EOCT REVIEW

EOCT 1 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 b)350 cars c) 446.6 cars d) 372 cars ANSWER - D

EOCT 2 What is the y intercept of the equation 6x² + y = 18 (0, 18) (0,3) (18, 0) (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

EOCT 3 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? F(x)=x² -4x +5 c) F(x)= x² -2x +1 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

EOCT 4 Which of the following quadratic equations in standard form has the vertex of (1, -1) F(x) = -2x² -4x +1 F(x) = 2x² -4x +1 F(x) = -2x² +4x +1 F(x) = 2x² +4x -1 ANSWER – B Find the vertex of each function using the –b/2a formula

EOCT 5 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. Looking at the chart, which data set has the lowest mean? Doctors C. Cannot be Determined B. Nurses D. They have the same mean ANSWER – B Add up all the data points and divide by 5. Who has the lowest mean? Nurses 48 50 49 47 51 Doctors 53 54 52

EOCT 6 Simplify 2 ³ 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

EOCT 7 Which of the following is the solution to: 2x -3 ≤ 7 -2 ≤ x ≤ 7 c) x ≤ 5 x ≥ 2 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

EOCT 8 Simplify the expression 3i(-4 + i) and express as a complex number in standard form. -3- 12i -3 -21i -12i +3i² i(-12 + 3i) ANSWER – A Multiply it out to get -12i + 3i². Replace i² with -1

EOCT 9 Which of the following arithmetic series has a sum of 100 Σ 5 +3 (n+2) B) Σ 4+2(n+3) C) Σ 6+3(n+3) D) Σ 5 = 3(n-1) ANSWER – A Start with 1 and sub in for n up to 5. Add up the numbers until you get 100 5 5 n=1 n=1 5 5 n=1 n=1

EOCT 10 What is the domain of the function y = x³? 0 ≤ x ≤ ∞ 3 ≤ x ≤ ∞ ANSWER – C Remember, the domain is all real numbers Domain Hint When in doubt ALL REALZ

EOCT Day 11 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? 35 c) 135 100 d) 155 ANSWER – A Monday 10, Tuesday 15, Wednesday 20, Thursday 25 Friday 30, Saturday 35

EOCT Day 12 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? Male and female test scores Average EOCT scores for boys Average EOCT scores for girls Average EOCT scores of boys and girls Answer – D Look at the underlined section of what exactly is being compared

EOCT Day 13 Find the domain of the inverse for the following function y = x³ 0 ≤ x ≤ ∞ c) - ∞≤ x ≤ ∞ 3 ≤ 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

EOCT Day 14 Which of the following is −16 in imaginary form? 4 −1 4i 4 −1 4i 16i -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.

EOCT Day 15 What is the linear regression equation for the chart below A) y = 3x B) y = 2x + 1 C) y = 2x + 5 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 x Y 2 5 3 7 4 9 11

EOCT Day 16 Which of the following is the solution for 2x² + 5 = -13? x = 3i x = -9 x = 9i ANSWER – B Subtract 5 from both sides, divide by sides by 2 and x² = -9. Square root both sides. −9 = 3i

EOCT Day 17 Compare the standard deviation of Louise and Thelma’s bowling scores. Whose standard deviation is higher? Thelma c) they are the same 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 T 85 176 111 201 159 187 134 L 99 83 102 175 126 79 223

EOCT Day 18 Given y = ½(x – 2)² + 1, what is the vertex? (2, 1) B) (2, -1) c) (-2, 1) D) (-2, -1) ANSWER – A The vertex is ALWAYS the value inside the parenthesis with the value changed and

EOCT Day 19 Write −2 −4 in standard form -i 2 +4 i 2 - 4 -4 + i 2 ANSWER – C “Standard form” means the real part comes first THEN the imaginary part. −2 = i 2

EOCT Day 20 What is the inverse of y = x² x = 𝑦 y = x² x² = y y = 𝑥 ANSWER – D Inverse is all about how to ‘undo’ the original. How do you ‘undo’ an x²? With a 𝑥 ?

EOCT 21 A)Σ 10 – (2 + n) B)Σ 12 – (3 - n) Which of the following arithmetic series has a sum of 60 A)Σ 10 – (2 + n) B)Σ 12 – (3 - n) C) Σ 11 + (4 – n) D) Σ 9 + (n + 3) ANSWER – C Replace n with 1, 2, 3, and 4, add! 4 n = 1 n = 1

EOCT 22 How is the graph y = -x² different from the graph y = x²? The graph y = -x² is shifted down 1 unit The graph y = -x² is reflected over the x axis and opens upward The graph y = -x² is reflected over the x axis and opens downward The graph y = -x² is shifted left 1 unit ANSWER – C When there is a reflection of a quadratic, the parabola opens downward

EOCT 23 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 B) y = -2.3x +1.5 c) 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

EOCT Day 24 Which of the following functions is represented by the graph 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

EOCT Day 25 In comparing the graphs y = |x| and y = 4|x|, the graph y = 4|x|: Opens down, is narrower Opens up, is wider Opens down is wider 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.

EOCT 26 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” Mode B) Mean C) Median D) Mode ANSWER – MEDIAN When the numbers are put in order, the median is the middle number

EOCT Day 27 -3 c) − 11 2 -5 D) -7 ANSWER – B What is the next number in the pattern -3, - 7 2 , −4, − 9 2 , ….. -3 c) − 11 2 -5 D) -7 ANSWER – B The common difference is -0.5. So subtract 0.5 from each and the next term would be -5

ECOT Day 28 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. $0.20 c) $0.30 $0.25 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.

EOCT 29 Solve the inequality algebraically x² + 2x ≥ 48. -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.

EOCT 30 What is the discriminant of 5x² -3x – 12 = 0 -231 B) 249 C) 243 D) -240 ANSWER B Formula for the discriminant b²-4ac. Plugged in would be -3² - 4(5)(-12) = 249

EOCT 31 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? The average number of customers was greater for lunch The average number of customers was greater for dinner There was more variation in the number of customers for lunch There was more variation in the number of customers for dinner ANSWER – C Variation means standard deviation. Lunch has the largest standard deviation. Mean Standard Deviation Lunch 40.0 8.7 Dinner 2.0

EOCT 32 What function does the scatter plot resemble? Linear Quadratic Absolute Value Rational ANSWER – B The scatter plot looks like ½ of a quadratic parabola

EOCT 33 You have a budget of $100 to spend on books and movies. A book costs $19.00 and a movie costs $15.00. Which inequality best describes the amount of books (b) and movies (m) you can buy? 15b + 19m ≤ 100 15b + 19m ≥ 100 19b + 15m ≤ 100 19b + 15m ≥ 100 ANSWER – C 19$ of BOOKS + 15$ of MOVIES must be LESS THAN 100

EOCT 34 Which function(s) below are one-to-one I II I only c) I and II II only d) neither I or II ANSWER C Both functions pass the HORIZONTAL LINE test

EOCT 34 Which of these is a root of the equation graphed below? x = 1 c) x = -3 x = -2 d) x = 3 ANSWER C The graph crosses at x = -3 and x = -1 but only x = -3 is listed.

EOCT 34 Use the discriminant to determine the roots of the equation 9x² - 30x + 25 = 0. No real roots c) 2 real roots 1 real root 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!