Question 1Mid
If and , what is the value of ?
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Answer: B — 29
Use the identity . Since and , we have , so .
Study on the flyISEE UpperMathematics AchievementAlgebraic expressions and solving equations
Mathematics Achievement
Algebraic expressions and solving equations — ISEE Upper Mathematics Achievement practice questions
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What this topic is
Writing an equation from a description is as important as solving one in Algebraic expressions and solving equations.
A cost made of a fixed fee plus a charge per hour translates to total equals fee plus rate times hours, and wrong choices usually swap which number multiplies the hours. Solving a linear equation means undoing operations in reverse order, distributing first when parentheses are present.
Harder items use identities: the square of a sum equals the sum of the squares plus twice the product, so knowing a sum and a product gives the sum of the squares without finding either number. Checking answers by substitution catches arithmetic slips.
Sample questions
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Question 2Easier
A bicycle rental costs a one-time fee of 13 dollars plus 9 dollars for each hour. Let be the total cost for hours. Which equation represents the total cost?
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Answer: D —
The hourly charge is dollars, and the one-time fee adds 13 dollars, so .
Question 3Easier
If , what is the value of ?
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Answer: A — 5
Dividing both sides by 3 gives . Subtracting 4 gives .
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Practice 207 Algebraic expressions and solving equations questions in the app
More ISEE Upper topics
Mathematics Achievement
- Numbers and operations (factors, multiples, properties)
- Fractions, decimals, and percents; percent change
- Ratios and proportions; distance-rate-time
- Exponents, powers, roots; scientific notation
- Inequalities
- Linear equations and graphs
- Polynomials and function notation
- Plane geometry (polygons, triangles, angles)
- Coordinate geometry (midpoint, distance)
- Solid geometry (surface area, volume)
- Trigonometry
- Measurement and units
- Data analysis and probability
Harder than the exam: ISEE Upper Challenge · Competition-style problems
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