Onlinetuition.com SPM Mathematics
(B) Speed – Time Graph 1. The gradient of a speed-time graph is the rate of change of speed or acceleration. 2. (a) From O to P: Gradient = positive → (Speed of object increasing or accelerating). (b) From P to Q: Gradient = 0 → (Object is moving at uniform speed). (c) From Q to R: Gradient = negative … Read more
7.1 Quantity Represented by the Gradient of a Graph The gradient of graph is the rate of change of a quantity on the vertical axis with respect to the change of another quantity on the horizontal axis. (A) Distance – Time Graph 1. The gradient of a distance-time graph is speed. 2. (a) From O … Read more
Example 1: On the graph in the answer space, shade the region which satisfies the three inequalities y ≥ –x + 10, y > x and y < 9. Answer: Solution: 1. The region that satisfies the inequality y ≥ –x + 10 is the region on and above the line y = –x + 10. 2. The region that … Read more
6.1.1 Position of a point relative to the graph of y = ax+ b 1. When y = ax + b, the point is on the line. 2. When y < ax + b, the point is below the line. 3. When y > ax + b, the point is above the line. 6.1.2 Identifying the region satisfying the respective inequalities. … Read more
Question 3: (a) The Venn diagrams in the answer space shows sets P and Q such that the universal set, ξ = P υ Q. Shade the set P ∩ Q. (b) The Venn diagrams in the answer space shows sets X and Y and Z, such that the universal set, ξ = X υ Y υ Z. Shade the set (X υ Z) ∩ Y. Solution: (a) … Read more
Question 1: The Venn diagrams in the answer space shows sets X, Y and Z such that the universal set, ξ = X ∪ Y ∪ Z On the diagrams in the answer space, shade ( a ) X’ ∩ Y , ( b ) ( X ∪ Y’ ) ∩ Z Solution: (a) • … Read more
4.4.2 Operations on Sets, SPM Practice Paper 1 (Short Questions) Question 5: Diagram below shows a Venn diagram with the number of elements of set P, set Q and set R. It is given that the universal set, ξ=P∪Q∪R and n( Q‘ )=n( Q∩R ). Find the value of x. Solution: n(Q)’ = n(Q ∩ R) 3 … Read more
Question 1: List all the subsets of set P = {r, s}. Solution: There are 2 elements, so the number of subsets of set P is 2n = 22= 4. Set P = {r, s} Therefore subsets of set P = {r}, {s}, {r, s}, { }. Question 2: Diagram above shows a … Read more
4.3b Union of Sets 1. The union of set A and set B, denoted by A υ B is the set consisting of all elements in set A or set B or both the sets. The Venn diagram of A υ B is illustrated as below: 2. The union of set A, set B and set C, denoted by A υ B υ C is the … Read more
4.3a Intersection of Sets 1. The intersection of set P and set Q, denoted by P ∩ Q is the set consisting of all elements common to set P and set Q. 2. The intersection of set P, set Q and set R, denoted by P ∩ Q ∩ R is the set consisting of all elements common … Read more