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Geometry ACT Review 3 1. If 𝑥 = 10−2 , what is the value of 30x? 2. If 𝑥 = 10−3 , what is 20 ? 𝑥 3. If 2𝑥 = 70 then x falls between which 2 consecutive integers ? 4. If 3𝑥 = 54, then x falls between which two consecutive integers? 5. If the integer 5 × 2𝑛 is exactly divisible by just 8 positive integers, then n=? 6. A group of cells grows in number as described by the equation 𝑦 = 16(2)𝑡 ,where t represents the number of days and y represents the number of cells. According to this formula, how many cells will be in a group at the end of 3 days? 7. A group of cells grows in number as described by the equation 𝑦 = 12(3)𝑡 ,where t represents the number of days and y represents the number of cells. According to this formula, how many cells will be in a group at the end of 5 days? 8. What is the value of (𝑥 − 𝑦)2 𝑤ℎ𝑒𝑛 𝑥 = 3 𝑎𝑛𝑑 𝑦 = −2? 9. What is the value of (𝑥 − 𝑦)2 𝑤ℎ𝑒𝑛 𝑥 = −4 𝑎𝑛𝑑 𝑦 = 2? 10. If there are 9 × 108 ℎ𝑦𝑑𝑟𝑜𝑔𝑒𝑛 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 in a volume of 3 × 104 cubic centimeters, what is the average number of hydrogen molecules per cubic centimeter? 11. If there are 12 × 1012 ℎ𝑦𝑑𝑟𝑜𝑔𝑒𝑛 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒𝑠 in a volume of 6 × 104 cubic centimeters, what is the average number of hydrogen molecules per cubic centimeter? Geometry ACT Review 3 12. Determine the missing value. 13.What is the value of y in terms of x for the figure below? 14. Determine the value of x in the picture below. 15. . In the figure below, all distances are in feet and all angles are right angles. A straight line drawn from point W to point Z would be how long, in feet? Geometry ACT Review 3 16. if r=3, b=2, and g= - 9, what does (𝑟 + 𝑏 − 𝑔)(𝑏 + 𝑔) equal? 17. A function 𝑓(𝑥)𝑖𝑠 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑎𝑠 𝑓(𝑥) = −3𝑥 2 . What is f(-5)? 18. A function 𝑓(𝑥)𝑖𝑠 𝑑𝑒𝑓𝑖𝑛𝑒𝑑 𝑎𝑠 𝑓(𝑥) = −8𝑥 2 + 2𝑥. What is f(-3)? 19. If x=-1, then – (𝑥 2 ) + 3𝑥 − 4 =? 1 𝑡 20. For a population that grows at a constant rate of r% per year, the formula 𝑃(𝑡) = 𝑝 (𝑎 + 100) models the population t years after an initial population p people is counted. The population of the city of San Jose was 654,000 in 1980. Assume the population grows at a constant rate of 3% per year. According to this formula, write an expression for the population of San Jose in the year 1990? 21. A formula used to compute the current value of a savings account is 𝐴 = 𝑃(1 + 𝑟)𝑛 , where A is the current value; P is the amount deposited; and n is the number of compounding periods. What is the value of a savings account after 4 years if $15,000 is deposited at 5% annual interest compounded yearly? 22. The relationship between temperature expressed in degrees Fahrenheit (F) and degrees Celsius (C) is given by 9 the formula 𝐹 = 𝐶 + 32. If the temperature is 24 degrees Fahrenheit, what is it in degrees Celsius? 5 23. Which of the following is a factored form of 3𝑥 2 − 7𝑥 − 6? 24. What are the real solutions of the equation |𝑥|2 + 2|𝑥| − 24 = 0? 25. What values of x are solutions for 𝑥 2 + 3𝑥 = 18?