Core Algebra and graphs

Topics

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Sample objectives

What this unit covers

• Introduction to algebra: Understand that letters can symbolize general numbers. Substitute numerical values into expressions and formulas.
• Algebraic manipulation: Perform algebraic manipulation by simplifying expressions through combining like terms, such as transforming 2a + 3b + 5a - 9b into 7a - 6b. Expand products of algebraic expressions, for example, expanding 3x(2x - 4y) and products of two brackets with one variable, like (2x + 1)(x - 4). Factor expressions by identifying and extracting common factors, ensuring complete factorization, as in the case of 9x + 15xy being factored to 3x(3x + 5y).
• Indices II: Understand and apply the concept of indices, including positive, zero, and negative values. Be able to simplify expressions using the rules of indices, such as simplifying 3^2 • (5x) • 12a^5 ÷ 3a^-2 • 6x^7y^4 × 5x^-5y. Knowledge of logarithms is not necessary.
• Equations: 1 Create basic expressions and equations, such as expressing a number that is 2 more than n, including forming linear simultaneous equations. 2 Solve linear equations with one variable, for example: 3x + 4 = 10. 3 Solve simultaneous linear equations involving two variables, such as: 5 - 2x = 3(x + 7). 4 Rearrange simple formulas to make a specific variable the subject, including cases where the variable appears only once and does not involve powers or roots.
• Inequalities: Understand and illustrate inequalities on a number line, using open circles for strict inequalities (less than, greater than) and closed circles for inclusive inequalities (less than or equal to, greater than or equal to). For example, represent the inequality -3 < x ≤ 1 on a number line.
• Sequences: 1. Extend a specified number sequence or pattern by identifying the next two terms. For example, determine the next two terms in the sequence: 1, 3, 6, 10, 15, … , … 2. Identify patterns within sequences, including the rules that connect terms and the relationships among various sequences. 3. Calculate and apply the nth term for the following types of sequences: (a) linear (b) simple quadratic, such as determining the nth term for the sequence 2, 5, 10, 17 (c) simple cubic.
• Graphs in practical situations: 1 Utilize and understand graphs in real-world contexts, such as interpreting the slope of a straight-line graph, which may include travel and conversion graphs, as a measure of change over time. 2 Create graphs based on provided data, for instance, constructing a distance-time graph to illustrate a journey.
• Graphs of functions: Create value tables and draw, identify, and understand graphs for functions in the following formats: • ax + b • ± x² + ax + b • (x ≠ 0) x, where a and b are whole number constants. Additionally, solve related equations using graphical methods, such as determining where a line intersects with a curve and finding and interpreting roots graphically.
• Sketching curves: Identify, draw, and understand the graphs of these types of functions: (a) linear (b) quadratic. You need to know about symmetry and roots, but turning points are not necessary to understand.