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SPM Additional Mathematics 2023, Paper 1 (Question 4 & 5)


Question 4:
 Diagram 3 shows point A lies on the circumference of a unit circle. 
Express in terms of p and / or q of.
(a) tan β,
(b) cot (180o + β)
[2 marks]

Solution:

(a)

tanβ= Opposite  Adjacent (TOA)tanβ=pq

(b)
tan(A+B)=tanA+tanB1tanAtanBcot(180+β)=1tan(180+β)=1tan180+tanβ1tan180tanβ=10+tanβ1(0)tanβ=1tanβ1=1tanβ=1pq=qp


Question 5:
 Diagram 4 shows three points on a Cartesian plane. 
 (a) State SP [1 mark]. 
 (b) It is given that PQ=5i_+mj_
 (i) If SP+3PQ=13i_+15j, find the value of m by using vector’s  arithmetic operations 
 (ii) Hence, determine the unit vector in the direction of PQ
[4 marks]
Solution:
(a)
SP=SO+OP=(i+2j)+(i+5j)=i2ji+5j=2i+3j

(b)(i)
SP+3PQ=13i_+15j_(2i_+3j_)+3(5i_+mj_)=13i_+15j_2i_+3j_+15i_+3mj_)=13i_+15j_13i_+(3m+3)j_=13i_+15j_
3m+3=153m=12m=4

(b)(ii)
PQ=5i_+4j_|PQ|=52+42|PQ|=41
 Unit vector =5i_+4j_41

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