## Grade 9 Math

Name: ____________

Final Exam Review Checklist

Use this checklist as a guide to the information you are expected to know for the Final Exam. You can check off the boxes as you have mastered the material in preparation for the exam.

Unit 1(10%)

Determine the square roots of integers (both perfect squares and non-perfect squares).

Determine the square root of fractions (both perfect and non-perfect squares).

Determine the area of a square (with side lengths that are integers, fractions or decimals).

Determine whether or not fractions and decimals are perfect squares.

Use a diagram to determine the square root.

Estimate square roots of non-perfect squares (using benchmarks).

Find a number given its square root (Ex: Find a number whose square root is 1.5)

Place the square roots of decimals on a number line.

Find perimeter of a square given its area.

Use the Pythagorean Theorem to find missing side lengths.

Estimate the square roots of non-perfect square decimals and fractions.

Find the surface area of composite objects, including combinations of rectangular prisms, triangular prisms, and cylinderso

Note: Only formula given is SA cylinder = 2 𝜋𝑟2 + 2𝜋𝑟ℎ

Determine if a given solution has an error or notUnit 2(10%)

Know what a power is (know what a base and exponent is within the power).

Write the base and exponent given a power.

Write volume and area as powers.

Write powers as repeated multiplication.

Write repeated multiplication as powers.

Evaluate expressions that involve powers and more than one operation (USE the ORDER OF OPERATIONS).

Use the exponent laws (next 5 bullets)o

When multiplying powers in the same base, ADD the exponents.o

When dividing powers in the same base, SUBTRACT the exponents.o

When evaluating a power of a power (ex: (23)4 = 212 ), multiply the two exponents together and keep the base.o

When evaluating the power of a product (𝑒𝑥: (2 × 3)2 = 22× 32 = 4 x 9 = 36), you can apply the exponent to both numbers that you are multiplying.o

When evaluating the power of a quotient (ex: (78_{13}) 3

=78_{13}3_{3} = 474552_{2197} = 216 ), you can
apply the exponent to both numbers to be divided.

Evaluate order of operations expressions that involve some or all of the exponent laws.

Determine if a given solution has an error or notUnit 3(14%)

Know what rational numbers are (fractions and decimals that terminate or repeat).

Write a rational number between two given rational numbers (ex: write a number between -0.25 and -0.26).

Place rational numbers on a number line.

Put rational numbers in order from least to greatest OR greatest to least.

Tell which rational number is less when given a choice.

Word problems with rational numbers.

Determine from a group of numbers whether or not a number is rational.

Add rational numbers (using a number line or common denominators).

Subtract rational numbers (using a number line or common denominators).

Determine the missing number in addition or subtraction statements.

Multiply rational numbers (be sure to reduce if you are using fractions!!).

Dividing rational numbers (reciprocal or common denominators for fractions).

Order of operations with rational numbers (be CAREFUL!!).Unit 4(13%)

Know what a relation is.

Create a table of values (input/output table) given a relation.

Given a pattern (diagram) write a relation to represent it.

Write a relation (equation) given a table of values.

Given a relation, evaluate for a given number (ex: given P = 2n + 1, find P when n = 3 Ans: P = 2 (3) + 1 = 6 + 1 = 7).

Know the difference between an expression (no equal sign) and an equation.

Represent a relation in words, in a table, in a graph and in an equation.

Know the difference between discrete and continuous data (i.e. when to join the dots and when you do not join them).

Solve problems by creating a table of values, an equation and solving.

Given a graph, determine if a relation is linear.

Given a table of values, determine if a relation is linear.

Given an equation, determine if a relation is linear.

Create a table of values given an equation and values for x.

Word problems.

Know the three types of lines and their equations: Horizontal (Eqn: y = a number), Vertical (Eqn: x = a number) and Oblique (Equation has 2 variables).

Write the equation of horizontal and vertical lines given a graph.

Recognize the alternate form for an oblique line (ex: 2x + 2y = 7).

Given any graph and any linear equation, match the equation to the graph.

Use a graph to gain information (extrapolate and interpolate). You may have to extend the graph to find missing information (see pgs 195 – 198).Unit 5(10%)

Know the difference between a monomial, binomial and trinomial.

State whether or not a given expression is a monomial, binomial or trinomial.

Give examples of expressions that are polynomials and those that are not.

State the degree of any given polynomial.

Know the difference between like and unlike terms.

Simplify polynomials (by adding and subtracting like terms).

Add polynomials with and without algebra tiles.

Find the perimeter of a figure whose sides are polynomials.

Subtract polynomials with and without algebra tiles (or change to addition and then add).

Find the missing side of a figure given perimeter and all sides except one.

Multiply a polynomial by a constant (a number without a variable) using algebra tiles.

Multiply a polynomial by a constant (a number without a variable) without using tiles.

Find area of a figure whose sides are polynomials (rectangles, squares).

Find the missing side of a figure given area and the other necessary sides.

Multiply a monomial by a monomial.

Multiply a monomial by a binomial.

Divide a monomial by a monomial.

Divide a binomial by a monomial.

Determine if a given solution has an error or not.Unit 6(13%)

Solve equations (find the value of the variable) using inverse operations (this is referring to the box diagrams on page 267).

Write an equation given words (for example: three more than four times a number is nine)

Write words given an equation.

Solve word problems that involve equations.

Solve equations that involve the distributive property (ex: 2(x+3) =8).

Solve equations that involve rational expressions (example: 34

𝑥 + 2 =

1 2).

Solve equations using balance scales.

Solve equations using algebra tiles.

Solve equations with variables on both sides (ex: 2 – 3n = 2n + 7)

Solve with variables and distributive property on both sides (4(g + 5) = 5(g – 3)).

Solve with rationals and distribution (ex: 7_{2}(𝑚 + 12) = 5

_{2}(20 + 𝑚)).

Solve inequalities and put solutions on a number line.

Write a solution given a number line.Unit 7 (13%)

Know how to find a scale factor.

Know what a scale factor is.

Draw enlargements and reductions given scale factors.

Identify scale diagrams.

Know what similar figures are (same shape, different size OR same angles, proportional side lengths).

Solve proportions ( 𝑥 2.5=

7.5 1.5

).

Solve similar triangle word problems (set up a proportion, cross multiply and solve).

Identify line symmetry.

Identify rotational symmetry.

Identify angle of rotation and order of rotation.

Draw the reflection or rotation of a figure across a line or around a point.

Determine if a given solution has an error or notUnit 8(10%)

Know the properties:o When a tangent line meets a radius in any circle, they form a right angle.

o When a radius meets a chord and cuts it in half, it forms a 90 degree angle OR when a radius meets a chord at a 90 degree angle, the chord is cut in half.

o An inscribed angle is half the measure of a central angle on the same arc.

o Inscribed angles subtended by the same arc have the same measure.

o The angles in a triangle add up to 180 degrees.

o Angles on a straight line add up to 180 degrees.

o Angles in a circle equal 360 degrees.

o An angle inscribed on a semicircle is equal to 90 degrees.

Solve problems with circles (find missing side lengths and angle measurements)

Know the terms perpendicular bisector, diameter, radius, tangent, chord

Know the difference between theoretical probability, experimental probability and subjective judgment.

Be able to determine whether a decision is based on theoretical probability, experimental probability or subjective judgment.

Explain what assumptions are being made in certain decision making situations

Know the factors that might lead to difficulty with data collection AND be able to recognize them in examples (bias, use of language, timing, privacy, cultural sensitivity, ethics, cost and time, p. 432).

Know the difference between a sample and a population.

Know when to use a sample vs. when to use a census.

Know what a valid conclusion is and what it means to draw a valid conclusion (for instance, if 80% of people preferred hot dogs to hamburgers, it would not be valid to state that the majority of the people prefer hamburgers).

Know how to select a sample.