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

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?

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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 $127-120=7.$

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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 $M$?

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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 $M(10, 10):$

$d=\sqrt{(10-6)^2 + (10-7)^2} = \sqrt{4^2 + 3^2}=\sqrt{16 + 9}=\sqrt{25}=5.$

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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.

To study further for the SAT, visit:

• SAT Numbers and Operations
• SAT Algebra
• SAT Functions

• SAT General Tips