Gr.10 Math

Linear Equations

100

Solve the equation: 7x = -56

x=-8

200

Simplify the expression: 2y+4x-3+2x-y+1

6x+y-2

300

Solve the equation: 6(y - 2)÷3 = 8                        

y=6

400

Solve the equation: -2(y+8)=(5y+25)÷-2

y=7

500

Mike rents a car from the car rental company for a deposit of $200 plus $57 per day. Write the equation for Mike's total rental cost: C represents dollars, and d represents days. Can Mike rent the car for a week if he has $600? 

C=200+57d

Mike can rent the car for a week.

C=200+57(7)

C=599

$600(the amount of Mike's money)＞$599(the rental cost)

Linear Relations

100

Find the y-intercept of y=-4x+2

y-intercept:2

200

Find the slope of y=7x-6

Slope:7

300

How would a line slope if it had a negative slope?

The line will slant downward from left to right.

400

What is the equation of the line with y-intercept 6 and slope -3?

Equation: y=-3x+6

500

If a line passes through points (-1, 3) and (-2, 10), what is the equation of the line?

y= -7x -4

Similar Triangles and Trigonometry

100

How many inches is 12.7 cm?

5 inches

200

Tan45°=

1

300

Cos x= 0.62932 Find angle x

x=51

400

Triangle ABC is similar to triangle DEF, state the pairs of corresponding angles and corresponding sides.

∠A=∠D

∠B=∠E

∠C=∠F

AB=DE

BC=EF

CA=FD

500

Jack is standing 15 metres away from the base of a building. He looks at the top of the building at an 75° angle. How tall is the building?

tan 75°= h/15

h=15×tan 75°

h=56

The height of the building is 56 metres.

Volume and Surface Area

100

Rectangle

Length=12cm

Width=7cm

Find the area

A=lw

Area=12×7

=84cm²

The area is 84cm²

200

Circle

Diameter=12mm

Find the perimeter

C=𝝅d or C=2𝝅r

C=𝝅(12)

C=37.7mm

The perimeter is 37.7mm

300

Rectangular prism

Length=16cm

Width=6cm

Height=4cm

Find the surface area

A=2(wh+lw+lh)

A=2(6×4+16×6+16×4)

A=368cm²

The surface area is 368cm²

400

Sphere

Diameter=18cm

Find the volume

V=4𝝅r³/3

V=4𝝅(18÷2)³/3

V=3053.6cm³

The volume is 3053.6cm³

500

Cylinder

Diameter=15cm

Height=5cm

Find the surface area

A_total=2𝝅r²+2𝝅rh

A_total=2𝝅(15÷2)²+2𝝅(15÷2)(5)

A_total=589cm²

The surface area is 589cm²

Quadratic Relations

100

What is the formula for the quadratic equation?

y=ax²+bx+c

200

When a quadratic relation is graphed, what is formed?

A parabola

300

Expand and simplify the following expressions

(x+5)(x-3)

(x+5)(x-3)

=x²−3x+5x−15

=x²+2x−15 

400

Factor the following binomials

25n²-4

√25n²=5n √4=2

Answer=(5n+2)(5n-2) 

500

Factor fully

2x²+2x−40

GCF=2

2x²+2x−40

2(x²+x−20)

5(-4)=-20

5+(-4)=1

Answer=2(x−4)(x+5)