SAT Math Practice Questions Set 2

SAT Math Practice Questions Set 2

SAT Math Practice Questions Set 2 is a targeted problem set designed to strengthen the exact algebra, functions, geometry, and data skills tested on the SAT Math section. This page explains the core ideas you need, walks through solved examples, then gives you a full set of SAT Math Practice Questions Set 2 with answers and explanations so you can diagnose weak spots fast.

For official exam structure and scoring context, see the College Board SAT page. For extra skill practice and video explanations, Khan Academy SAT prep is a reliable companion. If you want more sets by difficulty, use these: easy SAT Math practice, medium SAT Math practice, and hard SAT Math practice.

Concept Explanation

SAT Math Practice Questions Set 2 focuses on the high-frequency SAT Math skills: linear equations/inequalities, systems, functions, exponent rules, geometry (including circles), and interpreting data. The SAT rewards efficient reasoning: you often don’t need heavy computation—just the right setup and a clean finish.

1) Linear equations and rearranging

A linear equation is an equation where the variable has power 1, like $2x-3=11$. On the SAT, you’ll often solve for a variable, isolate a parameter, or interpret slope/intercept.

Slope-intercept form

$$y = mx + b$$ where $m$ is slope (rate of change) and $b$ is the $y$-intercept.

Point-slope form

$$y - y_1 = m(x - x_1)$$ helpful when you know a point and a slope.

2) Systems of equations

A system is two (or more) equations solved together to find the values that satisfy all equations at once. Typical methods: substitution, elimination, or interpreting intersections of lines.

3) Functions and evaluating expressions

A function assigns each input exactly one output. SAT questions commonly test evaluating $f(a)$, composing $f(g(x))$, interpreting graphs/tables, and identifying linear vs. non-linear change.

4) Exponents and radicals

Exponent rules simplify expressions by combining powers and bases. The SAT frequently uses these identities:

• $$a^m a^n = a^{m+n}$$
• $$\frac{a^m}{a^n} = a^{m-n}$$ (for $a \neq 0$)
• $$(a^m)^n = a^{mn}$$
• $$a^{-n} = \frac{1}{a^n}$$
• $$\sqrt{a} = a^{1/2}$$

5) Geometry basics you actually use

SAT geometry is mostly about a small set of formulas plus smart diagram reading. Common tools:

• Triangle area: $$A = \frac{1}{2}bh$$
• Circle area and circumference: $$A = \pi r^2, \quad C = 2\pi r$$
• Pythagorean theorem: $$a^2 + b^2 = c^2$$

For a quick reference on circle definitions and parts, see Wikipedia’s circle article. For official math practice framing, the SAT suite overview at College Board practice and preparation is useful.

6) Data: mean, median, percent, and linear models

Data questions test whether you can interpret summaries and relationships, not whether you can do long arithmetic. Know percent change and mean/median effects when adding or removing values.

• Percent change from $A$ to $B$: $$\frac{B-A}{A} \times 100\%$$

If you want focused algebra-only sets that pair well with SAT Math Practice Questions Set 2, use SAT Algebra practice questions with answers and medium SAT Algebra practice.

Solved Examples

Solved examples show the exact reasoning patterns you’ll reuse in SAT Math Practice Questions Set 2: isolate variables, use structure, and check for traps like extraneous solutions or misread units.

1. Linear equation with distribution

   Solve $3(2x-5)+4=2x+1$.

   1. Distribute: $3(2x-5)=6x-15$.
   2. Rewrite: $6x-15+4=2x+1 \Rightarrow 6x-11=2x+1$.
   3. Subtract $2x$: $4x-11=1$.
   4. Add 11: $4x=12$.
   5. Divide by 4: $x=3$.

2. System by elimination

   Solve the system:

   $$\begin{aligned} 2x+y&=11\\ 3x-y&=4 \end{aligned}$$
   1. Add the equations to eliminate $y$: $(2x+y)+(3x-y)=11+4\Rightarrow 5x=15$.
   2. Solve: $x=3$.
   3. Substitute into $2x+y=11$: $2(3)+y=11\Rightarrow y=5$.
   4. Solution: $(x,y)=(3,5)$.

3. Function evaluation and simplification

   Let $f(x)=2x^2-3x+1$. Find $f(-2)$.

   1. Substitute $x=-2$: $f(-2)=2(-2)^2-3(-2)+1$.
   2. Compute powers: $(-2)^2=4$, so $2\cdot 4=8$.
   3. Compute $-3(-2)=+6$.
   4. Add: $8+6+1=15$.
   5. Answer: $15$.

4. Circle geometry (area difference)

   A circle has radius 6. Another circle has radius 10. What is the difference in their areas?

   1. Use $A=\pi r^2$.
   2. Larger area: $\pi(10^2)=100\pi$.
   3. Smaller area: $\pi(6^2)=36\pi$.
   4. Difference: $100\pi-36\pi=64\pi$.

Practice Questions

These SAT Math Practice Questions Set 2 problems cover easy, medium, and hard difficulty across algebra, functions, geometry, and data—similar to what you’ll see on test day.

1. (Easy) Solve for $x$: $5x-7=3x+9$.
2. (Easy) If $g(x)=x-4$, what is $g(12)$?
3. (Easy) A jacket is discounted from $80 to $60. What is the percent decrease?

4. (Medium) Solve the system: $$\begin{aligned} x+y&=9\\ 2x-y&=6 \end{aligned}$$
5. (Medium) Simplify: $\frac{(2a^3b^2)(3a^2b)}{6ab^2}$.
6. (Medium) The line passes through $(4,1)$ and $(10,13)$. What is its slope?
7. (Hard) If $f(x)=kx+3$ and $f(5)=18$, what is $k$?
8. (Hard) Solve for $x$: $\sqrt{x+5}=x-1$.
9. (Hard) A rectangle has perimeter 50 and length 3 more than twice its width. Find the width.
10. (Hard) The mean of 6 numbers is 12. Five of the numbers are 10, 11, 12, 12, and 15. What is the sixth number?

Answers & Explanations

These are the full solutions to SAT Math Practice Questions Set 2, written to show the fastest SAT-style path and the most common mistakes to avoid.

1. Answer: $x=8$

   Explanation: Start with $5x-7=3x+9$. Subtract $3x$ from both sides to group $x$-terms: $2x-7=9$. Add 7: $2x=16$. Divide by 2: $x=8$.

2. Answer: $8$

   Explanation: With $g(x)=x-4$, plug in 12: $g(12)=12-4=8$.

3. Answer: $25\%$

   Explanation: Percent decrease is $$\frac{ \text{decrease}}{ \text{original}} \times 100\%$$ The decrease is $80-60=20$. So $$\frac{20}{80} \times 100\% = 25\%$$

4. Answer: $(x,y)=(5,4)$

   Explanation: Add the equations to eliminate $y$: $$(x+y)+(2x-y)=9+6 \Rightarrow 3x=15 \Rightarrow x=5$$ Substitute into $x+y=9$: $5+y=9\Rightarrow y=4$.

5. Answer: $a^4b$

   Explanation: $$\frac{(2a^3b^2)(3a^2b)}{6ab^2}$$ Multiply the numerator: coefficients $2\cdot 3=6$, and add exponents for like bases: $$(2a^3b^2)(3a^2b)=6a^{3+2}b^{2+1}=6a^5b^3$$ Now divide by $6ab^2$: $$\frac{6a^5b^3}{6ab^2}=a^{5-1}b^{3-2}=a^4b$$

6. Answer: $2$

   Explanation: Slope is rise over run: $$m=\frac{13-1}{10-4}=\frac{12}{6}=2$$

7. Answer: $3$

   Explanation: Given $f(x)=kx+3$ and $f(5)=18$: $$5k+3=18 \Rightarrow 5k=15 \Rightarrow k=3$$

8. Answer: $x=4$

   Explanation: Start with $$\sqrt{x+5}=x-1$$ Domain restriction: right side must be nonnegative, so $x-1\ge 0\Rightarrow x\ge 1$. Square both sides: $$x+5=(x-1)^2=x^2-2x+1$$ Bring all terms to one side: $$0=x^2-3x-4$$ Factor: $$x^2-3x-4=(x-4)(x+1)=0$$ So $x=4$ or $x=-1$. Only $x=4$ satisfies $x\ge 1$ and the original equation. Check: $\sqrt{9}=3$ and $4-1=3$. Works.

9. Answer: $11$

   Explanation: Let width be $w$. Length is $2w+3$. Perimeter 50 means: $$2\big((2w+3)+w\big)=50$$ Simplify inside: $(2w+3)+w=3w+3$. Then: $$2(3w+3)=50 \Rightarrow 6w+6=50 \Rightarrow 6w=44 \Rightarrow w=\frac{44}{6}=\frac{22}{3}$$ That value is valid algebraically, but check the wording: “length 3 more than twice its width” is $L=2w+3$, which we used correctly. So the width is $\frac{22}{3}$ (about $7.33$).

10. Answer: $12$

    Explanation: Mean of 6 numbers is 12, so the total sum is $6\cdot 12=72$. Sum of the five known numbers is $10+11+12+12+15=60$. The sixth number is $72-60=12$.

If you want more targeted practice after SAT Math Practice Questions Set 2, these pages pair well by difficulty and topic: medium SAT Math practice questions and hard SAT Algebra practice questions.

Frequently Asked Questions

These FAQs answer common “what is,” “how to,” and “why” questions students ask while using SAT Math Practice Questions Set 2.

What is the best way to use SAT Math Practice Questions Set 2?

Do the practice questions timed, then review every missed question by rewriting the setup and identifying the exact skill (systems, exponents, functions, geometry, or data). Re-do missed questions 48 hours later without notes.

How many SAT Math questions should I do per day to improve?

Doing 10–20 focused questions daily with full error review usually beats doing 50 questions with no review. Consistency and correcting patterns (like sign errors or wrong equation setup) drive score gains.

Why do I get square root equations wrong on the SAT?

Squaring both sides can create extraneous solutions, so you must check answers in the original equation. Also watch domain restrictions like requiring $x-1\ge 0$ when it equals a square root.

How do I know whether to use substitution or elimination for a system?

Use elimination when coefficients line up easily (or can be made to line up with small multipliers). Use substitution when one equation is already isolated or easy to isolate, such as $y=2x-1$.

What geometry formulas are most common on SAT Math?

Circle area/circumference, triangle area, and the Pythagorean theorem show up often. You also need comfort with slope and distance on the coordinate plane, especially when geometry is embedded in a graph.

Where can I find official SAT-style practice besides this set?

The College Board practice resources and Khan Academy SAT prep provide official-style questions and explanations aligned to SAT content.