iii) What is the radius of the circle 3x 2 + 3y 2 + 5x
chapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?
chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "
DEPARTMENT OF MATHEMATICS
DEPARTMENT OF MATHEMATICS AS level Mathematics Core mathematics 1 C1 2015-2016 Name: Page C1 workbook contents Indices and Surds Simultaneous equations Quadratics Inequalities Graphs Arithmetic series
PhysicsAndMathsTutor.com
1. The diagram above shows the sector OA of a circle with centre O, radius 9 cm and angle 0.7 radians. Find the length of the arc A. Find the area of the sector OA. The line AC shown in the diagram above
Edexcel New GCE A Level Maths workbook
Edexcel New GCE A Level Maths workbook Straight line graphs Parallel and Perpendicular lines. Edited by: K V Kumaran kumarmaths.weebly.com Straight line graphs A LEVEL LINKS Scheme of work: a. Straight-line
Sample Paper from Solomon Press Time: 1 hour 30 minutes
FOR EDEXCEL GCE Examinations Advanced Subsidiary Core Mathematics C2 Sample Paper from Solomon Press Time: 1 hour 30 minutes Instructions and Information Candidates may use any calculator EXCEPT those
Preliminary Mathematics
NORTH SYDNEY GIRLS HIGH SCHOOL 2011 YEARLY EXAMINATION Preliminary Mathematics General Instructions Reading Time 5 minutes Working Time 2 hours Write using black or blue pen Board-approved calculators
Higher Mathematics 2009 v C8,C9 cn
Higher Mathematics 009 v10 qu Mk Code cal Source ss pd ic C B A U1 U U3.01.01 8 C8,C9 cn 08507 3 4 1 8 8 Find the coordinates of the turning points of the curve with equation y = x 3 3x 9x + 1 and determine
*X100/301* X100/301 MATHEMATICS HIGHER. Units 1, 2 and 3 Paper 1 (Non-calculator) Read Carefully
X00/0 NATINAL QUALIFICATINS 007 TUESDAY, 5 MAY 9.00 AM 0.0 AM MATHEMATICS HIGHER Units, and Paper (Non-calculator) Read Carefull Calculators ma NT be used in this paper. Full credit will be given onl where
Q1. If (1, 2) lies on the circle. x 2 + y 2 + 2gx + 2fy + c = 0. which is concentric with the circle x 2 + y 2 +4x + 2y 5 = 0 then c =
Q1. If (1, 2) lies on the circle x 2 + y 2 + 2gx + 2fy + c = 0 which is concentric with the circle x 2 + y 2 +4x + 2y 5 = 0 then c = a) 11 b) -13 c) 24 d) 100 Solution: Any circle concentric with x 2 +
SYSTEM OF CIRCLES OBJECTIVES (a) Touch each other internally (b) Touch each other externally
SYSTEM OF CIRCLES OBJECTIVES. A circle passes through (0, 0) and (, 0) and touches the circle x + y = 9, then the centre of circle is (a) (c) 3,, (b) (d) 3,, ±. The equation of the circle having its centre
WEDNESDAY, 18 MAY 9.00 AM AM. 1 Full credit will be given only where the solution contains appropriate working.
X00/0 NATINAL QUALIFICATINS 0 WEDNESDAY, 8 MAY 9.00 AM 0.0 AM MATHEMATICS HIGHER Paper (Non-calculator) Read carefull Calculators ma NT be used in this paper. Section A Questions 0 (40 marks) Instructions
1. Number a. Using a calculator or otherwise 1 3 1 5 i. 3 1 4 18 5 ii. 0.1014 5.47 1.5 5.47 0.6 5.1 b. Bus tour tickets . Algebra a. Write as a single fraction 3 4 11 3 4 1 b. 1 5 c. Factorize completely
WEDNESDAY, 20 MAY 9.00 AM AM
X00// NATIONAL QUALIFIATIONS 05 WENESAY, 0 MAY 9.00 AM 0.0 AM MATHEMATIS HIGHER Paper (Non-calculator) Read carefully alculators may NOT be used in this paper. Section A Questions 0 (0 marks) Instructions
SYSTEM OF CIRCLES If d is the distance between the centers of two intersecting circles with radii r 1, r 2 and θ is the
SYSTEM OF CIRCLES Theorem: If d is the distance between the centers of two intersecting circles with radii r 1, r 2 and θ is the 2 2 2 d r1 r2 angle between the circles then cos θ =. 2r r 1 2 Proof: Let
Pure Mathematics Year 1 (AS) Unit Test 1: Algebra and Functions
Pure Mathematics Year (AS) Unit Test : Algebra and Functions Simplify 6 4, giving your answer in the form p 8 q, where p and q are positive rational numbers. f( x) x ( k 8) x (8k ) a Find the discriminant
Created by T. Madas VECTOR PRACTICE Part B Created by T. Madas
VECTOR PRACTICE Part B THE CROSS PRODUCT Question 1 Find in each of the following cases a) a = 2i + 5j + k and b = 3i j b) a = i + 2j + k and b = 3i j k c) a = 3i j 2k and b = i + 3j + k d) a = 7i + j
CBSE Class IX Mathematics Term 1. Time: 3 hours Total Marks: 90. Section A
CBSE sample papers, Question papers, Notes for Class 6 to 1 CBSE Class IX Mathematics Term 1 Time: 3 hours Total Marks: 90 General Instructions: 1. All questions are compulsory.. The question paper consists
Paper collated from year 2007 Content Pure Chapters 1-13 Marks 100 Time 2 hours
1. Paper collated from year 2007 Content Pure Chapters 1-13 Marks 100 Time 2 hours 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Mark scheme Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question
QUESTION BANK ON STRAIGHT LINE AND CIRCLE
QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,
1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM.
1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM. 2. Let ABCD be a cyclic quadrilateral inscribed in a circle
Add Math (4047/02) Year t years $P
Add Math (4047/0) Requirement : Answer all questions Total marks : 100 Duration : hour 30 minutes 1. The price, $P, of a company share on 1 st January has been increasing each year from 1995 to 015. The
Sample Aptitude Test Questions
Sample Aptitude Test Questions 1. (a) Prove, by completing the square, that the roots of the equation x 2 + 2kx + c = 0, where k and c are constants, are k ± (k 2 c). The equation x 2 + 2kx ± 81 = 0 has
DEPARTMENT OF MATHEMATICS
DEPARTMENT OF MATHEMATICS AS level Mathematics Core mathematics 2 - C2 2015-2016 Name: Page C2 workbook contents Algebra Differentiation Integration Coordinate Geometry Logarithms Geometric series Series
the coordinates of C (3) Find the size of the angle ACB. Give your answer in degrees to 2 decimal places. (4)
. The line l has equation, 2 4 3 2 + = λ r where λ is a scalar parameter. The line l 2 has equation, 2 0 5 3 9 0 + = µ r where μ is a scalar parameter. Given that l and l 2 meet at the point C, find the
Cambridge International Examinations Cambridge Ordinary Level
Cambridge International Examinations Cambridge Ordinary Level * 9 4 5 1 6 2 0 9 2 4 * ADDITIONAL MATHEMATICS 4037/12 Paper 1 October/November 2015 2 hours Candidates answer on the Question Paper. No Additional
e x for x 0. Find the coordinates of the point of inflexion and justify that it is a point of inflexion. (Total 7 marks)
Chapter 0 Application of differential calculus 014 GDC required 1. Consider the curve with equation f () = e for 0. Find the coordinates of the point of infleion and justify that it is a point of infleion.
Mathematics Extension 1
NSW Education Standards Authority 08 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Extension General Instructions Reading time 5 minutes Working time hours Write using black pen Calculators approved
Calculus With Analytic Geometry by SM. Yusaf & Prof.Muhammad Amin
The Sphere Definition: The set of all points in space that are equidistant from a fixed point is called a sphere. The constant distance is called the radius of the sphere and the fixed point is called
Christmas Calculated Colouring - C1
Christmas Calculated Colouring - C Tom Bennison December 20, 205 Introduction Each question identifies a region or regions on the picture Work out the answer and use the key to work out which colour to
Equation of a Straight Line (H)
Equation of a Straight Line (H) A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. Name: Total Marks: 1. The line L1 is shown in the diagram below.
NATIONAL QUALIFICATIONS
H Mathematics Higher Paper Practice Paper A Time allowed hour minutes NATIONAL QUALIFICATIONS Read carefull Calculators ma NOT be used in this paper. Section A Questions ( marks) Instructions for completion
P1 Chapter 6 :: Circles
P1 Chapter 6 :: Circles jfrost@tiffin.kingston.sch.uk www.drfrostmaths.com @DrFrostMaths Last modified: 11 th August 2017 Use of DrFrostMaths for practice Register for free at: www.drfrostmaths.com/homework
2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB.
2009 FGCU Mathematics Competition. Geometry Individual Test 1. You want to prove that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex. Which postulate/theorem
KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION
KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 04 (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS X Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks) LA (4 marks) Total Unit
SOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c)
![SOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c)](/thumbs/79/80187791.jpg "SOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c)")
1. (A) 1 1 1 11 1 + 6 6 5 30 5 5 5 5 6 = 6 6 SOLUTIONS SECTION A. (B) Let the angles be x and 3x respectively x+3x = 180 o (sum of angles on same side of transversal is 180 o ) x=36 0 So, larger angle=3x
Math : Analytic Geometry
7 EP-Program - Strisuksa School - Roi-et Math : Analytic Geometry Dr.Wattana Toutip - Department of Mathematics Khon Kaen University 00 :Wattana Toutip wattou@kku.ac.th http://home.kku.ac.th/wattou 7 Analytic
Differentiation Past Papers Unit 1 Outcome 3
PSf Differentiation Past Papers Unit 1 utcome 3 1. Differentiate 2 3 with respect to. A. 6 B. 3 2 3 4 C. 4 3 3 2 D. 2 3 3 2 2 2. Given f () = 3 2 (2 1), find f ( 1). 3 3. Find the coordinates of the point
St Andrew s Academy Mathematics Department Higher Mathematics VECTORS
St Andrew s Academy Mathematics Department Higher Mathematics VECTORS hsn.uk.net Higher Mathematics Vectors Contents Vectors 1 1 Vectors and Scalars EF 1 Components EF 1 Magnitude EF 4 Equal Vectors EF
Right Triangles
30 60 90 Right Triangles The 30-60 -90 triangle is another special triangle. Like the 45-45 -90 triangle, properties of the 30-60 -90 triangle can be used to find missing measures of a triangle if the
Higher Mathematics Course Notes
Higher Mathematics Course Notes Equation of a Line (i) Collinearity: (ii) Gradient: If points are collinear then they lie on the same straight line. i.e. to show that A, B and C are collinear, show that
2016 SEC 4 ADDITIONAL MATHEMATICS CW & HW
FEB EXAM 06 SEC 4 ADDITIONAL MATHEMATICS CW & HW Find the values of k for which the line y 6 is a tangent to the curve k 7 y. Find also the coordinates of the point at which this tangent touches the curve.
Cambridge International Examinations Cambridge Ordinary Level
Cambridge International Examinations Cambridge Ordinary Level *8790810596* ADDITIONAL MATHEMATICS 4037/13 Paper 1 October/November 2017 2 hours Candidates answer on the Question Paper. No Additional Materials
(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2
CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5
H I G H E R M A T H S. Practice Unit Tests (2010 on) Higher Still Higher Mathematics M A T H E M A T I C S. Contents & Information
M A T H E M A T I C S H I G H E R Higher Still Higher Mathematics M A T H S Practice Unit Tests (00 on) Contents & Information 9 Practice NABS... ( for each unit) Answers New format as per recent SQA changes
Question 1 ( 1.0 marks) places of decimals? Solution: Now, on dividing by 2, we obtain =
Question 1 ( 1.0 marks) The decimal expansion of the rational number places of decimals? will terminate after how many The given expression i.e., can be rewritten as Now, on dividing 0.043 by 2, we obtain
Old Past Papers- Polynomials
Old Past Papers- Polnomials 1. (a) Expressf(x) =x 2 4x +5intheformf(x) = (x a) 2 +b. 2 (b) On the same diagram sketch: (i)thegraphof =f(x); (ii)thegraphof =10 f(x). 4 (c)findtherangeofvaluesofxforwhich10
Polynomials and Quadratics
PSf Paper 1 Section A Polnomials and Quadratics Each correct answer in this section is worth two marks. 1. A parabola has equation = 2 2 + 4 + 5. Which of the following are true? I. The parabola has a
(b) the equation of the perpendicular bisector of AB. [3]
![(b) the equation of the perpendicular bisector of AB. [3]](/thumbs/95/126119012.jpg "(b) the equation of the perpendicular bisector of AB. [3]")
HORIZON EDUCATION SINGAPORE Additional Mathematics Practice Questions: Coordinate Geometr 1 Set 1 1 In the figure, ABCD is a rhombus with coordinates A(2, 9) and C(8, 1). The diagonals AC and BD cut at
International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS PAPER 2 MAY/JUNE SESSION 2002
International General Certificate of Secondary Education CAMBRIDGE INTERNATIONAL EXAMINATIONS ADDITIONAL MATHEMATICS 0606/2 PAPER 2 MAY/JUNE SESSION 2002 2 hours Additional materials: Answer paper Electronic
CBSE Board Class X Mathematics Board Paper 2015
CBSE Board Class X Mathematics Time: 3 hours Total Marks: 90 General Instructions: (i) All questions are compulsory. (ii) The question paper consists of 31 questions divided into four sections A, B, C
Possible C2 questions from past papers P1 P3
Possible C2 questions from past papers P1 P3 Source of the original question is given in brackets, e.g. [P1 January 2001 Question 1]; a question which has been edited is indicated with an asterisk, e.g.
Sample Question Paper Mathematics First Term (SA - I) Class IX. Time: 3 to 3 ½ hours
Sample Question Paper Mathematics First Term (SA - I) Class IX Time: 3 to 3 ½ hours M.M.:90 General Instructions (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided
0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
STEP Support Programme. STEP 2 Complex Numbers: Solutions
STEP Support Programme STEP Complex Numbers: Solutions i Rewriting the given relationship gives arg = arg arg = α. We can then draw a picture as below: The loci is therefore a section of the circle between
Here is a link to the formula booklet:
IB MATH SL2 SUMMER ASSIGNMENT review of topics from year 1. We will be quizzing on this when you return to school. This review is optional but you will earn bonus points if you complete it. Questions?
2016 AMC 12A. 3 The remainder can be defined for all real numbers x and y with y 0 by x rem(x,y) = x y y
What is the value of! 0!? 9! (A) 99 (B) 00 (C) 0 (D) (E) For what value of x does 0 x 00 x = 000 5? (A) (B) (C) (D) 4 (E) 5 The remainder can be defined for all real numbers x and y with y 0 by x rem(x,y)
VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)
BY:Prof. RAHUL MISHRA Class :- X QNo. VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CIRCLES Subject :- Maths General Instructions Questions M:9999907099,9818932244 1 In the adjoining figures, PQ
King Fahd University of Petroleum and Minerals Prep-Year Math Program Math (001) - Term 181 Recitation (1.1)
Recitation (1.1) Question 1: Find a point on the y-axis that is equidistant from the points (5, 5) and (1, 1) Question 2: Find the distance between the points P(2 x, 7 x) and Q( 2 x, 4 x) where x 0. Question
1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT.
1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would prove l m? 1) 2.5 2) 4.5 3)
TARGET : JEE 2013 SCORE. JEE (Advanced) Home Assignment # 03. Kota Chandigarh Ahmedabad
TARGT : J 01 SCOR J (Advanced) Home Assignment # 0 Kota Chandigarh Ahmedabad J-Mathematics HOM ASSIGNMNT # 0 STRAIGHT OBJCTIV TYP 1. If x + y = 0 is a tangent at the vertex of a parabola and x + y 7 =
Maharashtra Board Class X Mathematics - Geometry Board Paper 2014 Solution. Time: 2 hours Total Marks: 40
Maharashtra Board Class X Mathematics - Geometry Board Paper 04 Solution Time: hours Total Marks: 40 Note: - () All questions are compulsory. () Use of calculator is not allowed.. i. Ratio of the areas
Name: Teacher: GRADE 11 EXAMINATION NOVEMBER 2016 MATHEMATICS PAPER 2 PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
GRADE 11 EXAMINATION NOVEMBER 2016 MATHEMATICS PAPER 2 Time: 3 hours Examiners: Miss Eastes; Mrs Rixon 150 marks Moderator: Mrs. Thorne, Mrs. Dwyer PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. Read
Maths Higher Prelim Content
Maths Higher Prelim Content Straight Line Gradient of a line A(x 1, y 1 ), B(x 2, y 2 ), Gradient of AB m AB = y 2 y1 x 2 x 1 m = tanθ where θ is the angle the line makes with the positive direction of
1.30 pm 2.30 pm. Mathematics Module M4 Paper 1 (Non-calculator) Higher Tier [GMM41] 1 hour.
![1.30 pm 2.30 pm. Mathematics Module M4 Paper 1 (Non-calculator) Higher Tier [GMM41] 1 hour.](/thumbs/89/98210090.jpg "1.30 pm 2.30 pm. Mathematics Module M4 Paper 1 (Non-calculator) Higher Tier [GMM41] 1 hour.")
Centre Number 71 Candidate Number General Certificate of Secondary Education 2006 Mathematics Module M4 Paper 1 (Non-calculator) Higher Tier [GMM41] GMM41 MONDAY 5 JUNE 1.30 pm 2.30 pm TIME 1 hour. INSTRUCTIONS
EdExcel Further Pure 2
EdExcel Further Pure 2 Complex Numbers Section : Loci in the Argand diagram Multiple Choice Test Questions 1 are about the following loci: P: z i = 2 Q: z i = z R: arg( z i) = S: z i = 2 z 1) Which of
Draft Version 1 Mark scheme Further Maths Core Pure (AS/Year 1) Unit Test 1: Complex numbers 1
1 w z k k States or implies that 4 i TBC Uses the definition of argument to write 4 k π tan 1 k 4 Makes an attempt to solve for k, for example 4 + k = k is seen. M1.a Finds k = 6 (4 marks) Pearson Education