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1.2: Practice Questions

Difficulty Level: At Grade Created by: CK-12

Directions: The following question (1) is an example of a grid-in math problem. On the SAT, you will solve the problem and indicate your answer by darkening the ovals on the special grid provided. Since you do not have this type of answer sheet to practice on, simply write your response. For more information about grid-in questions, please visit sat.collegeboard.com/practice/sat-practice-questions-math/student-produced-response.

1. (Numbers and Operations) — The average of five non-repeating positive odd numbers is 73\begin{align*}73\end{align*}. If x\begin{align*}x\end{align*} is the greatest of these integers, what is the greatest possible value of x\begin{align*}x\end{align*}?

Directions: For this section, solve each problem and decide which is the best of the choices given. You may use any available space for scratchwork.

1. (Numbers and Operations) — How many unique real roots does the equation y=x210x+25\begin{align*}y = x^2 - 10x + 25\end{align*}have?
1. No solutions.
2. 0\begin{align*}0\end{align*}
3. 1\begin{align*}1\end{align*}
4. 2\begin{align*}2\end{align*}
5. 3\begin{align*}3\end{align*}
2. (Algebra and Functions) — If g(x)=4x4x\begin{align*}g(x) = 4x - 4x\end{align*}, what is the value of g(32)\begin{align*}g \left(\frac{3}{2}\right)\end{align*}?
1. 2\begin{align*}-2\end{align*}
2. 6\begin{align*}6\end{align*}
3. 8\begin{align*}8\end{align*}
4. 2\begin{align*}2\end{align*}
5. 0\begin{align*}0\end{align*}
3. (Algebra and Functions) — If f(x)=x+9\begin{align*}f(x) = x + 9\end{align*}, which of the following is a solution of f(5a)+3=f(3a)+11\begin{align*}f(5a) + 3 = f(3a) + 11\end{align*}? In other words, what might be the value of ‘a\begin{align*}a\end{align*}’?
1. There are no solutions.
2. 6\begin{align*}6\end{align*}
3. 8\begin{align*}8\end{align*}
4. 53\begin{align*}\frac{5}{3}\end{align*}
5. 4\begin{align*}4\end{align*}
4. (Algebra and Functions) — If the mean of x\begin{align*}x\end{align*} and 4x\begin{align*}4x\end{align*} is 10\begin{align*}10\end{align*}, then x=\begin{align*}x =\end{align*}
1. 20\begin{align*}20\end{align*}
2. 16\begin{align*}16\end{align*}
3. 4\begin{align*}4\end{align*}
4. 10\begin{align*}10\end{align*}
5. 5\begin{align*}5\end{align*}
5. (Geometry) — If a line is perpendicular to the line y=3x4\begin{align*}y = 3x - 4\end{align*} and passes through the point (0,6)\begin{align*}(0, 6)\end{align*}, what is the equation of the perpendicular line?
1. y=3x+6\begin{align*}y = 3x + 6\end{align*}
2. y=3x+6\begin{align*}y = -3x + 6\end{align*}
3. y=13x+6\begin{align*}y = \frac{-1}{3x + 6}\end{align*}
4. y=13x6\begin{align*}y = \frac{-1}{3x - 6}\end{align*}
5. y=13x+6\begin{align*}y = \frac{1}{3x + 6}\end{align*}
6. (Geometry) — What is the height of a building if the angle to the top is 27\begin{align*}27^\circ\end{align*} when you are standing 150 feet\begin{align*}150 \ feet\end{align*}away from the building’s base? Round to the nearest whole number.
1. 68\begin{align*}68\end{align*}
2. 134\begin{align*}134\end{align*}
3. 76\begin{align*}76\end{align*}
4. 330\begin{align*}330\end{align*}
5. 168\begin{align*}168\end{align*}
7. (Geometry)Which of the following equations defines g(x)\begin{align*}g(x)\end{align*} in terms of f(x)\begin{align*}f(x)\end{align*}?
1. g(x)=f(x2)+3\begin{align*}g(x) = f(x - 2) + 3\end{align*}
2. g(x)=f(x+2)+3\begin{align*}g(x) = f(x + 2) + 3\end{align*}
3. g(x)=f(x2)3\begin{align*}g(x) = f(x - 2) -3\end{align*}
4. \begin{align*}g(x) = f(x + 2) - 3\end{align*}
5. \begin{align*}g(x) = f(x - 2)\end{align*}
8. (Probability and Statistics)The following chart gives the graduation ages of 10 students?

What is the median age of the graduating students?

1. \begin{align*}16\end{align*}
2. \begin{align*}16.5\end{align*}
3. \begin{align*}17\end{align*}
4. \begin{align*}17.5\end{align*}
5. \begin{align*}18\end{align*}

10. (Probability and Statistics)Assume that the edge of the smaller shaded square is \begin{align*}1 \ inch\end{align*} and the edge of the larger square is \begin{align*}2 \ inches\end{align*}.

What percent of the diagram is unshaded?

1. \begin{align*}35\%\end{align*}
2. \begin{align*}30\%\end{align*}
3. \begin{align*}15\%\end{align*}
4. \begin{align*}10\%\end{align*}
5. \begin{align*}25\%\end{align*}

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