16 Questions
What mathematical terms and verbs should you be fluent in understanding for this test?
Transpose, expand, simplify, evaluate
What is the equipment needed for the test?
Blue or black pen, calculator
What percentage of the test questions are categorized as complex unfamiliar?
20%
What is the main focus of Topic 2 - Equations?
Rearranging/transposing algebraic equations to make a desired variable the subject
How would you solve a multistep equation involving fractions?
By first clearing the fractions by multiplying both sides of the equation by the least common denominator.
Explain the process of solving an equation with variables on both sides.
You would first simplify the equation by collecting like terms on each side before isolating the variable term to one side.
How do you solve a multi-step linear equation derived from a real-life scenario?
You would first translate the given scenario into an equation, solve it step by step using inverse operations, and then interpret the solution in the context of the scenario.
What is the point of intersection on a graph and how would you state it?
The point of intersection is where two lines on a graph meet, and it is stated as a set of coordinates in the form (x, y).
How do you verify a solution for a pair of simultaneous equations through substitution?
You substitute the solution values into both equations to check if they satisfy both equations simultaneously.
Explain the process of solving simultaneous equations algebraically using the substitution method.
You solve one equation for one variable, then substitute that expression into the other equation to solve for the other variable.
Expand and simplify: $4(y - 5)$
$4y - 20$
What is the solution to the simultaneous equations: 2 burgers + 3 bowls of chips = $24 and 4 burgers + 2 bowls of chips = $40?
Burger cost: $8, Bowl of chips cost: $4. Assumption: Prices of burgers and chips are constant for both families.
Find the value of $x$ in the equation: $3(x + 2) = 21$
$x = 5$
Calculate the side length of a cube with volume 125cm$^3$.
Side length = 5 cm
Solve the equation: $-4x(x + 1) + 3(x + 2x)$
$-4x^2 - 4x + 3x + 6x$
Using the substitution method, solve the simultaneous equations: $2m + 3n = 24$ and $4m - 2n = 40$
$m = 8, n = 4$
Study Notes
Topic 1: Algebra
- Use algebraic vocabulary to identify different parts of an algebraic expression or equation: term, variable, pronumeral, coefficient, and constant.
- Solve algebraic equations through substitution.
- Complete a table of values for a given function by substituting into an equation.
- Simplify algebraic expressions by: • Identifying and collecting like terms (+ and -) • Multiplying (× and ÷)
- Expand an algebraic expression using the 'Distributive Law' to then simplify where required.
Simplifying Expressions
- Simplify expressions by combining like terms (+ and -)
- Simplify expressions by multiplying and dividing to simplify
- Expand and simplify expressions using the Distributive Law
Topic 2: Equations
- Rearrange/transpose an algebraic equation to make a desired variable the subject.
- Solve multistep equations using inverse operations in the correct order (SADMOB) while showing correct setting out, including: • Equations involving fractions • Variable on both sides • Brackets
- Solve multi-step linear equations that are derived from worded scenarios that model real-life applications.
- Identify the point of intersection on a graph by stating the solution as a set of coordinates.
- Verify a solution for a pair of simultaneous equations through substitution.
- Solve simultaneous equations algebraically using the substitution method.
- Set up a problem with more than one variable by constructing a set of suitable simultaneous equations that model a real-life application.
- Efficiently use algebra in a variety of contexts to solve and evaluate problems.
Solving Equations
- Transpose to make the pronumeral in the brackets the subject
- Solve simple equations using algebra
- Solve worded life-related problems using algebra – simple equations
- Solve simultaneous equations graphically
- Solve simultaneous equations algebraically using the substitution method
- Solve worded life-related problems using algebra – simultaneous equations
This quiz provides details about the assessment for the 10 IGM class in Term 1, 2023. It includes information about the test format, equipment needed, time allowed, and task overview.
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