Algebra
Solve for x: 2x+3=11
x=4
How many degrees are in a triangle?
180
If you buy 3 pencils for $2 each, how much do you pay?
3x2=$6
What is x in the equation: x2−9=0
3, -3
What’s the next number: 3, 6, 9, 12, … ?
15
Simplify: 3(2x−5)+4x
10x-15
Find the area of a rectangle with length 5 and width 8
40
A car travels 60 km in 1.5 hours. What is its speed in km/h?
Speed = 60/1.5=40km/h
Factor: x2+5x+6
(x+2)(x+3)
Evaluate 24+32
16+9=25
Factor completely, x2-9x+20
(x-4)(x-5)
The hypotenuse of a right triangle is 13 and one side is 5. Find the other side
132-52=x2
x2=144
x=12
A rectangle’s length is 3 times its width. If the perimeter is 48 cm, find the length and width.
w+3w+3w+w=48
8w=48
w=6
Solve: x2−4x−12=0
(x-6)(x+2)
x=6,-2
If f(x)=2x+1 what is f(4)?
f(4)=9
Solve: (x-3)/2=4x+1
x=-5/7
A regular hexagon has sides of length 4. Find its perimeter
6x4=24
A store has a sale: buy 2 apples, get the 3rd half-price.
Apples cost $3 each.
You buy 9 apples.
How much does it cost in total?
Every third apple only costs $1.5.
3+3+1.5+3+3+1.5+3+3+1.5=$22.5
Solve using the quadratic formula: 2x2−3x−2=0
2 and -1/2
Simplify (x3)2/x4
x2
Solve for x: x3−3x2−4x+12=0
x=-2,2,3
One way to do this is through factoring by grouping.
x3−3x2−4x+12= x2(x-3)-4(x-3)
since the terms in the brackets are the same, we can factor it out of both terms, giving us (x2-4)(x-3)
A circle and a square have the same perimeter. The circle’s radius is r. Show an expression for their areas related to each other. (hint: the perimeter of a circle is 2πr.)
since their perimeters are equal, 2πr=4x
the area of a circle is x2 we can divide both sides by 4 and square it to get an expression of area.
(π2r2)/2=x2
A water tank fills at 7 L/min.
A small drain pipe leaks 1.5 L/min.
The tank must reach 200 L to overflow.
It already has 35 L inside.
How long until it overflows?
Net fill=7-1.5=5.5 L/min
Amount needed = 200−35=165L
time=165/5.5=30 minutes
The product of three consecutive integers is 210. What are the integers?
An Integer is a whole number(like 1,3)
Consecutive means right after each other(like 27,28,29)
5,6 and 7. 5x6x7=210
A pattern of tiles is made like this:
Row 1 has 3 tiles.
Row 2 has 6 tiles.
Row 3 has 9 tiles.
and so on
If this pattern continues, how many tiles are there in Row 20 and what is the total number of tiles in all 20 rows?
630
Tiles in row 20: 3x20
each row has 3 more tiles
3+6+9+...+60
factor out 3: 3(1+2+3+...+20)
calculate: 3 x210=630