Algebra & Functions
Simplify: 2(x+3)2 - x2
3x2+12x+18
In triangle ABC, angle A = 30°, angle B = 60°. What type of triangle is it?
Right triangle
Simplify:
(4/5)÷(8/15)
3/2
What’s the smallest 2-digit number divisible by both 3 and 4?
12
How many 3-letter “words” can you make from A, B, C (letters can repeat)?
33=27
A rectangle's length is 3 more than twice its width. If the area is 99, what is the width?
6
A trapezoid has bases 6 and 10 and height 5. What is its area?
40 square units
An item costs $80, then goes on sale for 25% off, plus 10% tax. What’s the final price?
$72.6
Find the sum of all the prime factors of 210
2+3+5+7=17
How many ways can 4 students sit in a row of 4 chairs?
4! = 24
Solve the system:
3x-2y=4
5x+y=19
x=3, y=2
A cube has surface area 150. What is its volume?
125
A car travels 300 miles in 5 hours. How far will it travel in 7.5 hours?
450 miles
What is the remainder when 2,345 is divided by 6?
What is 5?
A bag has 4 red, 3 blue, 3 green marbles. What’s the probability of drawing 2 green marbles in a row without replacement?
3/10 x 2/9 = 1/15
What is the 20th term of the arithmetic sequence:
5, 8, 11,...
62
Find the slope of the line through points (3,4) and (7,10).
3/2
A price increases by 10%, then decreases by 10%. What is the net change?
1% decrease
Write 321 in base 5.
2241 (base 5)
You roll two dice. What’s the probability the sum is divisible by 4?
9/36 = 1/4
Let f(x) = x2-6x+5
For what value of x does f(x)=0?
x=1 and x=5
A circle has radius r. A sector spans 60°. What fraction of the area is that?
1/6 of the total area
If (2x+3)/(x+1) =1, solve for x.
x=-2
Q: Two kids make the following claims:
Alex: “Both of us are lying.”
Bella: “Exactly one of us is lying.”
Who is telling the truth?
Bella (She's telling the truth; Alex is lying)
A spinner has values 1, 2, 3, 4. What is the expected value if you spin once?
Since there are 4 values and each is equally likely:
Each outcome has probability 1/4
Expected value=∑(value×probability)
1/4(1) + 1/4(2) + 1/4(3) + 1/4(4)