SSAT Upper Level Math : How to find algebraic patterns

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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Example Question #1 : Ssat Upper Level Quantitative (Math)

Find the sum of this infinite geometric series:

Possible Answers:

Correct answer:

Explanation:

The sum of an infinite series with first term  and common ratio  is 

Set , and evaluate:

Example Question #1 : How To Find Algebraic Patterns

Give the next number in the following sequence:

 _____

Possible Answers:

Correct answer:

Explanation:

The sequence is generated by alternately adding 2, then multiplying by 2:

, which is the correct choice.

Example Question #3 : How To Find Algebraic Patterns

Define an operation on the real numbers as follows:

Find the value of  that makes this statement true:

Possible Answers:

There is no such value of .

Correct answer:

Explanation:

Replace  in the defintiion:

Now, set this equal to 32 and solve for :

Example Question #3 : Ssat Upper Level Quantitative (Math)

What number replaces the circle?

Possible Answers:

Correct answer:

Explanation:

The sequence is formed by alternately multiplying by a number, then adding the same number; the number incrementally increases every other term. 

 

, the number which replaces the square.

, the number which replaces the circle.

Example Question #2 : How To Find Algebraic Patterns

 is defined as the greatest integer less than or equal to .

Evaluate the expression for :

Possible Answers:

Correct answer:

Explanation:

Substitute:

Example Question #5 : Ssat Upper Level Quantitative (Math)

 is defined as the least integer greater than or equal to .

Evaluate for  :

Possible Answers:

Correct answer:

Explanation:

Substitute :

Example Question #6 : Ssat Upper Level Quantitative (Math)

What number replaces the circle in this sequence?

Possible Answers:

Correct answer:

Explanation:

This sequence is alternately generated by subtracting two and multiplying by two. 

We can therefore find the numbers that replace the square and the circle by reversing the pattern - alternately dividing by two and adding two beginning at 36:

 - this replaces the circle

 - this replaces the square

Example Question #3 : How To Find Algebraic Patterns

In the following number sequence, what number goes in place of the circle?

Possible Answers:

Correct answer:

Explanation:

The sequence comprises the squares of the odd integers, in order:

...

The next number, which replaces the circle, is 

.

Example Question #4 : How To Find Algebraic Patterns

Define an operation on the set of real numbers as follows:

Evaluate:

Possible Answers:

The expression is undefined.

Correct answer:

Explanation:

Example Question #5 : How To Find Algebraic Patterns

In the following number sequence, what number goes in place of the circle?

Possible Answers:

Correct answer:

Explanation:

The sequence is generated by alternately dividing by 2 and adding 6:

 - This number replaces the square.

 - This number replaces the circle.

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