Grade 10 Mathematics Exam Review PDF

MPM 2D1 GRADE 10 MATHEMATICS – EXAM REVIEW UNIT 1: LINEAR SYSTEMS  Solving a system by elimination or substitution  Word problems o Creating “let statements” o Creating equations o Solving for unknowns  How many solutions do...

MPM 2D1 GRADE 10 MATHEMATICS – EXAM REVIEW UNIT 1: LINEAR SYSTEMS  Solving a system by elimination or substitution  Word problems o Creating “let statements” o Creating equations o Solving for unknowns  How many solutions does a system have? (0, 1, infinite) UNIT 2: C0-ORDINATE GEOMETRY  Length of a line  Midpoint of a line  Equation of a circle  Equation of: perpendicular bisector, median, altitude  Verifying properties of triangles and quadrilaterals UNIT 3 – 4: QUADRATICS ALGEBRA OF QUADRATICS  Polynomials: expanding (FOIL), simplifying  Factoring: common, by grouping, simple trinomials, complex trinomials, difference of squares, perfect square trinomials  Completing the square: to convert from standard to vertex  Solving quadratic equations using quadratic formula QUADRATIC FUNCTIONS  Determine the KEY PROPERTIES of a quadratic function: vertex, x-intercepts using algebra  Graph a quadratic function with at least 5 points given any form  Determine the equation of a quadratic function given the vertex or x-intercepts and a point  State the transformations from y = x to y = a(x-h) + k, given transformations state the equation 2 2  Determine how many x-intercepts a function has given in vertex form  State the domain and range for a function  Determine how many solutions a quadratic equation has using the discriminant QUADRATIC WORD PROBLEMS  Projectiles  Revenue  Geometry questions  Determine zero’s, maximum/minimum UNIT 5-6: SIMILAR TRIANGLES AND TRIGONOMETRY  Creating similarity statements, proving similar triangles  Solving for unknown side lengths using proportionality statements  SOH CAH TOA, SINE LAW, COSINE LAW  Solving for unknown sides and angles using above laws  Solving with 2 triangles  Angle of elevation and depression  Word problems: o Draw diagrams o Bearings o Clocks, o 2 angles of elevation UNIT 1: SYSTEMS 1. Solve the system. a) b) c) 2. How many solutions do the following systems have? a) b) 3. Three basketballs and 2 baseballs cost $55. Eight basketballs and 5 baseballs cost $145. Determine the cost of one basketball and one baseball. 4. Andrew wants to make 1.8L of a 15% solution of Hydrochloric acid. In the lab he has 10% HCl and 30% HCl. How much of each solution does he need to combine to make the desired solution? UNIT 2: CO-ORDINATE GEOMETRY 1. Answer the following questions with respect to the points A(–4, 8) and B (5, –2) a. Calculate the slope, midpoint and length of the line b. Determine the equation of the perpendicular bisector 2. What is the equation of a circle with a diameter of 11 units? 3. Does the point (3, 6) lie on, inside or outside the circle defined by the equation 4. What is the diameter of a circle with the equation x2 + y2 = 200? 5. A triangle has vertices at D(5,6), E(2, -8) and F(-4, 10). a) Classify this triangle as scalene, isosceles, equilateral and provide proof algebraically. b) Determine the equation of the median from vertex F. 6. A quadrilateral has vertices at A(1, 4), B(6, -2), C(5, -7) and D(0,-1). Classify the quadrilateral. UNIT 3,4: QUADRATICS ALGEBRA 1. Expand and simplify a) ) b) c) 2. Explain how to identify a polynomial that is a difference of squares. 3. Factor completely and then solve for “x” a) b) c) d) 4. Solve for “x”. a) b)  5. Convert to vertex form. a) b) QUADRATIC FUNCTIONS 1. For the function b) Determine the zero’s. c) Determine the vertex. d) State the transformations in the proper order compared to the function y = x2 e) State the domain and range for the function f) Graph the function. 6. Determine the equation of the quadratic function given the following information a) The zeros are -2 and 6 and the point (3, 5) is on the parabola. b) The vertex is (-5, 3) and the point (-3, 15) is on the parabola. c) Graph one of the parabolas using 5 points. 7. How many x-intercepts do the following quadratics have? a) b) c) d) e) f) g) WORD PROBLEMS 1. Projectile: A bottle rocket is launched upward and its height above the ground in meters in relation to time in seconds is modeled by the function a. What is the maximum height reached by the rocket? b. What is the initial height of the rocket? c. When will the rocket return to the ground? d. How long did it take the rocket to reach a height of 40 m? e. At 5 seconds, is the rocket on the way up or down? 2. Revenue: A computer software company sells programs for $30 each. At this price 500 programs can be sold per month. A survey shows that each $2 increase will result in 10 fewer programs sold. a. What is the maximum revenue that can be generated? b. What price will generate the maximum revenue? c. At what price will the revenue be zero? 3. A bridge in the shape of a parabola is 50 m wide. It’s height is 20 m. a. What is the equation of the parabola that represents the shape of the bridge? b. Lights are to installed on the underside of the bridge where it is 4m high. How far in from either end will the lights be? UNIT 5-6: TRIGONOMETRY 1. Describe under what conditions you would use each of the following formulas or laws. a. SOH CAH TOA b. Pythagorean Theorem c. Sine Law d. Cosine Law 2. Solve for all unknown sides and angles. 12.9 G H a. c. A C 12.1 m 9.5 m 15.5 21.2 x B E 41 7.6 m y I b. D 10.2 cm 80 E 8.0 cm F 3. Identify the similar triangles and provide proof. Solve for “x” and “y” a. b. A A D 26 8 y 6 C 17 B 23 C y x 12 x 8 B E 6 D E x+7 4. From a boat on the water, the angle of elevation of a cliff is 7. The boat moves 110 m away from the cliff and the new angle of elevation is 4. What is the height of the cliff? 5. Sam and Harry are hiking in the woods. Their walkie-talkies will only work up to a distance of 3 km. From their base camp, Sam hikes 4 km/hour in the direction of N 40 W. Harry hikes S 58 W at a speed of 3 km/hour. After 30 minutes of walking they each sit down and turn on their walkie-talkie. Will they be able to talk to each other? 6. Big Ben is a large tower in London England, with a clock at the top. The hands of the clock are 7.7m and 3.85m. What is the distance between the tips of the hands of the clock at 5 o’clock? 7. A triangular garden has side lengths of 3m, 5m and 6m. What is the area of the garden?