Question 1Easier
Which of the following gives both zeros of ?
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Answer: B — 0 and 6
Setting gives , so . Therefore the zeros are 0 and 6.
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Mathematics
Quadratic equations — ACT practice questions
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What this topic is
Three main methods solve Quadratic equations: factoring, completing the square and the quadratic formula.
Factoring works when the equation splits neatly, as x squared minus five x plus six equals zero becomes x minus two times x minus three equals zero, giving solutions two and three. Completing the square rewrites an expression into vertex form, a skill ACT Mathematics tests by asking which equation is equivalent to a given one.
Another frequent question gives one solution and asks for a missing coefficient, which is found by substituting the known solution. Forgetting the negative square root, and so losing one of the two solutions, is a mistake many wrong choices reflect.
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Question 2Easier
Which of the following is equivalent to ?
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Answer: A —
Adding 25 to both sides gives . The left side factors as , so .
Question 3Easier
One solution of the equation is . What is the value of ?
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Answer: C — 9
Substitute : .
Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.
More ACT topics
Mathematics
- Real number system and number properties
- Integer and rational exponents
- Radicals and roots
- Complex numbers
- Vectors and matrices
- Fractions, decimals, and operations
- Percents and percent change
- Ratios, rates, and proportional relationships
- Linear equations and expressions in one variable
- Inequalities (linear and compound)
- Systems of equations
- Polynomial expressions and factoring
- Radical and rational equations
- Exponential relationships
- Function notation and evaluating functions
- Linear functions and graphs
- Quadratic and polynomial functions
- Radical and rational functions
- Piecewise functions
- Exponential and logarithmic functions
- Key features and transformations of graphs
- Lines, angles, and polygons
- Triangles — congruence, similarity, Pythagorean theorem
- Circles — arcs, sectors, angles, equations
- Surface area and volume of solids
- Coordinate geometry — distance, midpoint, slope, line equations
- Conic sections
- Right-triangle trigonometry and trig functions
- Measures of center and spread
- Data collection methods and study design
- Bivariate data and relationships (scatterplots, correlation)
- Probability and sample spaces
- Counting, combinations, and permutations
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