Grade 9 Math Exam Review – Teacher Copy Unit 1 Review Notes – POWERS AND EXPONENT LAWS 1. 1 – What is a Power Ex.1: 45 = 4x4x4x4x4 = 1024 (use a calculator) Ex.2: a) 32 = 9 b) -32 = -9 c) (-3)2 = 9 1. 2 – Powers of Ten and Zero Exponent For Powers of Ten, the # of Zeroes = Value of Exponent Zero Exponents – always equal 1 Ex.1: a) (-9) 0 = 1 b) -90 = -1 Ex.2: Write 3452 using powers of 10 = 3000 + 400 + 50 + 2 = (3 x 103) + (4 x 102) + (5 x 101) + (2 x 100) 1. 3 – Order of Operations with Powers Ex.1: 33 + 23 = 27 + 8 = 35 Ex.2: [2 x (-3)3 – 6]2 = [2 x (-27) – 6]2 = [-54-6]2 = [-60]2 = 3600 1. 4 & 1.5 – Exponent Laws I and II Product of Powers Ex: 54 x 52 = 56 (same base – add exponents) Quotient of Powers Ex: 7 6 ÷ 72 = 74 (same base – subtract exponents) Power of a Power - multiply the exponents Ex: (32)4 = 38 Power of a Product - distribute the exponent Ex: (3 x 4)5 = 35 x 45 Power of a Quotient –distribute the exponent Ex: Ex: Unit 2 Review Notes - POLYNOMIALS 2. 1 – Modeling Polynomials
Rational Number: All numbers (including fractions), including terminating and repeating decimals Not a rational number: Ex. Write 2 rational numbers between -0.25 and -0.26 -0.251,-0.259 Ex. Order from greatest to least: -0.375, , -1.25, 0.7 Greatest to least: 6. 2 – Adding Rational Numbers – fractions must have a common denominator Ex: 6. 3 – Subtracting Rational Numbers – fractions must have a common denominator Ex: -2 6. 4 – Multiplying Rational Numbers – fractions cross cancel; then multiply straight across the top, then straight across the bottom Ex: *Cross-cancel 6. 5 – Dividing Rational Numbers – Invert and multiply Ex: 6. 6 – Order of Operations with Rational Numbers - BEDMAS Ex: Unit 7 Review Notes – Circle Geometry 7. 1 – Properties of Tangents to a Circle Tangents touch a circle at only one point. Tangents are perpendicular to the radius. Forms a 90° angle. Use the Pythagorean Theorem to solve right triangles. a2 + b2 = c2 (where “c” is the hypotenuse) 7. 2 – Properties of Chords in a Circle The perpendicular from the centre of a circle to a chord bisects the chord and forms a 90° angle. 7. 3 – Properties of Angles in a Circle Arcs: Minor Arc – short arc Major Arc – longer arc
Monomial – ___ term Ex: 5a Binomial – ____ terms Ex: 6x + 9 Trinomial – ___ terms Ex: 9x2-5x+2 Degree of term/polynomial – highest ___________________ Ex: 5y2 + 2 Degree ____ Ex: 18 Degree ____ Not a polynomial if: (1) there is a variable in the ______________ Ex: (2) there is a ____________ __________ of a variable Ex: 2. 2 – Like and Unlike Terms Ex: 2. 3 – Adding Polynomials Ex.1: Ex.2: Find the perimeter. 3x + 2 2x + 1 2. 4 – Subtracting Polynomials Ex: 2. 5 – Multiplying and Dividing a Polynomial by a Constant Ex.1: Ex.2: 2. 6 – Multiplying and Dividing a Polynomial by a Monomial Ex.1: Ex.2: Unit 3 Review Notes – EQUATION SOLVING & INEQUALITIES 3. 1 &3. 2 – Solving Equations – do the ______________ operation to get the _____________ alone. Ex.1: Ex.2: Ex.3: Ex.4: Ex.5: Ex.6:
6. 1 – What is a Rational Number? Rational Number: All numbers (including ______________), including _______________ and _________________ decimals Not a rational number: Write 2 rational numbers between -0.25 and -0.26 Order from greatest to least: 6. 2 – Adding Rational Numbers – fractions must have a ________________ ____________________ Ex: 6. 3 – Subtracting Rational Numbers– fractions must have a _____________ _________________ Ex: 6. 4 – Multiplying Rational Numbers – for fractions, first see if you can cross ______________; then multiply straight across the ____________, then straight across the __________________ Ex: 6. 5 – Dividing Rational Numbers – _______________ and _______________ Ex: 6. 6 – Order of Operations with Rational Numbers - _____________________ Ex: Unit 7 Review Notes – Circle Geometry 7. 1 – Properties of Tangents to a Circle Tangents touch a circle at only _______ point. Tangents are ______________ to the radius. Forms a ____° angle. Use the Pythagorean Theorem to solve ___________ triangles. Formula: __________________ (where “c” is the ________________) 7. 2 – Properties of Chords in a Circle
A shape has line symmetry when a line divides it into 2 congruent (_________) parts. Shapes can be reflected over _______________, _________________, or ______________ (diagonal) lines. Ex. Identify the triangles that are related to the shaded triangle by a line of reflection. Show the position of each line of symmetry. 8. 6 – Rotations & Rotational Symmetry A shape has rotational symmetry when it coincides with itself after a rotation of less than _____̊ about its ___________. The Order of Rotation is the # of times the shape _____________ with itself within one ______________. Angle of Rotation = ___ ̊___ Order of Rotation = ____ ̊___ Ex. Determine which hexagons below have rotational symmetry. State the order of rotation and the angle of rotation symmetry. 8. 7 – Identifying Types of Symmetry 3 Types of Transformations: ________________, _________________, and _________________ 2 Types of Symmetry: ____________ Symmetry & ___________________ Symmetry After a transformation, some images will have: __________ symmetry ___________ symmetry ________________ symmetry Both _________ symmetry & _______________ symmetry