NAME: Date: HOMEWORK: C1. Question Obtained. Total/100 A 80 B 70 C 60 D 50 E 40 U 39

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NAME: Date: HOMEWORK: C1 Question Obtained 1 2 3 4

1 NAME: Date: HOMEWORK: C1 Question Obtained Total/100 A 80 B 70 C 60 D 50 E 40 U 39

2 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 the vertices of a triangle ABC, as shown in Figure 2. The point D(8, 2) is the mid-point of AC. (a) Find the value of p and the value of q. (2) The line l, which passes through D and is perpendicular to AC, intersects AB at E. (b) Find an equation for l, in the form ax + by + c = 0, where a, b and c are integers. (5) (c) Find the exact x-coordinate of E. (2) N23490A 14

3 Question 1 continued Q8 (Total 9 marks) N23490A 15 Turn over

4 1 2. The line l 1 passes through the point (9, 4) and has gradient. 3 (a) Find an equation for l 1 in the form ax + by + c = 0, where a, b and c are integers. (3) The line l 2 passes through the origin O and has gradient 2. The lines l 1 and l 2 intersect at the point P. (b) Calculate the coordinates of P. (4) Given that l 1 crosses the y-axis at the point C, (c) calculate the exact area of OCP. (3) 16 *N23491C01624*

5 Question 2 continued (Total 10 marks) Q8 *N23491C01724* 17 Turn over

6 3. The line L has equation y = 5 2x. (a) Show that the point P (3, 1) lies on L. (1) (b) Find an equation of the line perpendicular to L, which passes through P. Give your answer in the form ax + by + c = 0, where a, b and c are integers. (4) Q3 (Total 5 marks) 4 *N20233A0420*

7 4. The line l 1 passes through the points P( 1, 2) and Q(11, 8). (a) Find an equation for l 1 in the form y = mx + c, where m and c are constants. (4) The line l 2 passes through the point R(10, 0) and is perpendicular to l 1. The lines l 1 and l 2 intersect at the point S. (b) Calculate the coordinates of S. (c) Show that the length of RS is 3 5. (d) Hence, or otherwise, find the exact area of triangle PQR. (5) (2) (4) 20 *N23557A02024*

8 Question 4 continued *N23557A02124* 21 Turn over

9 Question 4 continued 22 *N23557A02224*

10 Question 4 continued Q11 (Total 15 marks) TOTAL FOR PAPER: 75 MARKS END *N23557A02324* 23

11 The curve C has equation y = x ( x 6) +, x > 0. x The points P and Q lie on C and have x-coordinates 1 and 2 respectively. (a) Show that the length of PQ is 170. (b) Show that the tangents to C at P and Q are parallel. (4) (5) (c) Find an equation for the normal to C at P, giving your answer in the form ax + by + c = 0, where a, b and c are integers. (4) 18 *H26107A01824*

12 Question 5 continued *H26107A01924* 19 Turn over

13 Question 5 continued 20 *H26107A02024*

14 6. The line l 1 has equation y = 3 x + 2 and the line l 2 has equation 3 x + 2y 8 = 0. (a) Find the gradient of the line l 2. (2) The point of intersection of l 1 and l 2 is P. (b) Find the coordinates of P. (3) The lines l 1 and l 2 cross the line y = 1 at the points A and B respectively. (c) Find the area of triangle ABP. (4) 22 *H26107A02224*56

15 Question 6 continued *H26107A02324* 23 Turn over

16 Question 6 continued Q11 END (Total 9 marks) TOTAL FOR PAPER: 75 MARKS 24 *H26107A02424*

17 7. The point A ( 6, 4) and the point B (8, 3) lie on the line L. (a) Find an equation for L in the form ax + by + c = 0, where a, b and c are integers. (4) (b) Find the distance AB, giving your answer in the form k 5, where k is an integer. (3) Q4 (Total 7 marks) *N25561A0524* 5 Turn over

18 8. y l 2 Q l 1 P O R x Figure 2 The points Q (1, 3) and R (7, 0) lie on the line l 1, as shown in Figure 2. The length of QR is a 5. (a) Find the value of a. (3) The line l 2 is perpendicular to l 1, passes through Q and crosses the y-axis at the point P, as shown in Figure 2. Find (b) an equation for l 2, (c) the coordinates of P, (5) (1) (d) the area of PQR. (4) 22 *H29992A02228*

19 Question 8 continued *H29992A02328* 23 Turn over

20 Question 8 continued 24 *H29992A02428*

21 Question 8 continued Q10 (Total 13 marks) *H29992A02528* 25 Turn over

22 1 9. The line l 1 passes through the point A (2, 5) and has gradient. 2 (a) Find an equation of l 1, giving your answer in the form y = mx + c. The point B has coordinates ( 2, 7). (b) Show that B lies on l 1. (3) (1) (c) Find the length of AB, giving your answer in the form k 5, where k is an integer. (3) The point C lies on l 1 and has x-coordinate equal to p. The length of AC is 5 units. (d) Show that p satisfies p 2 4p 16= 0. (4) 20 *n30081a02028*

23 Question 9 continued *n30081a02128* 21 Turn over

24 Question 9 continued 22 *n30081a02228*

25 Question 9 continued Q10 (Total 11 marks) *n30081a02328* 23 Turn over

26 10. y l A (6, 7) C B (8, 2) O x Figure 1 The points A and B have coordinates (6, 7) and (8, 2) respectively. The line l passes through the point A and is perpendicular to the line AB, as shown in Figure 1. (a) Find an equation for l in the form ax + by + c = 0, where a, b and c are integers. (4) Given that l intersects the y-axis at the point C, find (b) the coordinates of C, (2) (c) the area of ΔOCB, where O is the origin. (2) 14 *H34262A01428*

27 Question 10 continued *H34262A01528* 15 Turn over

28 Question 10 continued 16 *H34262A01628*

29 Question 10 continued Q8 (Total 8 marks) *H34262A01728* 17 Turn over

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