grade 10 math game show

Linear Systems

100

Solve the following system of linear equations:

2x+3y=16

4x−y=9

 x = 3.07 and y = 3.28

200

Solve the following system of linear equations:

3x−2y=5

x+4y=11

x = 3 and y = 2

300

Solve the following system of linear equations:

5x+2y=20

3x−4y=−6

x = 2.62 y = 3.45

400

x+y=5

2x−y=1

x = 2 y = 3

500

Solve the following system of linear equations:

2x+3y−z=7

4x−y+2z=5

x+y+z=4

x = 1, y = 2 and z = 1

Quadratic Expressions and Relations

100

Factor the quadratic expression x2−5x+6.

x2−5x+6=(x−2)(x−3)

200

Solve the quadratic equation x2+4x−21=0.

x=−7 or x=3

300

Rewrite the quadratic expression x2+6x+5 in  the form of (x+p)2+q.

(x+3)²−4

400

Solve the quadratic equation 3x2−2x−8=0 using the quadratic formula.

x=2 and x=−3/4

500

A rectangular garden has an area of 48 square meters. The length is 2 meters more than twice the width. Find the dimensions of the garden.

The length is 2w+2=2(4)+2=10

Quadratics Equations

100

Solve the quadratic equation x2−4=0.

x = 2 or x = -2

200

Solve the quadratic equation 2x2−3x=0.

So, the solutions are x=0 and x=3/2

300

Solve the quadratic equation x2+6x+5=0 by completing the square.

so, x = -1 or -5

400

Solve the quadratic equation 3x2+x−4=0 using the quadratic formula.

x = 1 and x=−3/4.

500

The product of two consecutive positive integers is 182. Find the integers.

So, the integers are 13 and 14.

Trigonometry

100

In a right triangle, one of the angles is 30∘ and the hypotenuse is 10 units long. Find the length of the side opposite the 30∘ angle.

opposite=10×2/1=5

200

In a right triangle, the side opposite the angle θ is 4 units and the hypotenuse is 5 units. Find θ.

θ≈53.13∘

300

In a right triangle, the lengths of the legs are 6 units and 8 units. Find the length of the hypotenuse.

c=10

400

n a right triangle, one of the angles is 45∘ and the side adjacent to this angle is 7 units long. Find the length of the side opposite the 45∘ angle.

opposite=7

500

A ladder is leaning against a wall. The ladder is 15 meters long and makes an angle of 60∘ with the ground. How high up the wall does the ladder reach?

So, the ladder reaches 7.5 meters up the wall.

Analytic Geometry

100

Find the distance between the points A(2,3) and B(5,7).

d=5

200

Find the midpoint of the line segment joining the points C(−1,4) and D(3,−2).

M=(1,1)

300

Find the equation of the line passing through the points E(1,2) and F(4,8).

m=2

400

Find the point of intersection of the lines y=2x+3y  and y=−x+1y.

So, the point of intersection is (−3/2,3/5).

500

Find the equation of the circle with center (3,−2) and radius 5.

The equation of the circle is (x−3)2+(y+2)2=25.