Algebra for Year 10: Master Equations and Inequalities

Question 1

What is the standard form of a quadratic equation?

Accepted Answer

ax^2 + bx + c = 0

Answer

ax + b = 0

Answer

x^2 + y^2 = r^2

Answer

sin(x) = cos(x)

Question 2

Which expression is equivalent to 2x + 3y?

Accepted Answer

2(x + y)

Answer

x + y + y

Answer

y + 2y

Answer

x + x + y

Question 3

In algebra, what is a variable?

Accepted Answer

A symbol representing an unknown value

Answer

A number used to solve equations

Answer

A symbol representing an operation

Answer

A constant that doesn't change

Question 4

Which part of the expression 3x + 5 represents a variable that can change its value?

Accepted Answer

x

Answer

3

Question 5

Simplify the expression: (2x + 3)(x - 5)

Accepted Answer

2x^2 - 11x - 15

Answer

x^2 - 7x - 15

Question 6

Solve the equation: 2 to the power of x equals 16

Accepted Answer

x = 4

Answer

x = 2

Answer

x = 8

Answer

x = 16

Question 7

Simplify the expression $$x^2 + 6x + k$$ by completing the square.

Accepted Answer

$$(x + 3)^2 - 9 + k$$

Answer

$$(x + 9)^2 - 81 + k$$

Answer

$$(x - 3)^2 + 9 + k$$

Question 8

Which of the following is a rational algebraic expression?
(A) √2
(B) 3.14
(C) (√5 + √7)/2
(D) π

Accepted Answer

(√5 + √7)/2

Answer

√2

Answer

3.14

Answer

π

Question 9

What mathematical expression represents the sum of twice a number x and five?

Accepted Answer

2x + 5

Answer

5 - x

Answer

2(a + b)

Answer

√x

Question 10

Simplify the algebraic expression: 2(x - 3) + 5x

Accepted Answer

7x - 6

Answer

3x - 1

Answer

9x - 6

Answer

14x - 6

Question 11

Find the range of solutions for the inequality x + 4 > 7

Accepted Answer

x > 3

Answer

x < 3

Answer

x > 7

Answer

x < 7

Question 12

Identify the graphical representation of the inequality 2x + y > 4.

Accepted Answer

A line with a shaded area located above the line

Answer

A line with a shaded area located below the line

Answer

A parabola with a shaded area enclosed by the parabola

Answer

A parabola with a shaded area external to the parabola

Question 13

Simplify the expression: (a^2b)^3

Accepted Answer

a^6b^3

Answer

a^5b^3

Answer

a^6b^9

Answer

a^9b^6

Question 14

Which of the following is a quadratic equation?

Accepted Answer

x^2 - 4 = 0

Answer

2x + 5 = 11

Answer

3x - 5 > 10

Answer

(x + 2)(x - 3) = 0

Question 15

Simplify the expression: (2x - 3)(x + 4)

Accepted Answer

2x^2 + 5x - 12

Answer

2x^2 - 5x - 12

Answer

2x^2 + 11x - 12

Answer

2x^2 - 11x - 12

Question 16

Solve the equation: x^2 - 9 = 0

Accepted Answer

x = ±3

Answer

x = ±9

Answer

x = 3

Answer

x = 9

Question 17

Which of the following represents the graph of the equation y = 2x + 1?

Accepted Answer

A straight line with a gradient of 2 and a y-intercept of 1

Answer

A straight line with a gradient of 1 and a y-intercept of 2

Answer

A parabola with a vertex at (0, 1)

Answer

A circle with a radius of 1

Question 18

Which expression is equivalent to (x - 2)^2?

Accepted Answer

x^2 - 4x + 4

Answer

x^2 + 4x + 4

Answer

x^2 - 2x + 4

Answer

x^2 + 2x + 4

Question 19

Solve the following system of equations graphically: 
 x² - y² = 4
 x + y = 8

Accepted Answer

Two distinct real solutions

Answer

One real solution

Answer

Four real solutions

Answer

No real solutions

Question 20

Identify the algebraic equation among the given options:

Accepted Answer

x + 5 = 10

Answer

The sum of two numbers is 15

Answer

The area of a rectangle is 24cm²

Answer

5 is greater than 3

Question 21

Which of the following equations is a quadratic equation?

Accepted Answer

x² + 2x - 3 = 0

Answer

x - 5 = 0

Answer

2x + 5y = 10

Answer

x³ - 2x² + 1 = 0

Question 22

Factorise the expression: x² - 4

Accepted Answer

(x - 2)(x + 2)

Answer

(x - 4)(x + 4)

Answer

(x - 2)²

Answer

(x + 2)²

Question 23

Which graph represents the equation y = x²?

Accepted Answer

A parabola opening upwards

Answer

A straight line

Answer

A parabola opening downwards

Answer

A circle

Question 24

The coefficient of x in the expression 3x - 5 is:

Accepted Answer

3

Answer

-5

Answer

1

Answer

0

Question 25

The solution to the inequality x + 5 > 10 is:

Accepted Answer

x > 5

Answer

x < 5

Answer

x < -5

Answer

x > -5

Question 26

Simplify the expression: (x^2 y^-3)^2

Accepted Answer

x^4 y^6

Answer

x^4 y^-6

Answer

x^-4 y^6

Answer

x^-4 y^-6

Question 27

Factorise the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)^2

Answer

(x + 3)^2

Answer

It cannot be factorised

Question 28

Factor the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 1)

Answer

(x + 3)(x + 3)

Answer

(x - 9)(x - 1)

Question 29

Factor the expression: x^3 - 8

Accepted Answer

(x - 2)(x^2 + 2x + 4)

Answer

(x + 2)(x^2 - 2x + 4)

Answer

(x - 2)(x^2 - 2x - 4)

Answer

(x + 2)(x^2 + 2x - 4)

Question 30

Simplify the expression: (x^2 - y^2)/(x - y)

Accepted Answer

x - y

Answer

x + y

Answer

x^2 + y^2

Answer

x^2 - y^2

Question 31

Factorize the equation: x^2 + 5x + 6

Accepted Answer

(x + 2)(x + 3)

Answer

(x - 2)(x + 3)

Answer

(x + 1)(x + 6)

Answer

(x - 1)(x + 6)

Question 32

Which of the following is the graph of the equation y = -2x + 3?

Accepted Answer

A line with a slope of -2 and a y-intercept of 3

Answer

A line with a slope of 2 and a y-intercept of -3

Answer

A parabola with a vertex of (3, -2)

Answer

A circle with a radius of 3

Question 33

Solve the inequality: |x - 3| > 2

Accepted Answer

x < -1 or x > 5

Answer

x < 1 or x > 5

Answer

x > 1 or x < 5

Question 34

Evaluate the expression: 3^2 + 4^2

Accepted Answer

25

Answer

7

Answer

16

Answer

32

Question 35

Simplify the fraction: 12/18

Accepted Answer

2/3

Answer

3/4

Answer

4/6

Answer

6/8

Question 36

A rectangular garden has a length of (x + 3) meters and a width of (x - 1) meters. If the area of the garden is 20 square meters, what is the value of x?

Accepted Answer

x = 3

Answer

x = 7

Answer

x = -3

Answer

x = 10

Question 37

Factorise the expression: x^2 + 5x + 6

Accepted Answer

(x + 2)(x + 3)

Answer

(x + 1)(x + 6)

Answer

(x - 2)(x - 3)

Answer

(x - 1)(x - 6)

Question 38

Which of the following is a quadratic function?

Accepted Answer

y = x^2 - 5

Answer

y = 3x

Answer

y = 1/x

Answer

y = sqrt(x)

Question 39

Expand the expression: (x + 2)(x - 3)

Accepted Answer

x^2 + x - 6

Answer

x^2 - x - 6

Answer

x^2 + 5x - 6

Answer

x^2 - 5x - 6

Question 40

Which of the following is a rational number?

Accepted Answer

1/3

Answer

sqrt(2)

Answer

pi

Answer

e

Question 41

Find the value of y in the equation: 2y - 5 = 15

Accepted Answer

y = 10

Answer

y = 5

Answer

y = 20

Answer

y = 40

Question 42

Which inequality represents the solution set of x^2 - 4 > 0?

Accepted Answer

x < -2 or x > 2

Answer

x > -2 and x < 2

Answer

x > 2

Answer

x < -2

Question 43

Factorize the following expression: x^2 - 9

Accepted Answer

(x + 3)(x - 3)

Answer

(x - 3)(x + 3)

Answer

(x + 9)(x - 9)

Answer

(x - 9)(x + 9)

Question 44

Solve the one-step linear equation: 2x + 5 = 15

Accepted Answer

5

Answer

20

Answer

10

Question 45

Factor the quadratic expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x + 3)^2

Answer

(x - 9)(x + 1)

Answer

(x - 3)^2

Question 46

Solve the linear inequality: 2x - 5 < 10

Accepted Answer

x < 7.5

Answer

x < 5

Answer

x > 5

Answer

x > 7.5

Question 47

Write the equation of the line with a slope of 2 and a y-intercept of -3:

Accepted Answer

y = 2x - 3

Answer

y = 2x + 3

Answer

y = -2x - 3

Answer

y = -2x + 3

Question 48

Calculate the slope of the line passing through the points (2, 5) and (4, 9)

Accepted Answer

2

Answer

1

Answer

-2

Question 49

Find the vertex of the parabola y = x^2 - 4x + 3:

Accepted Answer

(2, -1)

Answer

(-2, -1)

Answer

(4, 3)

Answer

(0, 3)

Question 50

Factorize the expression: x^2 - 9.

Accepted Answer

(x + 3)(x - 3)

Answer

Cannot be factorized

Answer

(x + 3)^2

Answer

(x - 3)^2

Question 51

The sum of two numbers is 20. If one number is x, what is the other number?

Accepted Answer

20 - x

Answer

x - 20

Answer

x + 20

Answer

20/x

Question 52

What is the discriminant of the quadratic equation: x^2 + 5x + 6 = 0?

Accepted Answer

11

Answer

6

Answer

5

Answer

12

Question 53

What is the range of the function: f(x) = |x - 3|?

Accepted Answer

[0, ∞)

Answer

(0, ∞)

Answer

(-∞, 0)

Answer

(-∞, -3)

Question 54

A rectangle's length is (x + 5) cm and its width is (x - 2) cm. What is the rectangle's area?

Accepted Answer

x² + 3x - 10 cm²

Answer

2x + 3 cm²

Answer

2x² + 3x - 10 cm²

Answer

x² - 10 cm²

Question 55

Simplify the expression: (x + 2)(x - 2)

Accepted Answer

x² - 4

Answer

x² + 2x - 4

Answer

x² - 2x - 4

Answer

x² + 4

Question 56

Solve for x: 3x + 5 = 14

Accepted Answer

x = 3

Answer

x = -3

Answer

x = 1

Answer

x = 6

Question 57

Simplify the expression: 2(x + 3) - 4x

Accepted Answer

-2x + 6

Answer

-2x + 3

Answer

2x + 6

Answer

6x + 6

Question 58

Which inequality represents the statement: 'The temperature is at least 10 degrees Celsius'?

Accepted Answer

t ≥ 10

Answer

t > 10

Answer

t < 10

Answer

t ≤ 10

Question 59

If a = 4 and b = -2, what is the value of 3a - 2b?

Accepted Answer

16

Answer

-4

Answer

8

Answer

4

Question 60

A rectangular garden has a length of (x + 5) meters and a width of (x - 2) meters. What is the garden's area?

Accepted Answer

x² + 3x - 10 square meters

Answer

2x + 3 square meters

Answer

x² - 10 square meters

Answer

x² + 7x + 10 square meters

Question 61

Which of the following is NOT a solution to the inequality 2x - 1 > 5?

Accepted Answer

x = 2

Answer

x = 3

Answer

x = 5

Answer

x = 4

Question 62

Simplify the expression: 5a² - 2a + 3a² + 4a

Accepted Answer

8a² + 2a

Answer

8a² - 2a

Answer

2a² - 2a

Answer

2a² + 2a

Question 63

The perimeter of a square is represented by the expression 4x + 12. What is the length of one side of the square?

Accepted Answer

x + 3

Answer

x + 12

Answer

4x + 3

Answer

x + 4

Question 64

Which inequality is represented by the graph? (Provide a graph with a number line and a shaded region)

Accepted Answer

x < 3

Answer

x ≤ 3

Answer

x > 3

Answer

x ≥ 3