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Math 2 EOCT - Practice Test for Study Guide 1. What is the AREA of a square if the diagonal length is 8. If the pattern continues, how many total circles will it take to create the first 20 figures? A. B. C. D. 5√2? B. 25 2 A. 25 C. 50 D. 50 2 Use the quadratic graphed to answer #2-4. 2. What is the function's domain and range? A. D: 4 < x < ∞, R; 4 < y < ∞ B. D: -∞ < x < ∞, R; -∞ < y < 4 C. D: -∞ < x < ∞, R; -∞ < y < ∞ D. D: -∞ < x < 4, R; -∞ < y < ∞ 61 65 589 650 9. This graph shows a set of data from a study of the nitrogen concentration in plants with multiple base stems. Which equation BEST fits the data in the graph? 3. Find the interval of increasing. A. -∞ < x < 3 C. -∞ < y < 4 B. 3 < x < -∞ D. 4 < y < - ∞ 4. What is the function in vertex form? A. 𝑓(𝑥) = (𝑥 + 3)2 + 4 B. 𝑓(𝑥) = −(𝑥 + 3)2 + 4 2 C. 𝑓(𝑥) = −(𝑥 − 3) + 4 D. 𝑓(𝑥) = (𝑥 − 3)2 − 4 5. A student drew this diagram of a right triangle. What is the value of the tangent of angle R? A. C. 4 5 3 4 B. D. 10. Which expression is equivalent to 5 4 A. 4 3 6. The graph of an exponential function is shown on this coordinate plane. Which equation represents the function? A. 𝑓(𝑥) = −6(2𝑥 ) + 2 B. 𝑓(𝑥) = −6(2−𝑥 ) + 2 C. 𝑓(𝑥) = 6(2𝑥 ) − 2 D. 𝑓(𝑥) = 6(2−𝑥 ) − 2 7. The table compares the number of customers a restaurant had for lunch and dinner during a year. Which conclusion is correct? B. 19 3 29 3 − + 22 3 2 3 𝑖 𝑖 D. 2−𝑖 19 22 5 − 29 5 + 5 2 5 ? 𝑖 𝑖 11. This equation can be used to determine a number such that the square of the number is 25 less than 10 times the number: x2 = 10x - 25 Which of the following is equivalent to the equation? A. x2 = 5x B. x2 = -15x 2 C. (x - 5) = 0 D. (x + 5)(x -5) = 0 12. Which function has zeros at -2 and 4? A. 𝑓(𝑥) = 𝑥 2 + 2𝑥 − 8 C. 𝑓(𝑥) = 𝑥 2 − 2𝑥 − 8 B. 𝑓(𝑥) = 𝑥 2 − 2𝑥 + 4 D. 𝑓(𝑥) = 𝑥 2 + 2𝑥 − 4 13. Write the function f(x) = |x - 1| as a piecewise function? A. The average number of customers was greater for lunch. B. There was more variation in the number of customers for lunch. C. The average number of customers was greater for dinner. D. There was more variation in the number of customers for dinner. C. 12−5𝑖 x 1, if x 1 x 1, if x 1 A. f ( x ) x 1, if x 1 x 1, if x 1 B. f ( x ) x 1, if x 0 x 1, if x 0 C. f ( x) 14. A supply of hex nuts is produced and the production records indicate a mean mass of 7.8g with a standard deviation of 0.3g. Assuming a normal distribution, estimate the percent of hex nuts with mass less than 7.5g. A. 84% B. 66% C. 34% D. 16% 22. What is the value of x? 15. Which data set has the least amount of variability based on its standard deviation? 23. Which equation is equivalent to A) 3, 11, 20, 14, 20 C) 12, 10, 13, 25, 12 B) 10, 13, 10, 25, 16 D) 14, 10, 12, 14, 3 2 x 2 y 3 16. Which expression is equivalent to 1 3 xy 9y 4 A. 4x 2 4y 4 B. 9x 2 9x 2 C. 4y 4 2 4x 2 D. 9y 4 17. Solve 52x + 4 = 125x - 7 A. -11 B. 11 C. 17 D. 25 18. Segments ̅̅̅ 𝐾𝐽 and ̅̅̅̅ 𝐾𝐿 are tangent to circle P. m∠JML = 40°. What is the measure of ∠JKL? A. 140° C. 30° B. 100° D. 50° 19. What are the solutions of the equation: A. B. C. D. 20. Which function is NOT an inverse of itself? A. 𝑓(𝑥) = 1 − 𝑥 C. 𝑓(𝑥) = 𝑥 − 1 B. 𝑓(𝑥) = −𝑥 1 D. 𝑓(𝑥) = 𝑥 21. The graphs of the linear function 𝑓(𝑥) = −4 and the absolute value function 𝑓(𝑥) = −2|𝑥 − 2| + 3 are shown on this coordinate plane. Which of the following are the best approximate solutions of −2|𝑥 − 2| + 3 = −4? A. B. C. D. x = -0.5 & 3.5 x= -4 & 3 x = -1.5 & 5.5 x = -1 & 5 A. 24 C. 26.5 B. 25.5 D. 27.9 A. B. C. D. 24. An exercise ball has a volume of 2304𝜋 cubic inches. What is the surface area of the ball? A. 96 𝜋 sq. in. C. 288 𝜋 sq. in. B. 192 𝜋 sq. in. D. 576 𝜋 sq. in. 25. A sector of a circle measures 105°. The arc length of the sector is 7π meters. What is the area of the sector? A. 84π m2 C. 42π m2 B. 49π m2 D. 21π m2 KEY 1. A 7. B The bigger the standard deviation, the more variation there is in the data. 2. B The domain is x-values (look left to right) and the range is y-values (look up and down) 8. D 3. A 9. D The data points are curved which means it must be a quadratic function and not linear. The function opens down, so it has to have a in front. 4. C 𝑓(𝑥) = −(𝑥 − 3)2 + 4 Reflection Shift right Shift up 10. D Multiply numerator and denominator by conjugate of denominator 12 − 5𝑖 2 + 𝑖 ∙ 2−𝑖 2+𝑖 24 + 12𝑖 − 10𝑖 − 5𝑖 2 = 4 − 2𝑖 + 2𝑖 − 𝑖 2 24 + 2𝑖 − 5(−1) = 4 − (−1) 29 + 2𝑖 = 5 11. C 5. D 13. B 19. A 14. D 20. C 15. D Plug each data set into the calculator: 1) Clrdata 2) 1-var stat 3) Data (use arrow down key) 4) Statvar and look for σ. 21. C Look where the two functions intersect and estimate the x values. 16. A 1) Distribute the exponent of 22. A When a diameter or radius meets at a point of tangency, a right angle is created. Use Pythagorean thm. 102 + x2 = 262 X2 = 262-102 X = √262 − 102 = 24 23. D -2. 2−2 𝑥 −4 𝑦 6 3−2 𝑥 −2 𝑦 2 2) reciprocal negative exponents Reflection, growth, shift up 2. 22 𝑥 4 𝑦 2 3) Now simplify. 9𝑦 4 4𝑥 2 17. D 1) Get both to have same base # of 5. 52𝑥+4 = 53 (𝑥−7) 2) Since they both have same base, exponents are equal. 2𝑥 + 4 = 3(𝑥 − 7) 2𝑥 + 4 = 3𝑥 − 21 25 = 𝑥 18. B 6. A 𝑓(𝑥) = −6(2𝑥 ) + 2 32 𝑥 2 𝑦 6 12. C X = -2 and x = 4 (x + 2)(x - 4) = 0 X2 + 2x - 4x -8 = 0 X2 - 2x - 8 = 0 25. 24. D