Year 9 Maths Topics

2.4 Area of Circle

• This topic covers how to calculate the area of a circle.
• The formula for the area of a circle is $A = \pi r^2$, where $A$ is the area and $r$ is the radius of the circle.

5.1 Substitution

• This topic involves substituting numerical values into algebraic expressions and formulas to evaluate them.
• Example: If $x = 3$ and $y = 2$, find the value of $2x + 3y$.
  $2x + 3y = 2(3) + 3(2) = 6 + 6 = 12$

5.2 Inequalities

• This topic deals with expressing relationships where one quantity is greater than, less than, or equal to another.
• The symbols used are: > (greater than), < (less than), $\geq$ (greater than or equal to), and $\leq$ (less than or equal to).
• Example: x > 5 means x is greater than 5.

5.3 Using Index Laws

• This topic covers the rules for simplifying expressions involving exponents (indices).
• Index laws include:
  • $a^m \times a^n = a^{m+n}$
  • $\frac{a^m}{a^n} = a^{m-n}$
  • $(a^m)^n = a^{mn}$
  • $a^0 = 1$
  • $a^{-n} = \frac{1}{a^n}$
• Example: $2^3 \times 2^2 = 2^{3+2} = 2^5 = 32$

5.4 Expressions, equations, identities and formulae

• Expressions: Combinations of numbers, variables, and operations.
  • Example: $3x + 2y - 5$
• Equations: Statements that show two expressions are equal.
  • Example: $3x + 2 = 8$
• Identities: Equations that are true for all values of the variables.
  • Example: $(a + b)^2 = a^2 + 2ab + b^2$
• Formulae: Equations that express a relationship between two or more variables.
  • Example: $A = \pi r^2$

5.5 Solving Equations

• This topic focuses on finding the value(s) of the variable(s) that make an equation true.
• Techniques include isolating the variable by performing the same operation on both sides of the equation.
• Example: Solve $2x + 3 = 7$
  • $2x = 7 - 3$
  • $2x = 4$
  • $x = 2$

5.6 Changing the Subject

• This topic involves rearranging a formula to isolate a different variable.
• Example: Given $A = \pi r^2$, make $r$ the subject.
  • $r^2 = \frac{A}{\pi}$
  • $r = \sqrt{\frac{A}{\pi}}$

6.1 Planning a Survey

• This topic covers the steps involved in planning a survey, including defining the objectives, target population, sample size, and method of data collection.

6.2 Collecting Data

• This topic deals with different methods of collecting data, such as questionnaires, interviews, and observations. It also covers sampling techniques.

6.3 Calculating Averages and Range

• The three main types of averages are:
  • Mean: The sum of the values divided by the number of values.
    • $\text{Mean} = \frac{\sum x}{n}$
  • Median: The middle value when the data is arranged in order.
  • Mode: The value that appears most frequently.
• Range: The difference between the largest and smallest values.
  • $\text{Range} = \text{Largest value} - \text{Smallest value}$

6.4 Displaying and Analysing Data

• This topic covers various methods of displaying data, such as bar charts, pie charts, histograms, and scatter plots.
• It also involves analysing data to identify patterns, trends, and relationships.

7.1 Direct Proportion

• Two quantities are directly proportional if their ratio is constant.
• If $y$ is directly proportional to $x$, then $y = kx$, where $k$ is the constant of proportionality.

7.2 Solving Problems Using Direct Proportion

• Setting up a proportion equation and solving it.
• Example: If $y$ is directly proportional to $x$, and $y = 6$ when $x = 2$, find $y$ when $x = 5$.
  • $y = kx$
  • $6 = k(2)$
  • $k = 3$
  • $y = 3x$
  • When $x = 5$, $y = 3(5) = 15$

7.3 Translations and Enlargements

• Translation: Moving a shape without changing its size or orientation.
• Enlargement: Changing the size of a shape by a scale factor.
  • If the Scale factor is greater than 1 the image becomes larger
  • If the Scale factor is less than 1 the image becomes smaller

7.4 Negative and Fractional Scale Factor

• Negative Scale Factor: Enlargement with a negative scale factor reflects the shape in the center of enlargement.
• Fractional Scale Factor: A fractional scale factor between 0 and 1 reduces the size of the shape.

7.5 Percentage Change

• Percentage change is the change in a value expressed as a percentage of the original value.
• $\text{Percentage Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100$

8.1 Maps and Scales

• Maps use scales to represent real-world distances on a smaller surface.
• The scale is the ratio of a distance on the map to the corresponding distance on the ground.

8.3 Scales and Ratios

• Scales can be expressed as ratios. For example, a scale of 1:100 means that 1 unit on the map represents 100 units in reality.

8.4 Congruent and Similar shapes

• Congruent Shapes: Shapes that have the same size and shape.
• Similar Shapes: Shapes that have the same shape but different sizes. Corresponding angles are equal, and corresponding sides are in proportion.

8.5 Solving geometric problems

• Application of geometrical principles and theorems to solve problems involving shapes, sizes, and positions of figures.

9.1 Rates of Change

• Rate of change describes how one quantity changes in relation to another quantity.
• For example, speed is the rate of change of distance with respect to time.

9.2 Density and pressure

• Density: Mass per unit volume.
  • $\text{Density} = \frac{\text{Mass}}{\text{Volume}}$
• Pressure: Force per unit area.
  • $\text{Pressure} = \frac{\text{Force}}{\text{Area}}$

9.3 Upper and Lower Bounds

• When measurements are rounded, the true value lies within certain upper and lower bounds.
• For example, if a length is given as 8 cm to the nearest cm, the lower bound is 7.5 cm and the upper bound is 8.5 cm.

10.1 Drawing Straight line graphs

• A straight-line graph can be drawn from a linear equation of the form $y = mx + c$, where $m$ is the gradient and $c$ is the y-intercept.

10.2 Graphs of Quadratic Functions

• Graphs of quadratic functions (of the form $y = ax^2 + bx + c$) are parabolas.
• Key features include the vertex (maximum or minimum point) and the axis of symmetry.

10.4 Simultaneous equations

• Simultaneous equations are a set of two or more equations with the same variables.
• Solving simultaneous equations involves finding the values of the variables that satisfy all equations.
• Methods of solving include substitution, elimination, and graphical methods.