Grade 10 Math

Linear Systems

100

Find the x and the y values using elimination:

3x + 4y = 10

2x + 3y = 7

 x=2, y = 1

200

Find the x and y value by using substitution:

3x + 6y = 12

5x - 8y = 2

x = 2, y = 1

300

Find the x and y value by using substitution:

7x -5y = 1

8x + 4y = 40

x = 3, y = 4

400

Find the x and the y values using elimination:

3x + 2y = 8

2x - y = 3

x = 2, y = 1

500

Find the x and y value by using substitution:

2x + 7y = 34

5x - 4y = -1

x = 3, y = 4

Quadratic Expressions

100

Simplify the following expression:

3x² + 2x - 5

3x² + 2x - 5

200

Factor the quadratic expression:

(x - 2)²

(x - 2)(x - 2)

300

Evaluate the expression for x = −2:

2x² -5x +1

19

400

Factor the quadratic expression:

5x² + 10x + 5

5(x + 1)²

500

Expand and simplify the expression:

(2x−3)² 

4x² - 12x + 9

Quadratic Relations

100

 Find the vertex of the parabola defined by: 

y = x² −6x + 8

(3, -1)

200

Determine the axis of symmetry for the parabola: 

y = −x² + 4x − 2

x = 2

300

identify the direction of the opening of the parabola:

y = −2x² + 4x − 1

Opens downward 

400

Find the y-intercept of the quadratic relation:

y= −2x² + 6x − 4 

y = -4

500

 Determine the solutions for the quadratic relation:

 x² − 8x + 16 = 0

x = 4, x = 4

Quadratic Equations

100

Question: Solve the quadratic equation: 

2x² − 3x − 2 = 0

x = -1, x = 2

200

Find the solutions to the equation:

 x² + 7x + 12 = 0

x = -3, x = -4

300

Solve for x in the quadratic equation:

4x² + 4x + 1 = 0

x = -0.5, x = -0.5

400

Question: Determine the roots of the equation:

3x² + 5x + 2 = 0

x = -1, x = -2/3

500

Solve the quadratic equation: 

5x² + 10x + 5 = 0

x = -1

Trigonometry

100

Calculate the cosine of a 30^∘ angle.

0.866

200

 Determine the value of tan⁡(45∘).

1

300

 Calculate the cosine of a 90^∘ angle. 

0

400

A right angle triangle has one of its angles equal to 45^∘, What does the missing angle equal?

45^∘

500

SOH CAH TOA

Sin = Opp/Hyp 

Cos = Adj/Hyp

Tan = Opp/Adj