rational number, not an integer; the solutions of x2 – 2 = 0 are real numbers, not rational numbers; and the solutions of x2 + 2 = 0 are complex numbers, not real numbers. The same solution techniques used to solveequations can be used to rearrange formulas. For example, the formula for the area of a...
degree equations in one variable by applying the
properties of equality
Determine the solution set of first degree inequalities in one variable by applying the
properties of inequality; visualize solutions of simple mathematical inequalities on a
Solve problems using...
“debrief” the station
1. How do you solve linear equations?
2. How do you simplify algebraic expressions?
3. What is the commutative property?
4. What is the associative property?
5. What is the distributive property?
6. What are examples of...
of ﬁnding the solutions is called solving the equation. Two equations with exactly the same solutions are called equivalent equations. To solve an equation, we try to ﬁnd a simpler, equivalent equation in which the variable stands alone on one side of the “equal” sign. Here are the properties that we...
PROPERTIES, OPERATIONS, AND LINEAR EQUATIONS
The following 11 California content standards are included in the Number Properties, Operations, and Linear
Equations reporting cluster and are represented in this booklet by 22 test questions. These questions represent
PropertySolve each equation.
0 or x 3
The solution set is
Marla (x 7)(x x2 2x
Rosa (x 7)(x x2 2x
Larry (x 7)(x x2 2x
Who is correct? Rosa Explain the errors in the other two students’ work.
Sample answer: Marla used the...
the same for simple and more complex equations that are not so easily done with mental arithmetic. Learn how to perform the steps by working on easier problems first, and then the tougher equa tions will be easier to solve. See how the subtraction property of equality is applied in the next example...
occurring anywhere in the equation, and those with a negative solution
Solve simple linear inequalities in one variable, and represent the solution set on a number line
Experience of finding missing numbers in calculations
The idea that some operations are ‘opposite’ to each...
the properties of equalities and inequalities); (d) graphing. solves problems that use equations and inequalities.
*K to 12 Curriculum Guide – version as of January 31, 2012
K TO 12 MATHEMATICS
Content Standards The learner demonstrates understanding of… the...
the appropriate context and show ability to verify those meanings by definition, restatement, example, comparison, or contrast.
2.0 Reading Comprehension (Focus on Informational Materials)
Students read and understand grade-level-appropriate material. They describe and connect the essential...
specified variable. We use the same general strategy that we used to solve linear equations. We treat the other variables in the equation as if they were constants.
EXAMPLE 10 gle) for W.
Solve the literal equation P = 2L + 2W (perimeter of a rectan-
Gather all terms containing the...
, represent inequalities describing nutritional and cost constraints on combinations of different foods.
4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.
also be written as - x + y … 0.
Now Try Exercises 27, 29
Shading an Inequality Graphing calculators can be used to shade a solution set to an inequality. The left-hand screen shows how to enter the equation from Example 1(b), and the right-hand screen shows the resulting graph...
equations (for example, 5x + 7 = 23, 1.4x − 1.6 = 8.3, and 4x2 − 3 = 13) using tables, graphs and inverse operations. They recognise and use inequality symbols. They solve simple inequalities such as y ≤ 2x + 4 and decide whether inequalities such as x2 > 2y are satisfied or not for specific values of x...
underlying situation mathematically, perhaps with equations, with rules or with diagrams. D. Someexamples of mathematical models are: 1. Equations i. Business A recording studio invests $25 000 to produce a master CD of a singing group. It costs $50.00 to make each copy from the master and cover the...
solutions of equations and inequalities;
5. develop the ability to use concepts to model and solve real-world problems.
a) The Real Number System – R
Students should be able to:
1. use subsets of R;
2. use the properties of the...
write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A).
variable a symbol, usually a letter, used to show an amount that can change Example: x verbal using...
are relevant and used
2010 Secondary Education Curriculum Mathematics
Practical Relevant Use properties of equations and inequalities to solve related multi-step problems
Analyze, compare and contrast mathematical situations...
global information (i.e., a
global underestimator of it). This is perhaps the most important property of convex
functions, and explainssome of the remarkable properties of convex functions and
convex optimization problems. As one simple example, the inequality (3.2) shows
that if ∇f (x) = 0, then...