Algebraic expressions and solving equations — ISEE Upper practice questions

Algebraic expressions and solving equations on the ISEE Upper Mathematics Achievement section covers simplifying and evaluating expressions, using identities that connect sums and products of two variables to other quantities, isolating a variable after distributing, and turning a short word problem into an equation. A student has to expand or rearrange correctly, substitute related facts, and choose which equation matches a described cost or similar situation. Items are typically multiple choice with four options, often a single numerical value or one of several look-alike formulas. Common traps include distributing to only one term, mixing the one-time fee with the hourly rate, or expanding a square without the middle term.

Section: Mathematics Achievement 47 questions on the paper
204 practice questions in the app

Sample questions

Question 1

If $x+y=7$ and $xy=10$ , what is the value of $x^2+y^2$ ?

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Answer: B — 29

Use the identity $(x+y)^2=x^2+2xy+y^2$ . Since $x+y=7$ and $xy=10$ , we have $49=x^2+20+y^2$ , so $x^2+y^2=29$ .

Question 2

A bicycle rental costs a one-time fee of 13 dollars plus 9 dollars for each hour. Let $C$ be the total cost for $h$ hours. Which equation represents the total cost?

A $C=13h+9$
B $C=9(h+13)$
C $C=22h$
D $C=9h+13$

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Answer: D — $C=9h+13$

The hourly charge is $9h$ dollars, and the one-time fee adds 13 dollars, so $C=9h+13$ .

Question 3

If $3(y+4)=27$ , what is the value of $y$ ?

A5
B13
C $\dfrac{23}{3}$
D-5

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Answer: A — 5

Dividing both sides by 3 gives $y+4=9$ . Subtracting 4 gives $y=5$ .

Practice 204 Algebraic expressions and solving equations questions in the app

Algebraic expressions and solving equations — ISEE Upper practice questions

Sample questions

More ISEE Upper topics

Mathematics Achievement