SHSAT Math FREE Sample Practice Questions

3- B
The area of the square is 595.36. Therefore, the side of the square is the square root of the area.
\(\sqrt{595.36}=24.4\)
Four times the size of the square is the perimeter:\(4 \times 24.4 = 97.6\) For additional educational resources, .

4- A
The width of the rectangle is twice its length. Let \(x\) be the length. Then, width \(=2x\)
Perimeter of the rectangle is (2 (width + length) \(= 2(2x+x)=60 {\Rightarrow} 6x=60 {\Rightarrow} x=10\)
The length of the rectangle is 10 meters. For additional educational resources, .

5- D
average \(= \frac{sum \space of \space terms}{number \space of \space terms} {\Rightarrow} (average \space of \space 6 \space numbers) \space 12 = \frac{sum \space of \space terms}{6} ⇒\) sum of 6 numbers is
\(12 {\times} 6 = 72\)
(average of 4 numbers) 10 \(= \frac{sum \space of \space terms}{4}{\Rightarrow}\) sum of 4 numbers is \(10 {\times} 4 = 40\)
sum of 6 numbers \(-\) sum of 4 numbers = sum of 2 numbers
\(72 – 40 = 32\)
average of 2 numbers \(= \frac{32}{2} = 16 \) For additional educational resources, .

6- C
Let \(x\) be the number. Write the equation and solve for \(x\).
\(40\%\) of \(x=4{\Rightarrow} 0.40 x=4 {\Rightarrow} x=4 {\div}0.40=10\) For additional educational resources, .

The Ultimate Algebra Bundle From Pre-Algebra to Algebra II

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

7- C
First, find the sum of five numbers.
average \(=\frac{ sum \space of \space terms }{ number \space of \space terms } ⇒ 24 = \frac{ sum \space of \space 5 \space numbers }{5}
⇒\) sum of 5 numbers \(= 24 × 5 = 120\)
The sum of 5 numbers is 120. If a sixth number, 42 is added to these numbers, then the sum of 6 numbers is 162.
\(120 + 42 = 162\)
average \(=\frac{ sum \space of \space terms }{ number \space of \space terms } = \frac{162}{6}=27\) For additional educational resources, .

8- C
The ratio of boys to girls is 4:7.
Therefore, there are 4 boys out of 11 students.
First, divide the total number of students by 11, then multiply the result by 4.
\(44 {\div} 11 = 4 {\Rightarrow} 4 {\times} 4 = 16\)
There are 16 boys and \(28 (44 – 16)\) girls. So, 12 more boys should be enrolled to make the ratio 1:1 For additional educational resources, .

9- 2
Solve for \(y\).
\(4x-2y=6 {\Rightarrow} -2y=6-4x {\Rightarrow} y=2x-3\)
The slope of the line is 2. For additional educational resources, .

10- A
Let \(x\) be the number of new shoes the team can purchase. Therefore, the team can purchase \(120 x\).
The team had $20,000 and spent $14000. Now the team can spend on new shoes $6000 at most.
Now, write the inequality:
\(120x+14,000 {\leq}20,000\) For additional educational resources, .

The Ultimate Middle School Math Bundle Grades 6-8

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

Looking for the best resource to help you succeed on the SHSAT Math test? For additional educational resources, .

The Best Books to Ace the SHSAT Math Test

SHSAT Math Practice Workbook 2024 The Most Comprehensive Review for the Math Section of the SHSAT Test

Download

$20.99 Original price was: $20.99.$16.99Current price is: $16.99.

Rated 4.40 out of 5 based on 179 customer ratings

Satisfied 165 Students

Five SHSAT Math Sample Questions: Complete Solutions

The SHSAT (Specialized High School Admissions Test) math section tests speed, accuracy, and logical reasoning. Here are five realistic problems representing different question types you’ll encounter.

Problem 1: Arithmetic with Fractions and Decimals

Sample Question: \(0.6 + \frac{3}{4} – 0.05\) = ?

Solution: Convert to decimals: \(0.6 + 0.75 – 0.05 = 1.3\). Or convert to fractions if you prefer: \(\frac{3}{5} + \frac{3}{4} – \frac{1}{20} = \frac{12}{20} + \frac{15}{20} – \frac{1}{20} = \frac{26}{20} = \frac{13}{10} = 1.3\).

SHSAT Tip: Choose your approach based on what’s easier. If answers are decimals, stay with decimals. If they’re fractions, convert to fractions.

Problem 2: Percent and Proportional Reasoning

Sample Question: A store marks up all items 40%. If an item costs \$60 to the store, what is its sale price?

Solution: Markup is 40% of \$60: \(0.40 \times 60 = 24\). Sale price: \(60 + 24 = 84\). Or: \(60 \times 1.40 = 84\).

SHSAT Tip: Markup means add to cost. Discount means subtract from price. Don’t confuse them.

Problem 3: Algebra with Variables

Sample Question: If \(3a + 2 = 5a – 6\), what is \(a\)?

Solution: Rearrange: \(3a – 5a = -6 – 2\). Simplify: \(-2a = -8\). Divide: \(a = 4\).

SHSAT Tip: Move variable terms to one side and constants to the other. Keep track of signs carefully.

Problem 4: Data Interpretation with Averages

Sample Question: Maria’s test scores are 78, 85, 92, and 88. What must she score on the next test to have an average of 86?

Solution: Current total: \(78 + 85 + 92 + 88 = 343\). For an average of 86 over 5 tests: \(5 \times 86 = 430\). So the 5th score must be: \(430 – 343 = 87\).

SHSAT Tip: Use total = average × count. This is faster than setting up an equation.

Problem 5: Geometry with Angles

Sample Question: Two angles in a triangle measure 45° and 63°. What’s the measure of the third angle?

Solution: Angles in a triangle sum to 180°: \(45 + 63 + x = 180\). So \(x = 180 – 45 – 63 = 72\)°.

SHSAT Tip: Know the angle rules: triangle angles sum to 180°, straight line = 180°, angles around a point = 360°.

SHSAT Math Test Format

The SHSAT math section has about 52 questions in 90 minutes. That’s roughly 100 seconds per question, but timing strategy matters. Easier questions early let you move quickly. Save harder problems for when you have mental energy. Use estimation and elimination: cross out obviously wrong answers to improve your odds on tough questions.

The test focuses on arithmetic, algebra, geometry, and data interpretation. There are no obscure topics—everything is standard middle/early high school math. Your advantage comes from speed and accuracy, not exotic knowledge.

Study Tips for SHSAT Success

Take full-length SHSAT math practice tests under timed conditions. Analyze your mistakes—were they conceptual or careless? Did you run out of time? Focus accordingly. Build speed by doing easier problems in your head. Know essential SHSAT formulas cold.

Consistency beats intensity. Practice 30 minutes daily for 2-3 months beats cramming the week before. Each practice test is diagnostic—it tells you where to focus next.

Common SHSAT Math Mistakes

Don’t rush and misread the question. Don’t forget to check if a diagram is drawn to scale (often it’s not). Don’t assume geometric figures have special properties unless stated. Don’t make careless arithmetic errors—double-check addition and subtraction. Don’t leave questions blank; even a guess is better, and partial credit sometimes applies.

Read each problem twice. The first time, understand what’s being asked. The second time, solve it. This seemingly slow approach actually saves time by preventing restarts.

Timeline and Benchmarks

If you’re taking the SHSAT this year, start preparing 2-3 months ahead. Month 1: Review fundamentals in arithmetic and algebra. Month 2: Practice 1-2 problems per topic daily. Month 3: Full-length tests weekly, with detailed error analysis. Your goal is to score in the 90th percentile or higher for admission to top SHSAT schools—that typically means 75%+ accuracy.

You’ve got this. The math tested is straightforward. Your job is recognizing patterns and working methodically.

Five SHSAT Math Sample Questions: Complete Solutions

The SHSAT (Specialized High School Admissions Test) math section tests speed, accuracy, and logical reasoning. Here are five realistic problems representing different question types you’ll encounter.

Problem 1: Arithmetic with Fractions and Decimals

Sample Question: \(0.6 + \frac{3}{4} – 0.05\) = ?

Solution: Convert to decimals: \(0.6 + 0.75 – 0.05 = 1.3\). Or convert to fractions if you prefer: \(\frac{3}{5} + \frac{3}{4} – \frac{1}{20} = \frac{12}{20} + \frac{15}{20} – \frac{1}{20} = \frac{26}{20} = \frac{13}{10} = 1.3\).

SHSAT Tip: Choose your approach based on what’s easier. If answers are decimals, stay with decimals. If they’re fractions, convert to fractions.

Problem 2: Percent and Proportional Reasoning

Sample Question: A store marks up all items 40%. If an item costs \$60 to the store, what is its sale price?

Solution: Markup is 40% of \$60: \(0.40 \times 60 = 24\). Sale price: \(60 + 24 = 84\). Or: \(60 \times 1.40 = 84\).

SHSAT Tip: Markup means add to cost. Discount means subtract from price. Don’t confuse them.

Problem 3: Algebra with Variables

Sample Question: If \(3a + 2 = 5a – 6\), what is \(a\)?

Solution: Rearrange: \(3a – 5a = -6 – 2\). Simplify: \(-2a = -8\). Divide: \(a = 4\).

SHSAT Tip: Move variable terms to one side and constants to the other. Keep track of signs carefully.

Problem 4: Data Interpretation with Averages

Sample Question: Maria’s test scores are 78, 85, 92, and 88. What must she score on the next test to have an average of 86?

Solution: Current total: \(78 + 85 + 92 + 88 = 343\). For an average of 86 over 5 tests: \(5 \times 86 = 430\). So the 5th score must be: \(430 – 343 = 87\).

SHSAT Tip: Use total = average × count. This is faster than setting up an equation.

Problem 5: Geometry with Angles

Sample Question: Two angles in a triangle measure 45° and 63°. What’s the measure of the third angle?

Solution: Angles in a triangle sum to 180°: \(45 + 63 + x = 180\). So \(x = 180 – 45 – 63 = 72\)°.

SHSAT Tip: Know the angle rules: triangle angles sum to 180°, straight line = 180°, angles around a point = 360°.

SHSAT Math Test Format

The SHSAT math section has about 52 questions in 90 minutes. That’s roughly 100 seconds per question, but timing strategy matters. Easier questions early let you move quickly. Save harder problems for when you have mental energy. Use estimation and elimination: cross out obviously wrong answers to improve your odds on tough questions.

The test focuses on arithmetic, algebra, geometry, and data interpretation. There are no obscure topics—everything is standard middle/early high school math. Your advantage comes from speed and accuracy, not exotic knowledge.

Study Tips for SHSAT Success

Take full-length SHSAT math practice tests under timed conditions. Analyze your mistakes—were they conceptual or careless? Did you run out of time? Focus accordingly. Build speed by doing easier problems in your head. Know essential SHSAT formulas cold.

Consistency beats intensity. Practice 30 minutes daily for 2-3 months beats cramming the week before. Each practice test is diagnostic—it tells you where to focus next.

Common SHSAT Math Mistakes

Don’t rush and misread the question. Don’t forget to check if a diagram is drawn to scale (often it’s not). Don’t assume geometric figures have special properties unless stated. Don’t make careless arithmetic errors—double-check addition and subtraction. Don’t leave questions blank; even a guess is better, and partial credit sometimes applies.

Read each problem twice. The first time, understand what’s being asked. The second time, solve it. This seemingly slow approach actually saves time by preventing restarts.

Timeline and Benchmarks

If you’re taking the SHSAT this year, start preparing 2-3 months ahead. Month 1: Review fundamentals in arithmetic and algebra. Month 2: Practice 1-2 problems per topic daily. Month 3: Full-length tests weekly, with detailed error analysis. Your goal is to score in the 90th percentile or higher for admission to top SHSAT schools—that typically means 75%+ accuracy.

You’ve got this. The math tested is straightforward. Your job is recognizing patterns and working methodically.