 # Probability of Regular Pack of 52 Cards.

Question 1 A card is selected from a regular pack of 52 cards. Find the probability that it is neither black nor a picture card. There are 26 black cards, 6 black picture cards (J, Q, K) and 6 red picture cards. 6 black picture cards are included in 26 black cards. So the number […] Proof 1 $\sin (\alpha – \beta) = \sin \alpha \cos \beta – \cos \alpha \sin \beta$ \begin{align} \angle RPN &= 90^{\circ} – \angle PNR \\ &= \angle RNB \\ &= \angle QON \\ &= \alpha \\ \sin(\alpha – \beta) &= \sin \angle MOP \\ &= \displaystyle \frac{MP}{OP} \\ &= \frac{MR-PR}{OP} \\ &= […] # Trigonometric Ratios of Sums of Two Angles Proof 1 \( \sin (\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta \begin{align} \angle RPN &= 90^{\circ} – \angle PNR \\ &= \angle RNO \\ &= \angle RNO \\ &= \angle NOQ \\ &= \alpha \\ \sin (\alpha + \beta) &= \sin \angle AOC \\ &= \displaystyle \frac{MP}{OP} […] # Differentiation and Displacement, Velocity and Acceleration Distance Distance is the magnitude of the total movement from the start point or a fixed point. Displacement The displacement of a moving position relative to a fixed point. Displacement gives both the distance and direction that a particle is from a fixed point. For example, a particle moves \( 5 units forwards from […] $2 \times 2$ 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 […] # Mathematics Glossary

ABCDEFGHIJKLMNOPQRSTUVWXYZA Absolute error - The difference between the actual value and the measured value indicated by an instrument. Accessibility sampling - Selecting a sample from onlythose items that we most readily available. Acount servicing fee - Ongoing account keeping fees. Actual interest rate - Represents the actual oercentage return per year on an investment (the [...]