## 6.4.1 Linear Inequalities in Two Variables, SPM Paper 2 (Long Questions)

Question 1:On the graph in the answer space, shade the region which satisfies all three inequalities y > –2x + 8, y ≥ x + 1 and y ≤ 7.Answer:Solution: Question 2:On the graph in the answer space, shade the region which satisfies all three inequalities 2x + y ≥ 2, x + y < … Read more

## 6.1.1 Region Representing Inequalities in Two Variables (Examples)

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 Linear Inequalities in Two Variables

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

## 2.5.4 Graph of Functions (II), SPM Paper 2 (Long Questions)

Question 9: (a) Complete the table in the answer space for the equation y = 8 – 3x – 2×2 by writing down the values of y when x = –4 and x = 2. (b) For this part of the question, use graph paper. You may use a flexible curve rule. By using a … Read more

## 2.5.3 Graph of Functions (II), SPM Paper 2 (Long Questions)

Question 7: (a) The following table shows the corresponding values of x and y for the  equation y= –x3 + 3x + 1.    x –3 –2 –1 0 1 2 3 3.5 4 y 19 3 r 1 3 –1 s –31.4 –51 Calculate the value of r and s.   (b) For this part of the question, … Read more

## 2.5.2 Graph of Functions (II), SPM Paper 2 (Long Questions)

Question 5: (a) The following table shows the corresponding values of x and y for the equation y = 24 x    x –4 –3 –2 –1 1 1.5 2 3 4 y –6 k –12 –24 24 n 12 8 6 Calculate the value of k and n.   (b) For this part of … Read more

## 2.4.2 Graph of Functions (II), SPM Paper 1 (Short Questions)

2.4.2 SPM Practice (Short Questions)   Question 3: Which of the following graphs represent y = 2×3 – 16?   Solution: y = 2×3 – 16 On the y-axis, x = 0. y = 2(0)3 – 16 y = –16   The answer is C. Question 4: Which of the following graphs represent y = − … Read more

## 2.4.1 Graph of Functions (II), SPM Paper 1 (Short Questions)

2.4 SPM Practice (Short Questions)   Question 1: Which of the following graphs represent y = –x2 – x + 2?   Solution: 1.   The coefficient of x2 < 0, its shape is ∩. 2.   Find the x-intercepts by substituting y = 0 into the function. y = –x2 –x + 2 when y = … Read more

## 2.2 Solution of an Equation by Graphical Method

2.2 Solving equations graphically   The solution of the equation f (x) = g (x) can be solved by graphical method. Step 1: Draw the graphs of y = f (x) and y = g (x) on the same axes. Step 2: The points of intersection of the graphs are the solutions of the equation f … Read more

## 2.1.2 Types of Graphs of Functions.

(B) Types of graphs of functions.   (a) Linear function: y = mx + c Highest power of the variable x is 1. (i) y = mx + c, m > 0 (ii) y = mx + c, m < 0 (b) Quadratic function: y = ax2 + bx + c Highest power of the variable x … Read more