MPM 2D Review

Liniar systems

100

Find the point of intersection.

1. y= x + 4

2. y= -x + 2

(use of graph paper)

x = -1

y = 3

200

What are the three main methods of solving linear equations?

1. Substitution

2. Elimination 

3. Graphing

300

Solve the following system using the method of SUBSTITUTION.

x + 4y = 6

2x - 3y = 1

X = 2

y = 1

400

Solve the following linear system using ELIMINATION

3x + 2y = 19

5x - 2y = 5

x = 3 

y = 5

500

The Sports Shop sells Nike running shoes for $82 a pair and Air Jensen basketball shoes for $95 a pair. One day, the Sports Shop sells 75 pairs of Nike and Air Jensen shoes totaling $6241 in sales. How many pairs of each shoe were sold?

They sold 68 nikes and 5 Ajs

Analytic Geometry

100

Calculate the length and midpoint of the line segment joining the endpoints 𝐶(2, −4) and 𝐷(−3,5).

(use of graph paper)

(-1/2, 1/2) and the length at 10.3 units.

Negative one half and positive one half.

200

How do you find the median of a triangle?

1) Find the midpoint of the opposite side
2) Find the slope of the line connecting the vertex to the midpoint of the opposite side
3) Calculate the y-intercept of the line
4) Write the equation of the line.

300

Determine the equation of the altitude for vertex C. 

(handout)

y = -7/3x - 5/3

Negative seven over three x take away five over three.

400

Write the equation of a circle with center (0,0) and a radius of 3.

x² + y² = 9

500

A triangle has vertices 𝐶(1, 4), 𝐷(−2, 2), and 𝐸(3, 1). Determine if ∆𝐶𝐷𝐸 is a right triangle.

(use of graph paper)

There is a right angle at angle C.

Factoring

100

Simplify the following expression:

3𝑥+4𝑥+2𝑦

= 7x + 2y

200

Factor the following expression:

8x³ - 6x²y² + 4x²y

2x² (4x - 3y² + 2y)

300

Factor the following:

𝑥² + 11𝑥𝑦 + 24𝑦²

(x + 8y)(x + 3y)

400

Factor the following:

6x² + 14x + 4

2 (x+2)(3x+1)

500

Expand the following equation:

(4x²-3y)(4x²+3y)

16x⁴ - 9y²

Quadratics

100

State the direction of opening and 𝑦-intercept of the given quadratic, then make a table of values:

y= -3x² + 2

(Handout)

Parabola opens up

Y-int. (0,2)

(Following on paper)

200

Rewrite the following equation in vertex form by completing the square.

x² + 6x - 1

y = (x + 3)² - 10

300

Solve the following by using quadratic formula. 

0 = x² - 7x +12

X₁= 4

x₂ = 3

400

Find the vertex of the following quadratic

y = x² - 6x + 11

(3,2)

500

One leg of a right triangle is 1 cm longer than the other leg. The length of the hypotenuse is 9 cm greater than that of the shorter leg. Find the length of the three sides.

Side lengths are 20, 21, 29cm

Trigonometry

100

__________________________ is the branch of mathematics that deals with the relationships between the sides and the angles of triangles, and the calculations based on them.

Trigonometry

200

Find the length of side ′𝑏′ in each of the following triangle.

(Handout)

5.14 units

300

Solve for angle 𝜃:

cos𝜃 = 0.25

75.52 degrees

400

Find the length of side ′𝑓′

(Handout)

F = 4.09 degrees 

500

Find the length of side ′𝑎′

(Handout)

a = 19.96 units