NAME: HOMEWORK: C1 - mrvahora › 2014 › 10 › core...Leave blank 2. The line l 1 passes through the point (9, –4) and has gradient . (a) Find an equation for l 1 in the form

NAME: ________________________________________ Date: ________________ HOMEWORK: C1

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A 80

B 70

C 60

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1. Figure 2

The points A(1, 7), B(20, 7) and C(p, q) form the vertices of a triangle ABC, as shown inFigure 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)

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N23490A

yA(1, 7) B(20, 7)

C(p, q)

D(8, 2)

xO

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Q8

(Total 9 marks)

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2. The line l1 passes through the point (9, –4) and has gradient .

(a) Find an equation for l1 in the form ax + by + c = 0, where a, b and c are integers.

(3)

The line l2 passes through the origin O and has gradient –2. The lines l1 and l2 intersect

at the point P.

(b) Calculate the coordinates of P.

(4)

Given that l1 crosses the y-axis at the point C,

(c) calculate the exact area of �OCP.

(3)

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Q8

(Total 10 marks)

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4

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 youranswer in the form ax + by + c = 0, where a, b and c are integers.

(4)

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________________________________________________________________________________________________________________________________ Q3

(Total 5 marks)

*N20233A0420*

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4. The line l1 passes through the points P(–1, 2) and Q(11, 8).

(a) Find an equation for l1 in the form y = mx + c, where m and c are constants.(4)

The line l2 passes through the point R(10, 0) and is perpendicular to l1. The lines l1 and l2intersect at the point S.

(b) Calculate the coordinates of S.(5)

(c) Show that the length of RS is 3√5.(2)

(d) Hence, or otherwise, find the exact area of triangle PQR.(4)

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TOTAL FOR PAPER: 75 MARKS

END

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Q11

(Total 15 marks)

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5. The curve C has equation 0,4)6(2 >+−= xx

xxy .

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. (4)

(b) Show that the tangents to C at P and Q are parallel. (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)

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tester

Typewritten Text

(Total 13 Marks)

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6. The line 1l has equation 23 += xy and the line 2l has equation 0823 =−+ yx .

(a) Find the gradient of the line 2l . (2)

The point of intersection of 1l and 2l is P.

(b) Find the coordinates of P. (3)

The lines 1l and 2l cross the line 1=y at the points A and B respectively.

(c) Find the area of triangle ABP. (4)

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TOTAL FOR PAPER: 75 MARKSEND

Q11

(Total 9 marks)

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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)

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(Total 7 marks)

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8.

Figure 2

The points Q (1, 3) and R (7, 0) lie on the line l1, as shown in Figure 2.

The length of QR is a√5.

(a) Find the value of a.(3)

The line l2 is perpendicular to l1, passes through Q and crosses the y-axis at the point P, as shown in Figure 2.

Find

(b) an equation for l2,(5)

(c) the coordinates of P,(1)

(d) the area of ∆PQR.(4)

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y l2

Q l1

P

O R x

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(Total 13 marks)

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9. The line l1 passes through the point A (2, 5) and has gradient .

(a) Find an equation of l1, giving your answer in the form y = mx + c.(3)

The point B has coordinates (–2, 7).

(b) Show that B lies on l1.(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 l1 and has x-coordinate equal to p.

The length of AC is 5 units.

(d) Show that p satisfies

(4)

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–

p p2 4 16 0− − = .

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___________________________________________________________________________ Q10

(Total 11 marks)

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10.

A (6, 7)

l

O

C

x

y

B (8, 2)

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)

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(Total 8 marks)

NAME: HOMEWORK: C1 - mrvahora › 2014 › 10 › core...Leave blank 2. The line l 1 passes through...

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