FREE SIFT Math Practice Test
Free SIFT Math Practice Test (Timed & Auto-Scored)
Try this full-length, 30-question SIFT Math Skills practice test. It runs on a 40-minute timer with no calculator, just like the real test, and covers arithmetic, algebra, geometry, data and probability, and applied word problems. You get an instant 20 to 80 score estimate, a topic-by-topic breakdown, and full step-by-step solutions.
TL;DR: Aiming for Army aviation? The SIFT is the gate, and its Math Skills Test is tight: 40 questions in 40 minutes, no calculator allowed. It’s one of seven subtests on the Army’s Selection Instrument for Flight Training. Take this free practice test for a realistic look at the pacing and content. You’ll learn the rhythm as much as the math, which is half the battle on a no-calculator section.
Key takeaways:
- SIFT Math Skills Test has 40 questions and a 40-minute time limit.
- No calculator allowed on the math subtest.
- Math Skills is one of 7 subtests on the full SIFT (about 3 hours total).
- Minimum qualifying SIFT composite score is 40; competitive applicants score 50+.
- Test is administered on a computer at MEPS or a similar Army testing site.
Welcome to our FREE SIFT Math practice test, with answer key and answer explanations. This practice test’s realistic format and high-quality practice questions can help you succeed on the SIFT Math test. Does the test closely match what you will see on the real SIFT and it comes with detailed answer explanations.
For this practice test, we’ve selected 20 real questions from past exams for your SIFT Practice test. You will have the chance to try out the most common SIFT Math questions. For every question, there is an in-depth explanation of how to solve the question and how to avoid mistakes next time.
Use our free SIFT Math practice tests and study resources (updated for 2022) to ace the SIFT Math test! Make sure to follow some of the related links at the bottom of this post to get a better idea of what kind of mathematics questions you need to practice.
The Absolute Best Book to Ace the SIFT Math Test
1- Out of \(55{,}000\) voters in a city, \(2{,}500\) voted for a particular candidate. What fraction of voters voted for this candidate?
A. \(\frac{1}{22}\)
B. \(\frac{1}{20}\)
C. \(\frac{1}{18}\)
D. \(\frac{1}{15}\)
2- What is the value of \(4 \div \frac{1}{6}\)?
A. \(\frac{2}{3}\)
B. \(6\)
C. \(18\)
D. \(24\)
3- Simplify \((6x^3-8x^2+2x^4 )-(4x^2-2x^4+2x^3 )\).
A. \(2x^4+4x^3-4x^2\)
B. \(4x^4+4x^3-12x^2\)
C. \(4x^4-4x^3-12x^2\)
D. \(8x^4+8x^3-12x^2\)
4- The population of a city increased by \(15\%\) in the first year and by \(20\%\) in the second year. What is the total percent increase in population over the two years?
A. \(35\%\)
B. \(37\%\)
C. \(38\%\)
D. \(40\%\)
5- What is the surface area of a cylinder with a diameter of \(6\) inches and a height of \(8\) inches?
A. \(48 {\pi} \space in^2\)
B. \(57 {\pi} \space in^2\)
C. \(66 {\pi} \space in^2\)
D. \(288 {\pi} \space in^2\)
6- A cruise line ship left Port A and traveled 80 miles due west and then 150 miles due north. At this point, what is the shortest distance from the cruise to port A in miles? ____________
7- A shirt costing $200 is discounted \(15\%\). After a month, the shirt is discounted another \(15\%\). Which of the following expressions can be used to find the selling price of the shirt?
A. \((200) (0.70)\)
B. \((200) – 200 (0.30)\)
C. \((200) (0.15) – (200) (0.15)\)
D. \((200) (0.85) (0.85)\)
8- Solve: \(5 + 8 \times (- 2) – [4 + 22 \times 5] \div 6 = ? \)
A. \(-30\)
B. \(-20\)
C. \(-10\)
D. 0
9- Which of the following points lies on the line \(x+2y=4\)?
A. \((-2, 3)\)
B. \((1, 2)\)
C. \((-1, 3)\)
D. \((-3, 4)\)
10- 5 less than twice a positive integer is 83. What is the integer?
A. 39
B. 41
C. 42
D. 44
11- 11 yards 6 feet and 4 inches equal to how many inches?
A. 388
B. 468
C. 472
D. 476
12- Mr. Carlos’s family is choosing a menu for their reception. They have 3 choices of appetizers, 5 choices of entrees, and 4 choices of cake. How many different menu combinations are possible for them to choose from?
A. 12
B. 32
C. 60
D. 120
13- The average of five consecutive numbers is 38. What is the smallest number?
A. 38
B. 36
C. 34
D. 12
14- What is the difference between the smallest 4-digit number and the biggest 4-digit number?
A. 6666
B. 6789
C. 8888
D. 8999
15- How many tiles of \(8 cm^2 \) are needed to cover a floor of dimension 6 cm by 24 cm?
A. 6
B. 12
C. 18
D. 24
16- A ladder leans against a wall forming a \(60^ \circ \) angle between the ground and the ladder. If the bottom of the ladder is 30 feet away from the wall, how long is the ladder?
A. 30 feet
B. 40 feet
C. 50 feet
D. 60 feet
17- The average weight of 18 girls in a class is 60 kg, and the average weight of 32 boys in the same class is 62 kg. What is the average weight of all the 50 students in that class?
A. 60
B. 61.28
C. 61.68
D. 62.90
18- An angle is equal to one-fifth of its supplement. What is the measure of that angle?
A. 20
B. 30
C. 45
D. 60
19- In a stadium, the ratio of home fans to visiting fans in a crowd is 5:7. Which of the following could be the total number of fans in the stadium?
A. 12,324
B. 42,326
C. 44,566
D. 66,812
20- If \(40\%\) of a class are girls, and \(25\%\) of girls play tennis, what percent of the class plays tennis?
A. \(10\%\)
B. \(15\%\)
C. \(20\%\)
D. \(40\%\)
Best SIFT Math Prep Resource for 2027
Answers:
1- A
2,500 out of 55,000 equals to \(\frac{2500}{55000}= \frac{25}{550}= \frac{1}{22} \)
2- D
\(4 \div \frac{1}{6} = 24 \)
3- B
Simplify and combine like terms.
\((6x^3-8x^2+2x^4 )-(4x^2-2x^4+2x^3 ) {\Rightarrow} (6x^3-8x^2+2x^4 )-4x^2+2x^4-2x^3 {\Rightarrow}
4x^4+4x^3-12x^2\)
4- C
the population is increased by \(15\%\) and \(20\%\).
\(15\%\) increase changes the population to \(115\%\) of original population.
For the second increase, multiply the result by \(120\%\).
\((1.15) \times (1.20) = 1.38 = 138\%\)
38 percent of the population has increased after two years.
5- C
Surface Area of a cylinder \(= 2\pi\) r (r + h),
The radius of the cylinder is \(3(6 \div 2)\) inches and its height is 8 inches. Therefore,
Surface Area of a cylinder \(= 2\pi (3) (3 + 8) = 66\pi\)
6- 170
Use the information provided in the question to draw the shape.<br />\(80^2 + 150^2 = c^2 {\Rightarrow} 6400 + 22500 = c^2 {\Rightarrow} 28900 = c^2 {\Rightarrow} c = 170\).</p>
<p>7- <strong>D</strong><br />To find the discount, multiply the number by (\(100{\%} – \)Rate of discount).<br />Therefore, for the first discount we get: \((200) (100{\%} – 15{\%}) = (200) (0.85) = 170\)<br />For the next \(15{\%}\) discount: \((200) (0.85) (0.85)\)</p>
<p>8- <strong>A</strong><br />Use PEMDAS (order of operation):<br />\(5 + 8 \times (-2) – [4 + 22 \times 5] \div 6 = 5 + 8 \times (-2) – [4 + 110] \div 6 = 5 + 8 \times (-2) – [114] \div 6 = 5 + (-16) – 19<br />5 + (-16) – 19 = -11 – 19 = -30\)</p>
<p>9- <strong>A</strong><br />\(x+2y=4\). Plug in the values of \(x\) and \(y\) from the choices provided. Then:<br />A. \((-2,3) x+2y=4(\rightarrow )-2+2(3)=4(\rightarrow )-2+6=4\) This is true!<br />B. \((1,2) x+2y=4(\rightarrow )1+2(2)=4(\rightarrow )1+4=4\) (This is NOT true!)<br />C. \((-1,3) x+2y=4(\rightarrow )-1+2(3)=4(\rightarrow )-1+6=4\) (This is NOT true!)<br />D. \((-3,4) x+2y=4(\rightarrow )-3+2(4)=4(\rightarrow )-3+8=4\) (This is NOT true!)</p>
<p>10- <strong>D</strong><br />Let \(x\) be the integer. Then:<br />\(2x – 5 = 83\)<br />Add 5 both sides: \(2x = 88\)<br />Divide both sides by \(2: x = 44\)</p>
<p>11- <strong>C</strong><br />\(11 \times 36 + 6 \times 12 + 4 = 472\)</p>
<p>12- <strong>C</strong><br />To find the number of possible outfit combinations, multiply the number of options for each factor:<br />\(3 \times 5 \times 4 = 60\)</p>
<p>13- <strong>B</strong><br />Let \(x\) be the smallest number. Then, these are the numbers:<br />\(x, x+1, x+2, x+3, x+4 \)<br />average \(= \frac{sum of terms}{number of terms} \Rightarrow 38 = \frac{x+(x+1)+(x+2)+(x+3)+(x+4)}{5} \Rightarrow 38= \frac{5x+10}{5} \Rightarrow 190 = 5x+10 \Rightarrow 180 = 5x \Rightarrow x=36 \)</p>
<p>14- <strong>D</strong><br />The smallest 4, digit number is 1000, and the biggest 4-digit number is 9999. The difference is: 8999</p>
<p>15- <strong>C</strong><br />The area of the floor is: 6 cm \(\times\) 24 cm = 144 cm\(^2 \)<br />The number of tiles needed \(= 144 \div 8 = 18\)</p>
<p>16- <strong>D</strong><br />The relationship among all sides of a special right triangle<br />\(30^ \circ -60^ \circ – 90^ \circ \) is provided in this triangle:<br /><figure class=)
In this triangle, the opposite side of \(30^ \circ \) angle is half of the hypotenuse.
Draw the shape for this question:
The latter is the hypotenuse. Therefore, the latter is 60 ft.
17- B
average \(= \frac{sum of terms}{number of terms}\)
The sum of the weight of all girls is: \(18 \times 60 = 1080\) kg
The sum of the weight of all boys is:\( 32 \times 62 = 1984\) kg
The sum of the weight of all students is: \(1080 + 1984 = 3064\) kg
average \(= \frac{3064}{50}=61.28 \)
18- B
The sum of supplement angles is 180. Let \(x\) be that angle. Therefore,
\(x + 5x = 180\)
\(6x = 180\), divide both sides by 6: \(x = 30\)
19- A
In the stadium, the ratio of home fans to visiting fans in a crowd is \(5:7\). Therefore, total number of fans must be divisible by \(12: 5 + 7 = 12.\)
Let’s review the choices:
A. \(12,324: 12,324 \div 12 = 1027\)
B. \(42,326: 42,326 \div 12 = 3,527.166\)
C. \(44,566: 44,566 \div 12 = 3,713.833\)
D. \(66,812: 66,812 \div 12 = 5,567.666\)
Only choice A, when divided by 12, results in a whole number.
20- A
The percent of girls playing tennis is:
\(40 \% \times 25\% = 0.40 \times 0.25 = 0.10 = 10\%\)
Looking for the best resource to help you succeed on the SIFT Math test?
The Best Books to Ace the SIFT Math Test
Recommended EffortlessMath Books
For a structured prep workbook to study alongside this test, the SIFT Math for Beginners (resource currently unavailable) covers every Math Skills Test topic with worked examples. For full aviation-selection prep with multiple practice tests, see the SIFT Math Test Prep Bundle (resource currently unavailable).
Frequently Asked Questions
What is the SIFT math test?
The SIFT Math Skills Test is one of seven subtests on the Army’s Selection Instrument for Flight Training, the exam for future Army aviators. It measures arithmetic, algebra, geometry and word-problem skills, and you work without a calculator. Because it is computer adaptive, the questions adjust to how well you are doing. Check with your recruiter or official Army guidance for current timing and rules.
What kind of questions are on the SIFT math test?
Expect multiple-choice questions on percents, ratios, rates, exponents, linear equations, area and volume, and practical word problems. A typical item: a helicopter flies 240 miles in 2 hours, so its speed is 240 ÷ 2 = 120 miles per hour, and at that rate it covers 300 miles in 2.5 hours. SIFT questions reward quick, clean setups over long calculations.
How do I prepare for the SIFT math test?
Start with a timed practice test to see where you lose points, then rebuild those skills in short daily sessions. Drill mental math, fractions and percents, since no calculator is allowed on the SIFT, and practice turning word problems into equations. Many candidates prepare for several weeks. Finish with a few full timed sets so the pace feels normal on test day.
Is there a free SIFT math practice test?
Yes. You can take a free, timed SIFT math practice test online with an instant score estimate and step-by-step solutions. Treat it like the real SIFT: no calculator, no breaks and a firm timer. Afterward, sort your misses by topic, such as algebra or geometry, and retest those areas a week later to confirm the skills have stuck.
Related EffortlessMath Lessons
If a topic on this page feels rusty, these short lessons go deeper:
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