10MAT Algebra Revision

Question 1

What is an algebraic expression?

Answer 1

An algebraic expression is a mathematical phrase that can include numbers, variables, and operation symbols.

Question 2

True or False: A linear equation can be represented as y = mx + b.

Answer 2

True.

Question 3

Fill in the blank: The degree of a linear equation is ____.

Answer 3

1.

Question 4

What does ‘m’ represent in the linear equation y = mx + b?

Answer 4

‘m’ represents the slope of the line.

Question 5

What is the standard form of a linear equation?

Answer 5

Ax + By = C, where A, B, and C are constants.

Question 6

Identify the slope of the line represented by the equation y = 3x + 2.

Answer 6

3.

Question 7

True or False: The graph of a quadratic equation is a straight line.

Answer 7

False.

Question 8

What is the general form of a quadratic equation?

Answer 8

ax^2 + bx + c = 0.

Question 9

Fill in the blank: The vertex of a parabola is the ____ point.

Answer 9

highest or lowest.

Question 10

What is the axis of symmetry in a quadratic equation?

Answer 10

The line that divides the parabola into two mirror images.

Question 11

What is the formula to find the roots of a quadratic equation?

Answer 11

The quadratic formula: x = (-b ± √(b² - 4ac)) / 2a.

Question 12

True or False: The discriminant of a quadratic equation determines the number of real roots.

Answer 12

True.

Question 13

What does the discriminant (b² - 4ac) equal if there are two distinct real roots?

Answer 13

It is greater than zero.

Question 14

Define a linear relationship.

Answer 14

A relationship where a change in one variable results in a proportional change in another variable.

Question 15

What is a function in algebra?

Answer 15

A relation where each input has exactly one output.

Question 16

True or False: A quadratic function can be written in vertex form.

Answer 16

True.

Question 17

Write the vertex form of a quadratic equation.

Answer 17

y = a(x - h)² + k, where (h, k) is the vertex.

Question 18

What are the x-intercepts of a graph?

Answer 18

The points where the graph intersects the x-axis.

Question 19

What is the slope-intercept form of a linear equation?

Answer 19

y = mx + b.

Question 20

Fill in the blank: In the equation y = 2x + 5, the y-intercept is ____.

Answer 20

5.

Question 21

What does the term ‘rate of change’ refer to in a linear equation?

Answer 21

The slope of the line.

Question 22

Identify the graph type: A graph that opens upwards and has a minimum point.

Answer 22

A parabola.

Question 23

What is a quadratic function?

Answer 23

A function that can be described by a quadratic equation.

Question 24

True or False: The sum of the roots of a quadratic equation can be found using -b/a.

Answer 24

True.

Question 25

In the equation y = -x² + 4x - 3, what is the coefficient of x²?

Answer 25

-1.

Question 26

What is the purpose of factoring in algebra?

Answer 26

To simplify expressions or solve equations.

Question 27

Fill in the blank: A polynomial of degree 2 is called a ____.

Answer 27

quadratic.

Question 28

What is the relationship between the coefficients and the roots of a quadratic equation?

Answer 28

The sum of the roots equals -b/a, and the product equals c/a.

Question 29

True or False: All quadratic equations can be solved by factoring.

Answer 29

False.

Question 30

What is a common method to solve linear equations?

Answer 30

Isolating the variable.

Question 31

Identify the type of pattern: 2, 4, 6, 8, ...

Answer 31

An arithmetic sequence.

Question 32

What is the common difference in the sequence: 5, 10, 15, 20?

Answer 32

5.

Question 33

Fill in the blank: The formula for the n-th term of an arithmetic sequence is ____.

Answer 33

a_n = a_1 + (n - 1)d.

Question 34

What is a geometric sequence?

Answer 34

A sequence where each term is found by multiplying the previous term by a constant.

Question 35

Identify the type of sequence: 3, 9, 27, 81, ...

Answer 35

A geometric sequence.

Question 36

True or False: The graph of a linear equation is always a parabola.

Answer 36

False.

Question 37

What is the y-intercept of the line represented by the equation y = 4x - 7?

Answer 37

-7.

Question 38

What is the value of 'b' in the quadratic equation 2x² - 4x + 3 = 0?

Answer 38

-4.

Question 39

Fill in the blank: The vertex of the parabola y = x² - 6x + 8 is located at ____.

Answer 39

(3, -1).

Question 40

What does a negative slope indicate about a linear graph?

Answer 40

The graph decreases from left to right.

Question 41

What is the formula for the area of a rectangle?

Answer 41

Area = length × width.

Question 42

Fill in the blank: A linear equation in two variables can be graphed as a ____ line.

Answer 42

straight.

Question 43

What is the solution to the equation 2x + 3 = 7?

Answer 43

x = 2.

Question 44

True or False: All quadratic functions have a maximum or minimum point.

Answer 44

True.

Question 45

What is the formula to calculate the slope between two points (x₁, y₁) and (x₂, y₂)?

Answer 45

Slope = (y₂ - y₁) / (x₂ - x₁).

Question 46

Fill in the blank: The y-coordinate of the vertex can be found by substituting ____ into the original quadratic equation.

Answer 46

the x-coordinate.

Question 47

What type of line does a quadratic function represent when graphed?

Answer 47

A curve.

Question 48

True or False: The roots of a quadratic equation can be found using synthetic division.

Answer 48

True.

Question 49

What does 'a' represent in the quadratic equation ax² + bx + c?

Answer 49

'a' represents the coefficient of x².

Question 50

What is the value of the discriminant if there is one real root?

Answer 50

It equals zero.

Question 51

Identify the term: The highest power of the variable in a polynomial.

Answer 51

Degree.

Question 52

Fill in the blank: The graph of y = x² - 4 opens ____.

Answer 52

upwards.

Question 53

What is a system of linear equations?

Answer 53

A set of two or more linear equations with the same variables.

Question 54

True or False: A system of equations can have no solution.

Answer 54

True.

Question 55

What is the point of intersection of two lines called?

Answer 55

The solution of the system of equations.

Question 56

What is the method called when you add or subtract equations to eliminate a variable?

Answer 56

The elimination method.

Question 57

Fill in the blank: The quadratic formula is derived from the process of ____.

Answer 57

completing the square.

Question 58

What is the term used for the y-values of a function?

Answer 58

Outputs.

Question 59

True or False: The slope of a vertical line is undefined.

Answer 59

True.

Question 60

What does the term 'coordinate plane' refer to?

Answer 60

A two-dimensional surface where points are defined by pairs of numbers.

Question 61

Fill in the blank: The point (0, 0) is called the ____.

Answer 61

origin.

Question 62

What is the relationship between the slope and the angle of a line?

Answer 62

The slope is the tangent of the angle formed with the x-axis.

Question 63

What is the standard form of a quadratic function?

Answer 63

f(x) = ax² + bx + c.

Question 64

What is the axis of symmetry for the function y = x² + 4x + 4?

Answer 64

x = -2.

Question 65

Fill in the blank: The solutions to a quadratic equation can also be called the ____.

Answer 65

roots.

Question 66

What is the term for a sequence of numbers in which each term is a constant difference from the previous term?

Answer 66

Arithmetic sequence.

Question 67

True or False: A quadratic equation can have up to two real roots.

Answer 67

True.

Question 68

What is meant by 'factoring a quadratic expression'?

Answer 68

Rewriting it as a product of its linear factors.

Question 69

Fill in the blank: The slope of a horizontal line is ____.

Answer 69

0.