SPM 2018 Paper 1

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

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

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

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

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

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

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

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