Question 1Easier
What is the magnitude of the vector ?
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Answer: B — 10
Magnitude is .
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Vectors and matrices — ACT practice questions
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Practice 45 Vectors and matrices questions in the app
What this topic is
Vectors and matrices on the ACT Mathematics test covers vector length, matrix equality, and using given entries to find a related value.
A student has to compute magnitude from components, recognize when two matrices are the same, and combine named entries after a simple operation. The exam tends to ask for the magnitude of a vector, which matrix equals a given expression, or a value such as a plus b.
Answer choices are usually numbers or small matrices. Common traps include swapping components, treating matrix multiplication as commutative, and choosing a matrix with the right entries in the wrong order.
Sample questions
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Question 2Easier
Which of the following matrices is equal to ?
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Answer: A —
Scale first: . Subtracting entry by entry gives , , , and .
Question 3Mid
If , what is the value of ?
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Answer: C — 4
The second row gives . Then , so and .
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
- Fractions, decimals, and operations
- Percents and percent change
- Ratios, rates, and proportional relationships
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- Inequalities (linear and compound)
- Systems of equations
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- Quadratic and polynomial functions
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- Piecewise functions
- Exponential and logarithmic functions
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- Surface area and volume of solids
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- Conic sections
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