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Date May 2018 Marks available 2 Reference code 18M.1.SL.TZ1.T_5
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 1
Command term Find Question number T_5 Adapted from N/A

Question

The point A has coordinates (4 , −8) and the point B has coordinates (−2 , 4).

The point D has coordinates (−3 , 1).

Write down the coordinates of C, the midpoint of line segment AB.

[2]
a.

Find the gradient of the line DC.

[2]
b.

Find the equation of the line DC. Write your answer in the form ax + by + d = 0 where a , b and d are integers.

[2]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

(1, −2)    (A1)(A1) (C2)
Note: Award (A1) for 1 and (A1) for −2, seen as a coordinate pair.

Accept x = 1, y = −2. Award (A1)(A0) if x and y coordinates are reversed.

[2 marks]

a.

1(2)31    (M1)

Note: Award (M1) for correct substitution, of their part (a), into gradient formula.

=34(0.75)     (A1)(ft)  (C2)

Note: Follow through from part (a).

[2 marks]

 

b.

y1=34(x+3)  OR  y+2=34(x1)  OR  y=34x54      (M1)

Note: Award (M1) for correct substitution of their part (b) and a given point.

OR

1=34×3+c  OR  2=34×1+c     (M1) 

Note: Award (M1) for correct substitution of their part (b) and a given point.

3x+4y+5=0  (accept any integer multiple, including negative multiples)    (A1)(ft) (C2)

Note: Follow through from parts (a) and (b). Where the gradient in part (b) is found to be 50, award at most (M1)(A0) for either x=3 or x+3=0.

[2 marks]

 

 

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 5 —Calculus » SL 5.1—Introduction of differential calculus
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