User interface language: English | Español

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 Write down 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 ) 3 1     (M1)

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

= 3 4 ( 0.75 )      (A1)(ft)  (C2)

Note: Follow through from part (a).

[2 marks]

 

b.

y 1 = 3 4 ( x + 3 )   OR   y + 2 = 3 4 ( x 1 )   OR  y = 3 4 x 5 4       (M1)

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

OR

1 = 3 4 × 3 + c   OR  2 = 3 4 × 1 + c     (M1) 

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

3 x + 4 y + 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 5 0 , 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
Show 36 related questions
Topic 5 —Calculus » SL 5.4—Tangents and normal
Topic 5 —Calculus

View options