Example 1 Divide \( x^3 + 3x^3 + 2x + 1 \) by \( x+2 \). Example 2 Perform a long division: \( (4x^4-6x^3+2x^2-3x+5) \div (2x+1) \).

# Differentiation and Displacement, Velocity and Acceleration

Distance Distance is the magnitude of the total movement from the start point or a fixed point. For example, a particle moves \( 5 \) units forwards from \( O \), and moves \( 3 \) backwards. Its distance travelled is \( 5 + 3= 8 \) units. Displacement The displacement of a moving position […]

# Probability with Wins Draws and Loses in Go Matches

In a Go match between the Amy team and Ben team, a game is played on each of board \( 1 \), board \( 2 \), board \( 3 \) and board \( 4 \). On each board, the probability that the Amy team wins is \( 0.2 \), the probability of a draw is […]

# Calculating Chi-Squared

\( 2 \times 2 \) Contingency Table The following shows the results of a survey of a sample of \( 200 \) randomly chosen adults classified according to gender and sport. These are called observed values or observed frequencies. $$ \begin{array}{|c|c|c|c|} \hline & \text{loves sport} & \text{hates sport} & \text{sum} \\ \hline \text{male} & 72 […]

# Drawing Venn Diagrams Effectively

Consider the following situation to illustrate through Venn diagrams. Two Circles There are \( 50 \) students in a certain high school. \( 16 \) study Physics, \( 13 \) study Chemistry, and \( 15 \) study both Physics and Chemistry. Illustrate this information on a Venn diagram. $$ \begin{align} a+b+c+d &= 50 \text{ total […]