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Vector Basics: 20 MCQs with answers

All 20 multiple-choice questions from this kit, free and with no sign-up.

Full kit · everything Flashcards · 15 Quick Revision · 16

Warm-up · 8 questions

Q1. What is the solution to the equation $2x + 3 = 11$?

Beginner
A x = 3 B x = 4 C x = 5 D x = 7
Show answer & explanation

x = 4

Subtract 3 from both sides gives $2x = 8$, then divide by 2 to get $x = 4$.

Q2. Which of the following is a linear equation in one variable?

Beginner
A $x^2 + 2 = 5$ B $3x - 7 = 2x + 1$ C $xy = 6$ D $\frac{1}{x} = 3$
Show answer & explanation

$3x - 7 = 2x + 1$

A linear equation in one variable has the form $ax + b = 0$; $3x - 7 = 2x + 1$ simplifies to $x - 8 = 0$.

Q3. What is the slope of the line represented by $y = -3x + 5$?

Beginner
A 5 B -3 C -5 D 3
Show answer & explanation

-3

In slope-intercept form $y = mx + b$, $m$ is the slope, so $m = -3$.

Q4. Solve for $x$: $\frac{x}{3} + 2 = 5$

Beginner
A x = 1 B x = 6 C x = 9 D x = 3
Show answer & explanation

x = 9

Subtract 2: $\frac{x}{3} = 3$; multiply by 3: $x = 9$.

Q5. The equation $2x = 4x$ has exactly one solution.

Beginner
A True B False
Show answer & explanation

False

Q6. A linear equation can have more than one variable.

Beginner
A True B False
Show answer & explanation

True

Linear equations can have multiple variables, e.g., $2x + 3y = 6$ is a linear equation in two variables.

Q7. The point $(0,0)$ always satisfies the equation $y = mx$ for any $m$.

Beginner
A True B False
Show answer & explanation

True

Substitute $(0,0)$: $0 = m(0)$ is true for any $m$.

Q8. The ___ form of a linear equation is $y = mx + b$.

Beginner
Show answer & explanation

—

The slope-intercept form is $y = mx + b$ where $m$ is slope and $b$ is y-intercept.

Building up · 9 questions

Q9. Solve for $y$: $5y - 2 = 3y + 6$

Intermediate
A y = 1 B y = 4 C y = 8 D y = 2
Show answer & explanation

y = 4

Subtract $3y$ from both sides: $2y - 2 = 6$; add 2: $2y = 8$; divide by 2: $y = 4$.

Q10. Which point lies on the line $2x - y = 4$?

Intermediate
A (2, 0) B (1, -2) C (3, 2) D (0, 4)
Show answer & explanation

(2, 0)

Substitute (2,0): $2(2) - 0 = 4$, true. Others do not satisfy the equation.

Q11. The equation $4x + 2 = 4x - 3$ has:

Intermediate
A infinitely many solutions B no solution C one solution D two solutions
Show answer & explanation

no solution

Subtract $4x$ from both sides gives $2 = -3$, which is false, so no solution.

Q12. What is the $y$-intercept of the line $3x + 2y = 6$?

Intermediate
A 2 B -3 C 3 D 6
Show answer & explanation

3

Set $x=0$: $2y = 6$, so $y = 3$.

Q13. If $3(x - 4) = 2x + 1$, what is $x$?

Intermediate
A x = 11 B x = 7 C x = 5 D x = 13
Show answer & explanation

x = 13

Expand: $3x - 12 = 2x + 1$; subtract $2x$: $x - 12 = 1$; add 12: $x = 13$.

Q14. Which of the following lines is parallel to $y = 2x + 1$?

Intermediate
A $y = 2$ B $y = -2x + 1$ C $y = 2x - 3$ D $y = \frac{1}{2}x + 1$
Show answer & explanation

$y = 2x - 3$

Parallel lines have equal slopes; $y = 2x - 3$ has slope 2, same as $y = 2x + 1$.

Q15. The slope of a vertical line is zero.

Intermediate
A True B False
Show answer & explanation

False

A vertical line has undefined slope, not zero.

Q16. If two lines have the same slope and different y-intercepts, they are parallel.

Intermediate
A True B False
Show answer & explanation

True

Parallel lines have equal slopes and distinct y-intercepts.

Q17. A linear equation in one variable has exactly ___ solution(s) if it is conditional.

Intermediate
Show answer & explanation

—

A conditional linear equation has exactly one solution.

Topper level · 3 questions

Q18. What is the solution to the system $x + y = 5$ and $x - y = 1$?

Advanced
A (4, 1) B (2, 3) C (3, 2) D (1, 4)
Show answer & explanation

(3, 2)

Add equations: $2x = 6$, so $x = 3$; substitute: $3 + y = 5$, so $y = 2$.

Q19. The equation $2(x - 1) + 3 = 2x + 1$ is an example of:

Advanced
A linear inequality B conditional equation C contradiction D identity
Show answer & explanation

identity

Simplify: $2x - 2 + 3 = 2x + 1$ gives $2x + 1 = 2x + 1$, true for all $x$, so it's an identity.

Q20. If $ax + b = 0$ has solution $x = 3$, which of the following must be true?

Advanced
A $3a + b = 0$ B $a + 3b = 0$ C $b = 3a$ D $a = 3b$
Show answer & explanation

$3a + b = 0$

Substitute $x=3$: $a(3) + b = 0$, so $3a + b = 0$.

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