Skill Builder

Prime numbers are very special. A prime number is a number that is divisible evenly only by itself and 1. Hence, 18 is not a prime number because it can be formed as the product of 2 and 9, 3 and 6, or 18 and 1. In other words, it has many factors, other than itself and 1. In contrast, 23 is a prime number because its only factors are 1 and itself, 23. Some questions on the SHSAT will ask us to determine whether a number is, in fact, prime. To determine whether any given numb

Let's say we were given the following question on the SHSAT. Example 1 Compare 3⁄7 and 4⁄9. Which fraction is greater? One method of comparing the values of the two given fractions is to convert each fraction into decimal form. Doing so requires doing division. We would divide 3 by 7, and then repeat the process by dividing 4 by 9. Converting fractions to decimal form by doing division would lead us to the answer, but doing so would require computation and time. We would be

Exponents may seem rather straightforward and simple. And that's usually the case, particularly when dealing with common exponents like 2 and 3. Example: 3² = 3 x 3 = 9 There's no confusion here. To square a number simply means to multiply the number by itself. Likewise, to cube a number follows the same logic and simply means to multiply the number by itself three times. Example: 3³ = 3 x 3 x 3 = 27 But what about exponents that are 0? Negative? Or fractions? What do thos

These are two very common computation traps that can throw off even the most capable math students. 1) Dividing by ½ It's easy to think that some quantity divided by a half means that the result will be the same as dividing by 2. But, that's not the case at all. Example: 8 ÷ ½ = ? Many might confuse the above example with 8 ÷ 2 and think the answer is 4. But. dividing by ½ actually means to multiply by 2, which is the reciprocal of ½. The confusion may stem from the s

Time management during test-taking is more important than ever with the SHSAT transitioning to a digital format. Students can no longer skip tricky, difficult questions and return to them later. Once a question is answered, that answer is locked in, meaning the digital CAT format turns the SHSAT into a one-way street—students can only move forward. This change encourages students to be mindful of their time as they navigate their way through the test. With this in mind, it's

One of the simplest ways to boost your SHSAT math performance is to save time on routine calculations. A great place to start is memorizing a handful of common fractions and their decimal equivalents—so you can recognize them instantly and keep moving with confidence. Below are some of the most useful fraction–decimal pairs to know. 1/2 = 0.5 1/4 = 0.25 1/8 = 0.125 1/9 = 0.1̅1̅ (think of it as 1/3 of 1/3) 3/8 = 0.375 3/4 = 0.75 5/8 =

Right triangle questions show up often on the SHSAT and SAT. Sometimes they’re presented directly, and other times they’re hidden inside questions about rectangles or squares. For example, you might be given a rectangle that’s 12 feet long and 5 feet wide and asked to find the length of the diagonal. That diagonal is, in fact, the hypotenuse of a right triangle—so this becomes a right triangle problem. A great way to work faster (and more confidently) is to memorize three com

Every year, over 30,000 New York City middle schoolers take on the SHSAT. It’s a massive milestone, and the stakes feel incredibly high since it’s the single ticket into the city’s specialized high schools. But starting in the fall of 2026