These solutions are for the 2008-2009, 2009-2010 and 2010-2011 SHSAT Handbook Form A tests, which were all identical. Here are my fully worked out solutions to the math section. The test can be found here.

Regents Prep– Pay particular attention to the Solving Linear Systems Algebraically Using Addition or Subtraction part

Khan Academy

Relevant question from SHSAT handbook:

2012-2013 Handbook Form A

57) If , what is the value of in terms of ?

A)

B)

C)

D)

E)

Khan Academy

Regents Prep

Relevant questions from the SHSAT handbook:

2012-2013 Handbook Form A

68) If , what is the value of in terms of ?

F)

G)

H)

J)

K)

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Regents Prep

Khan Academy

Ratios and proportions show up a lot on the SHSATs! Mastering them will give you a nice score boost.

Links:

Regents Prep lessons and practice

Take special notice of this hint from the Regents Prep ratios lesson: When working with ratios such as 2 : 3 : 5, use 2x, 3x, and 5x to write an equation!

Khan Academy lessons and practice

Basic lesson and practice on averages:
http://www.regentsprep.org/Regents/math/ALGEBRA/AD2/indexAD2.htm

There are a couple types of tricky problems related to averages that often show up on the SHSATs:

Finding the average from a frequency table:
Practice 1:
http://www.bbc.co.uk/bitesize/ks3/maths/handling_data/measures_average/revision/7/
Practice 2- don’t worry about the second half of the page, which is more advanced:
https://www.mathsisfun.com/data/mean-frequency-table.html

Missing numbers in averages:
Lesson/ practice 1:
https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-data-statistics/cc-6th-mean-median-challenge/v/using-mean-to-find-missing-value
Practice 2:
http://www.softschools.com/math/topics/determining_a_missing_data_value_given_the_mean/

Multiplying square roots

The key fact of square roots is that they can be multiplied. For example, we can do 

We know this works because

so  

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You are likely to encounter one or two divisibility questions on the SHSAT.  The good news is that most of them are straightforward greatest common factor or least common multiple problems. If you don’t know how to find GCF and LCM using prime factorization, check out one of the first three links at the bottom of the page. This post is about understanding divisibility a little deeper. Continue reading →