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Overview Math Test - Calculator is the fourth section of the SAT, and the second math section of the test. You will have 55 minutes to answer 38 questions This is a little less than 1 ½ minutes per question. Although this section allows the use of a calculator, not all questions will require a calculator, and may be able to be solved faster without a calculator. Questions on the calculator portion of the math test may involve more complex models and reasoning, since you won’t be held back by having to make calculations by hand. SAT Math Test - Calculator 55 minutes 38 questions 1 minute and 26 seconds per question The SAT Math - Calculator test consists of a combination of multiple choice and fill-in-the-blank questions - 30 multiple choice and 8 “student-produced responses,” or grid-in questions. You will be provided with instructions about how to bubble in the grid-in questions, as seen below. Notice that the grid in questions cannot be negative, as there is no way to mark a negative sign. Also note that while you can either bubble an answer as a fraction or a decimal, you cannot bubble in a mixed number (must instead be written as an improper fraction). The SAT categorizes their math questions into one of four subsections: 1. Heart of Algebra These types of questions will focus on the skills learned in Algebra I, specifically dealing with linear equations and inequalities. Students may be asked to solve or interpret linear equations or inequalities with one or two variables, and may be asked to create, solve, and interpret systems of equations or inequalities. The SAT focuses on skills that may be useful in your future career, so many of the questions will be application questions where you must apply your knowledge of linear equations/inequalities to the real world. Example: “The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk, m, and cups of juice, j, a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?” 2. Problem Solving and Data Analysis These types of questions ask you to apply your knowledge of ratios, proportions, percentages, and unit conversion. You will also be tested on your knowledge and understanding of graphs and data. You may be asked how two variables on a graph are related, or to make inferences based on sample data. You may also be asked to apply your knowledge of measures of central tendency (mean, median, mode, range, standard deviation). Example: The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown. Based on the line of best fit, what is the predicted height for someone with a first metacarpal bone that has a length of 4.45 centimeters? 3. Passport to Advanced Math These types of questions will cover topics that are essential for students to master before continuing into advanced math. Students will be asked to create and solve quadratic equations. You may also be asked to add, subtract, multiply, and divide polynomial expressions, and understand the different characteristics of polynomial functions. You will be asked to solve equations that include rational exponents and radicals, and you will be expected to understand and use function notation. Example: x2 + y2 = 5 y = x2 − 3 x − y = 1 A system of three equations and their graphs in the xy-plane are shown above. How many solutions does the system have? 4. Additional Topics in Math This subsection focuses on geometric and trigonometric concepts, such as special right triangles and trigonometric ratios. You may be asked to solve for the area and volume of shapes. All necessary volume formulas will be provided on the formula sheet at the beginning of the test. You will also be tested on concepts such as degree-radian conversion, arc length, and trigonometric functions and identities. You may also be asked about similarity and congruence, and will have to apply various theorems to determine side or angle measurements. Example: The figure above shows a metal hex nut with two regular hexagonal faces and a thickness of 1 cm. The length of each side of a hexagonal face is 2 cm. A hole with a diameter of 2 cm is drilled through the nut. The density of the metal is 7.9 grams per cubic cm. What is the mass of this nut, to the nearest gram? (Density is mass divided by volume.) We break these subsections down even further to focus on the specific skills necessary to be successful on the SAT Math - Calculator Test. Systematic Approach to the SAT Math - Calculator Test When approaching a question, consider asking yourself the following questions: 1) What concept is being tested? Some questions will only involve one math concept, while others may require you to utilize a variety of mathematical knowledge. For example, the following question tests on a single concept (linear equations/slope). When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface? a) p = 0.44d + 0.77 b) p = 0.44d + 14.74 c) p = 2.2d − 1.1 d) p = 2.2d − 9.9 This question is testing you on your knowledge of slope and linear equations. In this problem, the diving depth is the independent variable, d, and the pressure is the dependent variable, p. Therefore, you are given two coordinate points in the problem, (9 ft, 18.7 lbs) and (14 ft, 20.9 lbs). You should recall the equation for slope is . We can then plug in these values to the equation to solve for the slope: Linear equations are written in the form y = mx + b. We can plug in our slope, 0.44, as well as one of our coordinate points, to solve for the y-intercept, b. y = mx + b 18.7 = 0.44(9) + b b = 14.74 Now we can plug in our m and b to the slope-intercept form linear equation to get y = 0.44x + 14.74 or p = 0.44d + 14.74. Therefore, the answer is B. However, many of the questions on the SAT Math - Calculator section will expect you to apply multiple concepts at once. The question below tests you on two concepts: Rearranging Equations and Simplifying Rational Expressions. If the expression is written in the equivalent form , what is A in terms of x? a) 2x + 1 b) 2x − 1 c) 4x2 d) 4x2 − 1 We are being asked to solve for A in terms of x. To get A by itself, we can subtract from both sides, resulting in . Since there is a common denominator, we can simplify the numerator, resulting in . However, this is not one of the answer choices. We must simplify this rational expression by factoring the numerator, creating . Lastly, the 2x − 1 in the numerator and denominator can cancel each other out, leaving us with 2x + 1. Therefore, the answer is A. 2) Can you recall formulas associated with the tested concept? Write down any formulas you know related to the tested concept. Even if you’re not sure how to solve the problem, seeing the formulas in front of you may cause you to recognize where to plug in the given values to solve the problem. 3) What is given in the problem? Convert any information provided in the problem into a mathematical expression or equation. This can be especially helpful with word problems. When students aren’t sure how to approach a problem, they tend to waste time by sitting there and staring at the problem. However, the answer to a question doesn’t usually magically appear before your eyes. By writing down the information provided in the problem, you can help your brain see the problem in a new way. 4) Draw a picture. Similarly, if a shape or image is described but not provided for you, draw a picture of what the question is telling you. 5) Will the calculator save time or waste time? Just because the calculator is allowed on this math section doesn’t mean that it will be useful for every problem. In fact, many problems in this section do not require a calculator at all, and the use of a calculator may actually slow you down. Take a look at the following question: A researcher places two colonies of bacteria into two petri dishes that each have area 10 square centimeters. After the initial placement of the bacteria (t = 0), the researcher measures and records the area covered by the bacteria in each dish every ten minutes. The data for each dish were fit by a smooth curve, as shown above, where each curve represents the area of a dish covered by bacteria as a function of time, in hours. Which of the following is a correct statement about the data above? a) At time t = 0, both dishes are 100% covered by bacteria. b) At time t = 0, bacteria covers 10% of Dish 1 and 20% of Dish 2. c) At time t = 0, Dish 2 is covered with 50% more bacteria than Dish 1. d) For the first hour, the area covered in Dish 2 is increasing at a higher average rate than the area covered in Dish 1. This question requires you to understand the information provided in a chart or graph. The question tells us that each petri dish has an area of 10 square centimeter. The graph shows that at time t = 0, Dish 1 has 1 sq cm covered, and Dish 2 has 2 sq cm covered. Since each dish has a total area of 10 sq cm, Dish 1 is ¹⁄₁₀ covered and Dish 2 is ²⁄₁₀ covered. Most high school students can recognize that ¹⁄₁₀ = 10% and ²⁄₁₀ = 20%. However, an overreliance on the calculator might result in a student wasting time using the calculator to convert the decimal to a percentage. The calculator can be very useful on some problems, but on others an expectation of calculator usage may result in valuable test time wasted. 6) If all else fails, make an educated guess. If you don’t understand the question after following these steps, or you feel that the question will take too long to answer, circle it and come back later, after completing all of the questions that you do know how to do. If you have time left, try to answer the question, and if not, make an educated guess given the information provided. Tips and Strategies Don’t rush through the easier questions. Since every question on the SAT is worth the same number of points, it is important to make sure that you don’t make any silly mistakes on the easier questions. By taking your time on the easier questions, you can make sure you are getting the maximum number of questions right that you can. Use your calculator to your advantage. Although this section is designated for calculator use, it is not necessary to use a calculator on all of these questions. It is helpful to know which types of questions are easier to do with a calculator and which are not. While the use of a calculator can speed up or aid you in certain questions, other questions may actually take more time with a calculator. For example, it might be faster to solve a quadratic equation or a system of equations with a calculator, but a question dealing with a graph or table may not require any calculations at all. Because the calculator may not be helpful for every problem, make sure you are comfortable switching back and forth between calculator and no calculator. For example, the question below involves interpreting a graph: According to the line graph above, between which two consecutive years was there the greatest change in the number of 3-D movies released? a) 2003-2004 b) 2008-2009 c) 2009-2010 d) 2010-2011 This question requires you to interpret the above graph to determine where the greatest change in number of 3-D movies released occurred. Simply looking at the graph, we can see that the slope is the steepest between 2010-2011, which means that is where the greatest change occurred. We can see that in 2010 there were about 26 3-D movies released, and in 2011 there were about 45 3-D movies released, which is a change of about 19 movies, the largest change over any one-year period. Some students may choose to use their calculator to do the simple arithmetic to determine the change between each of the given years, but that would likely take much more time than just looking at the graph. Answer every question, but don’t spend too much time with the ones you don’t know. There may be questions on the SAT Math - Calculator Test that you don’t know how to do. However, be sure to answer every question, even if you don’t know it, since there are no points for wrong answers. However, once you know that you don’t know how to do a question, mark it and move on from it so you can ensure that you can maximize your points with the ones that you do know. Be sure to leave a bit of time at the end so that you can go back to these questions. Remember that every question is worth the same amount - the easy questions are worth just as much as the hard ones. Therefore, make sure to spend enough time on the earlier questions to ensure you don’t make silly mistakes and lose easy points.
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