SAT Algebra Student-Produced Response
To solve SAT algebra student-produced response questions, you need to know how to:
- manipulate algebraic expressions
- work with polynomials
- work with fractions and decimals
- work with ratios, proportions and percents
- apply the rules of exponents
- solve simple inequalities
- work with absolute value
- evaluate functions
- work with linear and quadratic functions
- apply the definition of inverse and direct variation
- translate word problems into math
- solve word problems
Examples
If \(B=126.43,\) what is the difference between \(B\) when it is rounded up to the nearest ones and B when it is rounded down to the nearest tens?
Correct Answer: 7
Solution:
Tip: Follow directions exactly.
Notice that we are to round \(126.43\) up to the nearest ones although the tenths digit is less than 5. Rounding \(12\underline{6}.43\) up to the nearest ones, \(B\) becomes 127.Similarly, we are instructed to round 126.43 down to the nearest tens even though the ones digit is greater than 5. Rounding \(1\underline{2}6.43\) down to the nearest tens, \(B\) becomes 120.
The difference is \(127-120=7.\)
Common Mistakes:
- Round off / down 126.43 to the nearest one to get 126.
- Round off / up 126.43 to the nearest ten to get 130.
If you got this problem wrong, you should review SAT Numbers.
In the coordinate plane, the midpoint between \(A(6, 7)\) and \(B(14, 13)\) is \(M(x, y).\) What is the distance between \(A\) and \(M\)?
Correct Answer: 5
Solution:
Tip: Midpoint formula: \(M=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right).\)
Tip: Distance formula: \(d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}.\)
We find \(M\) using the midpoint formula:\[M(x, y) = \left(\frac{6+14}{2}, \frac{7+13}{2}\right) = \left(\frac{20}{2}, \frac{20}{2}\right)=\left(10, 10\right)\]
Now we use the distance formula to find the distance between \(A(6, 7)\) and \(M(10, 10):\)
\(d=\sqrt{(10-6)^2 + (10-7)^2} = \sqrt{4^2 + 3^2}=\sqrt{16 + 9}=\sqrt{25}=5.\)
Common Mistakes:
Subtracting in the Midpoint Formula instead of adding, like this: \(M=\left(\frac{x_{1}\fbox{-}x_{2}}{2}, \frac{y_{1}\fbox{-}y_{2}}{2}\right).\)
Subtracting in the Distance Formula instead of adding, like this: \(d=\sqrt{(x_{2}-x_{1})^{2}\fbox{-}(y_{2}-y_{1})^{2}}.\)
Adding in the distance formula instead of subtracting, like this:\(d=\sqrt{(x_{2}\fbox{+}x_{1})^{2}+(y_{2}\fbox{+}y_{1})^{2}}.\)
Finding the distance between \(A\) and \(B\) or between \(B\) and \(M,\) instead of between \(A\) and \(M\).
Mixing up the Midpoint and Distance formulas.
If you got this problem wrong, you should review SAT Coordinate Geometry.
For Further Study
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