Math 30-1 Sample Test Questions

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1 Math 30-1 Sample Test Questions Instructions: This sample test is designed to give the student some prior indication of what the course content for Math 30-1 is like It is to be used to help the student get through the course All students are encouraged to attempt these questions as they progress through the units Solutions are available as a separate download Use this sample test to help you prepare for the unit tests and the final diploma exam The teacher is available to help you with these questions; however, you must bring your own printed copy to the tutorial Polynomial Expressions and Functions 1 Given the polynomial function 3 f ( x) x 5x 4x 3 a) Determine the y intercept b) Determine the x intercepts using the factor theorem c) Sketch the graph below d) Use your graphing calculator to determine the coordinates of the maximum and minimum points e) For which values of the domain is it true that f( x) 0? A rectangular piece of metal is 50 cm long and 30 cm wide Each squares of length x cm are cut from the corners and the sides are folded up to make a metal box, having no lid a) Draw and label a diagram of the box b) Write a polynomial function to represent the volume of the box c) State the domain of this polynomial in the context of this problem

2 d) Graph the polynomial on your graphing calculator and determine the size of the square cut out from the corners to give a maximum volume for the box e) What will be the dimensions of the box of largest volume? f) What will be the value of the largest possible volume? Radical and Rational Functions 1 Given the radical function y 3 x a) Determine the non-permissible values b) State the domain of this function c) State the coordinates of the first point on the graph d) Sketch the graph below e) Solve the equation 3 x x 5 f) What is the extraneous solution to the equation in part e)? 3 Given the rational function ( x)( x1) y x 1 a) Determine the non-permissible value b) State the domain of this function c) State the equation of the vertical asymptote of the graph d) Determine the equation of the oblique (slant) asymptote of the graph e) Determine the y intercept of the graph f) Determine the x intercepts of the graph g) Sketch the graph below

3 h) Solve the equation ( x)( x1) x 1 Transforming Graphs of Functions 1 The function y f ( x) has been graphed below

4 a) On the same grid sketch the new graph after the transformations: vertical stretch by a factor of, horizontal stretch by a factor of ½, translation of up 1 unit and finally a translation of 5 units left b) State the equation of the transformed graph in the form: y a f ( bx c) d c) State the domain of the original graph d) State the range of the transformed graph e) Starting again with the original function y f ( x), determine the x intercepts of the graph of the function 1 y f ( x 5) 3 Given the function y x x a) List the transformations indicated by the expression: y f x b) Determine the new equation of the given function after the transformations of part a) have been applied 3 The function y g( x) has been graphed below Sketch the graph of the transformed function given by y g( x ) 1

5 Combining Functions 1 Given that f ( x) x 1, g( x) 4 x and h( x) x x a) Determine the value of f(3) 3 h( ) b) Determine the value of f(3) g( ) c) Determine the expanded expression for g( x) h( x) d) Determine the range of the function h( x) f ( x) g( x) Given that f ( x) x 4 and g( x) x a) Determine the value of f( g (11)) b) Determine the value of ( g f )(0) c) Determine the domain of f ( g( x )) d) Determine the domain of g f ( x ) e) Determine the range of g( f ( x )) Exponential and Logarithmic Functions 1 Solve for x in the equation Solve for x in the equation 5x x x 1 3 x 64 M 3 If log M 8 and log N, determine the value of log N 4 Solve for x in log(x 3) log( x ) 1

6 Trigonometry 1 Angle A has been drawn in standard position a) Determine the exact values for all six of the trigonometric ratios b) Determine the angle A to the nearest tenth of a radian c) Determine the angle A to the nearest degree d) Give one positive and one negative angle coterminal with angle A A sinusoidal wave has been graphed below a) Determine a sine representation of this wave in the form sin ( ) y a b x c d b) Determine a cosine representation of this wave in the form cos ( ) y a b x c d

7 3 The equation of a sinusoidal wave has the form y x a) State the amplitude of the wave b) State the period of the wave c) State the horizontal phase shift d) State the vertical displacement e) Sketch one period of the wave on the grid below 5sin Trigonometric Equations and Identities 1 Solve the equation 1 cos sin x x for x using exact values in the domain 0 x o Evaluate cos(75 ) Use exact values and rationalize the denominator 3 Given the trigonometric expression cot x 1 1 tan x1 tan x a) Verify the expression using x and exact values 3 b) Use the two column method to prove that the expression is an identity Permutations and Combinations 1 The letters from the word BEGINNING are to used to make code words a) Find the total number of distinct code words that could be made b) Determine the number of code words that start with a vowel and end with a consonant

8 c) Determine the number of code words that start with N and have the B and the E always together There are 5 boys and 4 girls in a classroom available to be members of a committee a) How many 4 member committees could there be? b) How many 5 member committees could there be that have girls serving as president and treasurer with boys involved in cleanup? 3 Determine the coefficient of 4 x in the binomial expansion of 1 8 x x