## SPM Additional Mathematics 2018, Paper 1 (Question 23 – 25)

Question 23 (4 marks):Diagram 10 shows the position of three campsites A, B and C at a part of a riverbank drawn on a Cartesian plane, such that A and B lie on the same straight riverbank.Diagram 10Sam wants to cross the river from campsite C to the opposite riverbank where the campsites A and … Read more

## SPM Additional Mathematics 2018, Paper 1 (Question 20 – 22)

Question 20 (3 marks):It is given that the curve y = (p – 2)x2 – x + 7, where p is a constant, intersects with the straight line y = 3x + 5 at two points.Find the range of values of p.Solution: y=( p−2 ) x 2 −x+7 ……… ( 1 ) y=3x+5 ……………………… ( 2 ) Substitute ( 1 … Read more

## SPM Additional Mathematics 2018, Paper 1 (Question 17 – 19)

Question 17 (4 marks): ( a ) Given P= log a Q, state the  conditions of a. ( b ) Given  log 3 y= 2 log xy 3 , express  y in terms of x. Solution: (a)a > 0, a ≠ 1(b) log 3 y= 2 log xy 3 log xy y log xy 3 = 2 log xy 3 log xy y=2 y= ( xy ) … Read more

## SPM Additional Mathematics 2018, Paper 1 (Question 14 – 16)

Question 14 (4 marks):It is given that p, 2 and q are the first three terms of a geometric progression.Express in terms of q(a) the first term and the common ratio of the progression.(b) the sum to infinity of the progression.Solution: (a) T 1 =p,  T 2 =2,  T 3 =q T 2 T 1 … Read more

## SPM Additional Mathematics 2018, Paper 1 (Question 11 – 13)

Question 12 (4 marks):Diagram 5 shows a circle with centre O.Diagram 5PR and QR are tangents to the circle at points P and Q respectively. It is given that the length of minor arc PQ is 4 cm and OR= 5 α  cm.  Express in terms of α,(a) the radius, r, of the circle,(b) the … Read more

## SPM Additional Mathematics 2018, Paper 1 (Question 8 – 10)

Question 8 (3 marks):Diagram 3 shows vectors OP → ,  OQ →  and  OM → drawn on a square grid.Diagram 3 ( a ) Express  OM →  in the form h p ˜ +k q ˜ ,  where h and k are constants. ( b ) On the diagram 3, mark and label  the point N such that  MN → + OQ → =2 OP → . Solution: (a) OM → = p ˜ +2 … Read more

## SPM Additional Mathematics 2018, Paper 1 (Question 5 – 7)

Question 5 (3 marks):Find the value of ( a )  lim x→1 ( 7− x 2 ), ( b ) f‘‘( 2 ) if f‘( x )=2 x 3 −4x+3. Solution: (a) lim x→1 ( 7− x 2 ) =7− ( 1 ) 2 =6 (b)  f‘( x )=2 x 3 −4x+3 f‘‘( x )=6 x 2 −4 … Read more

## SPM Additional Mathematics 2018, Paper 1 (Question 1 – 4)

Question 1 (2 marks):Diagram 1 shows a probability distribution graph for a random variable X, X ~ N(μ, σ2).Diagram 1It is given that AB is the axis of symmetry of the graph.(a) State the value of μ.(b) If the area of the shaded region is 0.38, state the value of P(5 ≤ X ≤ 15).Solution:(a)μ … Read more