Quant - Algebra & Equations

Question 1

What is the golden rule of solving equations?

Answer 1

Whatever you do to one side, do to the other.

Question 2

If ax = 0, what must be true?

Answer 2

Either a = 0 or x = 0.

Question 3

Distributive property formula?

Answer 3

a(b + c) = ab + ac

Question 4

How do you solve a proportion a/b = c/d?

Answer 4

Cross-multiply: ad = bc.

Question 5

If x² = 16, what are possible values of x?

Answer 5

4 and −4.

Question 6

Difference of squares formula?

Answer 6

a² − b² = (a − b)(a + b)

Take the same numbers, one minus and one plus.
Multiply them.
The middle disappears.
Only the squares remain.

Question 7

Perfect square trinomial formula?

Answer 7

a² + 2ab + b² = (a + b)²

Question 8

If (x + a)(x + b) expands, what is the middle term?

Answer 8

(a + b)x

Question 9

What is slope formula?

Answer 9

(y₂ − y₁)/(x₂ − x₁)

Question 10

Slope-intercept form?

Answer 10

y = mx + b

Question 11

What does slope represent?

Answer 11

Rate of change.

Question 12

Parallel lines have what in common?

Answer 12

Same slope.

Question 13

Perpendicular slopes relationship?

Answer 13

Negative reciprocals.

Question 14

If multiplying or dividing an inequality by a negative, what happens?

Answer 14

Flip the inequality sign.

Question 15

Exponent rule: xᵃ · xᵇ = ?

Answer 15

xᵃ⁺ᵇ

Question 16

Exponent rule: (xᵃ)ᵇ = ?

Answer 16

xᵃᵇ

Question 17

Exponent rule: x⁻ᵃ = ?

Answer 17

1 / xᵃ

Question 18

What is the quadratic formula?

Answer 18

x = (-b ± √(b² − 4ac)) / 2a

Question 19

What does discriminant (b² − 4ac) tell you?

Answer 19

Number and type of solutions.

Question 20

If discriminant > 0?

Answer 20

Two real solutions.

Question 21

If discriminant = 0?

Answer 21

One real solution.

Question 22

If discriminant < 0?

Answer 22

No real solutions.

Question 23

How do you solve systems quickly when equations are aligned?

Answer 23

Use elimination.

Question 24

When is substitution better?

Answer 24

When one variable is already isolated.

Question 25

If two linear equations have same slope but different intercepts?

Answer 25

No solution (parallel lines).

Question 26

If two linear equations are identical?

Answer 26

Infinitely many solutions.

Question 27

Standard form of a quadratic?

Answer 27

ax² + bx + c = 0

Question 28

Vertex form of quadratic?

Answer 28

a(x − h)² + k

Question 29

Vertex represents what?

Answer 29

Maximum or minimum point.

Question 30

What is absolute value equation strategy?

Answer 30

Solve both positive and negative cases.

Question 31

If |x − 3| = 5, solutions?

Answer 31

x = 8 or x = −2

Question 32

How do you add fractions algebraically?

Answer 32

Find common denominator first.

Question 33

When simplifying rational expressions, what can you cancel?

Answer 33

Common factors only (not terms).

Question 34

If denominator equals zero, expression is?

Answer 34

Undefined.

Question 35

How do you factor out common term?

Answer 35

Divide each term by greatest common factor.

Question 36

What is FOIL method?

Answer 36

First, Outer, Inner, Last multiplication.

Question 37

If x > 0 and y > 0, is xy > 0?

Answer 37

Yes.

Question 38

If x > 0 and y < 0, is xy > 0?

Answer 38

No, it’s negative.

Question 39

What is reciprocal of x/y?

Answer 39

y/x

Question 40

If x ≠ 0, what is x/x?

Answer 40

1

Question 41

How do you handle fractional exponents?

Answer 41

x^(1/2) = √x x^(1/3) = cube root of x

Question 42

What is completing the square used for?

Answer 42

Rewriting quadratics in vertex form.

Question 43

If equation is quadratic, how many solutions possible?

Answer 43

At most 2.

Question 44

Plug-in strategy is useful when?

Answer 44

Variables abstract and answers numeric.

Question 45

Back-solving is useful when?

Answer 45

Answer choices are numbers.

Question 46

If a function is linear, its graph is?

Answer 46

A straight line.

Question 47

If slope is zero, the line is?

Answer 47

Horizontal.

Question 48

If slope is undefined, the line is?

Answer 48

Vertical.

Question 49

How do you isolate a variable in multi-step equation?

Answer 49

Undo operations in reverse order.

Question 50

Elite algebra mindset?

Answer 50

Simplify first. Recognize structure. Avoid unnecessary calculation.