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Jeff’s Wholesale Auto Dealership holds an auction once a month. What is the average number of cars sold at the auction for the past 6 months? Month 1: 288 cars Month 4: 558 car Month 2: 432 cars Month 5: 366 cars Month 3: 330 cars Month 6: 258 cars a)318.9 cars ANSWER - D b)350 cars c) 446.6 cars d) 372 cars What is the y intercept of the equation 6x² + y = 18 (0, 18) B. (0,3) C. (18, 0) D. (3,0) ANSWER – A Put in standard form y=-6x² + 18 Make x = 0 and solve for y y=6(0)² + 18 y = 18 A. The graph of the function F(x) = x² has been translated so that its new vertex is (2,1). What is the new equation of the function in standard form? A) F(x)=x² -4x +5 c) F(x)= x² -2x +1 B) F(x)= x² +4x +1 d) F(X) = x² + 2x -1 Answer – A First put into vertex form –> F(x) = (x -2)² + 1 Remembering to switch the sign for the x value. Then FOIL it out Which of the following quadratic equations in standard form has the vertex of (1, -1) F(x) = -2x² -4x +1 B) F(x) = 2x² -4x +1 C) F(x) = -2x² +4x +1 D) F(x) = 2x² +4x -1 ANSWER – B Find the vertex of each function using the –b/2a formula A) Nina wanted to see whether doctors or nurses work more hours in a 5 day work week. She interviewed random doctors/nurses and asked them how many hours a week they work. Nurses 48 50 49 47 51 Doctors 53 54 53 51 52 Looking at the chart, which data set has the lowest mean? A. B. Doctors B. Nurses C. Cannot be Determined D. They have the same mean ANSWER – B Add up all the data points and divide by 5. Who has the lowest mean? Simplify 2 ³ A) 1/8 B)-8 C) -6 D) -1/8 ANSWER – A This is a simple calculator question. Type it in and solve. You’ll get 0.125. Take 1 divided by 8 to get your answer Look for the ^ button or the X button Which of the following is the solution to: 2x -3 ≤ 7 A) B) -2 ≤ x ≤ 7 x≥2 c) x ≤ 5 d) -2 ≤ x ≤ 5 ANSWER – D It is an AND problem. So… -7 ≤ 2x – 3 ≤ 7. Add 3 to both sides and divide by 2 Simplify the expression 3i(-4 + i) and express as a complex number in standard form. -3- 12i B) -3 -21i C) -12i +3i² D) i(-12 + 3i) ANSWER – A Multiply it out to get -12i + 3i². Replace i² with -1 A) Which of the following arithmetic series has a sum of 100 5 A) Σ 5 +3 (n+2) n=1 5 C) n=1 Σ 6+3(n+3) 5 B) Σ 4+2(n+3) n=1 5 D) Σ 5 = 3(n-1) n=1 ANSWER – A Start with 1 and sub in for n up to 5. Add up the numbers until you get 100 What is the domain of the function y = x³? 0≤x≤∞ B. 3 ≤ x ≤ ∞ C. -∞ ≤ x ≤ ∞ D. 0 < x < ∞ ANSWER – C Remember, the domain is all real numbers A. Domain Hint When in doubt ALL REALZ Andrea began an exercise program on Monday. The first day she did 10 sit-ups. Each day she added 5 more sit-ups. How many sit-ups will she have done at the end of the first Saturday of her program? A) 35 c) 135 B) 100 d) 155 ANSWER – A Monday 10, Tuesday 15, Wednesday 20, Thursday 25 Friday 30, Saturday 35 Joe decided to investigate whether HS girls or HS boys have higher EOCT scores. To do this he took a random sample of EOCT scores of both boys and girls. To come to his conclusion, Joe averaged the test scores for each group and compared the two. What are being compared? A) Male and female test scores B) Average EOCT scores for boys C) Average EOCT scores for girls D) Average EOCT scores of boys and girls Answer – D Look at the underlined section of what exactly is being compared Find the domain of the inverse for the following function y = x³ A) B) 0≤x≤∞ 3≤x≤∞ c) - ∞≤ x ≤ ∞ d) -∞ ≤ x ≤ 0 ANSWER – C Remember it is a cubic function, a cubic function and its inverse have a domain of all real numbers. HINT – when in doubt….ALL REALZ Which of the following is −16 in imaginary form? 4 −1 B) 4i C) 16i D) -4 Answer – B Remember, you cannot square root a negative. The negative under the root means your answer will have an i in it. So square root the number and add an i. A) What is the linear regression equation for the chart below x Y 2 5 A) y = 3x 3 7 B) y = 2x + 1 4 9 C) y = 2x + 5 5 11 D) NOT LINEAR ANSWER – B This is a calculator question. Press 2nd DATA and select 2 var. Then press DATA and enter your x and y values. Press STATVAR to find your equation in y = ax + b Which of the following is the solution for 2x² + 5 = -13? x = -3 B) x = 3i C) x = -9 D) x = 9i ANSWER – B Subtract 5 from both sides, divide by sides by 2 and x² = -9. Square root both sides. −9 = 3i A) Compare the standard deviation of Louise and Thelma’s bowling scores. Whose standard deviation is higher? T L 85 176 111 201 159 187 134 99 83 102 175 126 79 223 Thelma c) they are the same B) Louise d) cannot calculate ANSWER – B On your calculator press 2nd DATA and 1-VAR. Enter your x values with FRQ as 1. Press STATVAR and find Ơx A) Given y = ½(x – 2)² + 1, what is the vertex? (2, 1) c) (-2, 1) A) B) (2, -1) D) (-2, -1) ANSWER – A The vertex is ALWAYS the value inside the parenthesis with the value changed and Write −2 − 4 in standard form -i 2 + 4 B) i 2 - 4 C) -4 + i 2 D) -4 – i 2 ANSWER – C “Standard form” means the real part comes first THEN the imaginary part. −2 = i 2 A) What is the inverse of y = x² x= 𝑦 B) y = x² C) x² = y D) y = 𝑥 ANSWER – D Inverse is all about how to ‘undo’ the original. How do you ‘undo’ an x²? With a 𝑥? A) Which of the following arithmetic series has a sum of 60 4 A)Σ 10 – (2 + n) n=1 C) Σ 11 + (4 – n) B)Σ 12 – (3 - n) n=1 D) Σ 9 + (n + 3) ANSWER – C Replace n with 1, 2, 3, and 4, add! How is the graph y = -x² different from the graph y = x²? The graph y = -x² is shifted down 1 unit B) The graph y = -x² is reflected over the x axis and opens upward C) The graph y = -x² is reflected over the x axis and opens downward D) The graph y = -x² is shifted left 1 unit ANSWER – C When there is a reflection of a quadratic, the parabola opens downward A) Use the linear regression feature on your calculator to determine the equation of the linear function that can be used to model the relationship below. (7 hours, 16.8 miles), (7.7 hours, 19.2 miles), (9 hours, 23 miles), (11 hours, 26 miles) y = -2.3x – 1.5 c) y = 2.3x + 1.5 A) B) y = -2.3x +1.5 D) y – 2.3x – 1.5 ANSWER – C This is a calculator question. Press 2nd DATA and select 2 var. Then press DATA and enter your x and y values. Press STATVAR to find your equation in y = ax + b Which of the following functions is represented by the graph A) B) C) D) y = -4x + 6 y = 4x + 6 y = - 4x -6 y = -4x – 6 ANSEWR – B Since the line is moving upward, the slope is positive, the y-intercept is 6. Put into the form y = mx +b where m is the slope, b is the y intercept In comparing the graphs y = |x| and y = 4|x|, the graph y = 4|x|: Opens down, is narrower B) Opens up, is wider C) Opens down is wider D) Opens up is narrower ANSWER – D REMBEMBER – the 4 is positive so it opens up, the 4 is a whole number so it stretches making the V narrower. A) Which of the following measures of central tendency does the following algorithm describe? “Put the numbers in order and circle the one in the middle” A) Mode B) Mean C) Median D) Mode ANSWER – MEDIAN When the numbers are put in order, the median is the middle number What is the next number in the pattern 7 -3, - , 2 A) B) -3 -5 −4, 9 − , 2 ….. 11 − 2 c) D) -7 ANSWER – B The common difference is -0.5. So subtract 0.5 from each and the next term would be -5 In 1989 a movie ticket cost $3.00. In 1999 a movie ticket cost $5.50. Find the average rate of change of the price of a movie ticket. A) B) $0.20 $0.25 c) $0.30 D) $0.85 ANSWER – B The formula is 𝑦2 −𝑦1 . 𝑥2 −𝑥1 If you use 1999 as y2, 1989 as y1, 5.50 as x2 and 3.00 as x1 you would get 0.25. Solve the inequality algebraically x² + 2x ≥ 48. A) B) C) D) -8 ≤ x ≤ 6 x ≤ -8 or x ≥ 6 x ≥ 8 or x ≤ - 6 -6 ≤ x ≤ 9 ANSWER – C FIRST – it is a greatOR problem so OR must be in the answer. Then, once factored you’d get (x+6)(x-8)≥0. When solved you’d have to have a -6 and +8 in the answer. What is the discriminant of 5x² -3x – 12 = 0 A) -231 B) 249 C) 243 D) -240 ANSWER B Formula for the discriminant b²-4ac. Plugged in would be -3² - 4(5)(-12) = 249 The table compares the number of customers a restaurant had for lunch and dinner over a period of 1 year. Which of these is a correct conclusion? Mean Standard Deviation Lunch 40.0 8.7 Dinner 40.0 2.0 The average number of customers was greater for lunch B) The average number of customers was greater for dinner C) There was more variation in the number of customers for lunch D) There was more variation in the number of customers for dinner ANSWER – C Variation means standard deviation. Lunch has the largest standard deviation. A) What function does the scatter plot resemble? Linear B) Quadratic C) Absolute Value D) Rational ANSWER – B The scatter plot looks like ½ of a quadratic parabola A) You have a budget of $100 to spend on books and movies. A book costs $19.00 and a movie costs $15.00. Which inequality best describes the amount of books (b) and movies (m) you can buy? A) 15b + 19m ≤ 100 B) 15b + 19m ≥ 100 C) 19b + 15m ≤ 100 D) 19b + 15m ≥ 100 ANSWER – C 19$ of BOOKS + 15$ of MOVIES must be LESS THAN 100 Which function(s) below are one-to-one I A) B) II I only II only c) I and II d) neither I or II ANSWER C Both functions pass the HORIZONTAL LINE test Which of these is a root of the equation graphed below? x=1 c) x = -3 B) x = -2 d) x = 3 ANSWER C The graph crosses at x = -3 and x = -1 but only x = -3 is listed. A) Use the discriminant to determine the roots of the equation 9x² - 30x + 25 = 0. A) B) No real roots 1 real root c) 2 real roots d) 2 complex roots ANSWER – B Use the discriminant formula b² - 4ac. Plug in a = 9, b = -30, c = 25 and the answer will be 0. When the answer is zero, there is 1 real root! The graph of f(x) = 3𝑥 is translated down 2 units, what is the equation of the translation? A) f(x) = 3𝑥 + 2 B) f(x) = 3𝑥 - 2 C) f(x) = 3𝑥 −2 D) f(x) = 3𝑥+2 ANSWER – B If the graph moves down 2 places, there will be a 2 at the END of the equation. Solve for |x + 6| = 6 A) B) C) D) {-12} {12, 0} {0, -12} {0} ANSWER – C Set up the equation as x + 6 = 6 and x + 6 = -6 and solve for x by – 6 on both sides. 6-6 = 0 and -6 – 6 = -12 Which of the following is the equation to the graph: A) B) C) D) y = (x – 1)² - 4 y = (x – 1)² + 4 y = (x + 1)² - 4 y = (x + 1)² + 4 ANSWER – C The vertex of the parabola is (-1, -4). The -1 changes it sign, the -4 DOES NOT The tangent of <B is ________ B A) B) 95 7 95 12 C) 7 95 D) 12 7 12 adjacent 7 C ANSWER – A TANGENT = 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑠𝑖𝑑𝑒 𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑠𝑖𝑑𝑒 95 = 7 95 opposite A What is the range of the following equation f(x) = -|x – 3| + 2 y>3 B) y ≥ 2 C) y ≤ 3 D) y ≤ 2 ANSWER – D The vertex is (3, 2). Range ALWAYS deals with the y value of the vertex. Since it’s the graph opens down making it LESS than A) A grocery store sells 2 boxes of cereal for $4.95. Which method can be used to find the total cost (c) of purchasing n boxes of cereal? Multiply n by the cost of one box B) Divide n by c C) Multiply n by c D) Divide n by the cost of one box. ANSWER – A If you want to by 2 boxes, it would be n x 2. If you want to buy 8 boxes, it would be n x 8, etc. A) The table below gives the number of inner tubes, I, sold in a bike shop between 1985 and 1990. Determine which model best fits the data Year 1985 1986 1987 1989 1990 Inner Tubes 40 56 74 113 127 Linear c) Absolute Value B) Quadratic d) Exponential ANSWER – D As the years increase so does the number of inner tubes sold, but it does not increase at the same rate A) Simplify −36 A) B) C) D) -6i 6i -36i 36i ANSWER – B When taking the square root of a negative number, take the square root of the number and add and i Which term best describes the relationship between x and y Positive correlation c) positive causation B) Negative correlation d) negative causation ANSWER – A The graph is increasing making it a positive correlation A) Which of these is equal to Cos47° A) B) Tan73° Sin43° ANSWER – B COS47 = 0.682 SIN43 = 0.682 c) Tan137° d) Cos137° What is the product of (5 + 4i) and (3 – 2i)? A) B) C) D) 7 + 2i 8 + 2i 15 – 8i 23 + 2i ANSWER – A Product means add. Collect like terms 5 + 3 = 7. 4i + -2i = 2i Write the equation for the graph y = x² - 2 c) y = x² + 2 B) y = |x| -2 d) y = |x| + 2 ANSWER – B The graph is absolute value shifted DOWN 2 A) The data below represents the price of a pair of shoes at ten stores. Find the mean of the data. 77, 65, 59, 77, 63, 60, 60, 68, 77 A) B) 64 77 c) 60.8 d) 66.7 ANSWER – D There are 10 terms. Add up each and divide by 10 Which equation best models the data in the scatter plot? y = x + 1.5 c) y = x – 1.5 B) y = -x + 1.5 d) y = -x – 1.5 ANSWER – A The scatter plot has a positive slope and a y intercept of 1.5 A) Next Quiz - TODAY Which of the following best describes the graph below: A)It is one-to-one because it passes the horizontal line test B) It is not one-to-one because it does not pass the horizontal line test C) It is one-to-one because it passes the vertical line test. D) It is not one to one because it does not pass the vertical line test. ANSWER – A One-to-one deals with the HORIZONTAL LINE test and a cubic function passes it. What is the inverse of f(x) = 2x + A) g(x) = B) g(x) = C) g(x) = 1 𝑥 2 1 𝑥 2 1 𝑥 2 1 𝑥 2 − + + g(x) = − ANSWER – D D) 3 ? 4 4 3 3 8 4 3 3 8 3 4 First step is to ‘undo’ the by subtraction. Then divide everything by 2 Which of the following pairs are equal A) B) C) D) Tan31° and Sin51° Cos22° and Sin68° Tan40° and Sin40° Cos70° and Sin70° ANSWER – B Cos22° = 0.927 and Sin68° = 0.927 A photographer shines a camera light at a particular painting forming an angle of 40 ° with the camera platform. If the light is 58 feet from the wall where the painting hangs, how high above the platform is the painting hanging? 1.19ft O x B) 48.67ft 40° C) 69.12ft 58ft A D) 0.84ft ANSWER B We would use tan because X is the opposite side, and 58 is the 𝑥 adjacent side. So it would be Tan40 = and since x is in the 58 numerator, we would multiply tan40 x 58 = 48.67 A) What is the standard deviation of 120, 190, 145, 160, 210, 180, 175, 140, 180, 200? 170 B) 26.9 C) 177.5 D) 26.4 ANSWER B Press 2nd DATA and select 2-var. Press DATA and enter each x value with an FRQ as 1. Press STATVAR and look for δx A) What situation could the graph below represent? Dropping a book B) A person aging C) A full helium balloon D) A thrown ball ANSWER – D A thrown ball will look like a reflected parabola, it will go up, then down. A) Which type of graph would be the most appropriate to show how a group’s funds should be budgeted? Pictograph B) Line graph C) Bar graph D) Circle graph ANSWER – D A circle graph is usually used to show percent. A) Find the sum of the first 10 terms in this sequence -5 + 0 + 5 + 10 + …… A) B) C) D) 350 170 175 180 ANSWER B The first 10 terms would be -5 + 0 + 5 + 10 + 15 +20 + 25 + 30 + 35 + 40 – then simply add! Use the function below to answer the question. 2 f(x) = + 3 𝑥 What value is NOT contained in the domain? 0 B) 1 C) 2 D) 3 ANSWER – A You can NEVER have a 0 in the denominator of a fraction! A) Which scatter plot below would model a linear function? A) B) ANSWER - A C) D) Find the missing side 45 3 6 c) 3 2 B) 9 d) 6 2 ANSWER – C In a 45 -45-90 triangle, the hypotenuse is 3 Times longer than the leg A) Simplify 4−3 A) B) - 64 1 64 c) -12 1 d) −12 ANSWER – B When the exponent is negative, the answer is in 1 −3 fraction form. 4 = 0.015625. = 0.015625 64 Find the inverse of y = x³ + 2 A) B) C) D) y = 3x – 2 y=3 𝑥-2 y=3 𝑥+2 y= 2 x 3 –2 ANSWER – B You UNDO the +2 with a -2. You UNDO the x³ with a3𝑥 Use the linear regression feature on your calculator to determine the equation for the following relationship. (3ads, 52 clicks), (4ads, 69 clicks), (5ads, 78 clicks), (6ads, 83 clicks), (8ads, 97 clicks) y = -8.5x + 31.8 c) y = 8.5x – 31.8 B) y = 8.5x + 31.8 d) y = -8.5x – 31.8 ANSWER – B Press 2nd DATA and 2-var. Then DATA and enter your x and y values. Press STATVAR and look for a and b values and put in y = ax + b A) Given the equation f(x) = ½ (x – 2)² + 1, which way does the parabola open and what is the vertex? Opens up, vertex (-2, 1) B) Opens up, vertex (2, 1) C) Opens down, vertex (-2, 1) D) Opens down, vertex (2, 1) ANSWER – B The ½ is positive so it opens UP. Always change And keep A) Simplify x² · 𝑥 −4 A) 𝑥 −2 B) 𝑥 −8 1 c) 2 𝑥 1 d) 8 𝑥 ANSWER – C When you multiply bases, add the exponents. 2 + -4 = -2. But remember, NO NEGATIVE exponents. Put the exponent in the denominator of a fraction. The data set below displays the average weight for a Jack Russell Terrier. Using the line of best fit, determine the average weight for a Jack Russell when they are one year old. 2lbs B) 4 lbs C) 6 lbs D) 8 lbs ANSWER – A At age 1 (on the x axis because x axis always measures time, the weight would be 2 lbs A) What is the value of b? A) B) C) D) 2 2 2 1 2 2 4 45⁰ b ANSWER – B In a 45-45-90 triangle, the hypotenuse is 2 times longer than the leg. Simplify: (-3)³ A) B) C) D) 27 -27 27i -27i ANSEWR – B Simple calculator (-3) ^ 3 = -27. ONLY use i when it is a square ROOT of a negative number What is the y-intercept of f(x) = A) 1 x² 5 - 5? (0,5) B) (0, C) (0, 1 ) 5 1 - ) 5 (0, -5) ANSWER – D For ANY quadratic always list A, B, C D) A= 1 - , 5 B = 0, C = -5. The y-intercept is ALWAYS (0, c)