Algebra
Solve for x where 4x-9=19
4x=28⟹x=7
What is the specific name for a quadrilateral with exactly one pair of parallel sides?
Trapezoid
A t-shirt costs $20. If there is a 5% sales tax, how much is the tax amount?
$20 \times 0.05 = 1
If you flip a fair coin, what is the probability of landing on heads?
1/2 or 50%
This ancient Greek mathematician is famously associated with a theorem about the sides of a right triangle. Who is he?
Pythagoras
Simplify the expression: 5(3x−2)−2(4x+1).
15x−10−8x−2=7x−12
Two angles are supplementary. If one angle measures 75∘, what is the measure of the other angle?
180∘−75∘=105∘
You buy an item for $50 and get a 10% discount. What is the final price after the discount?
$50 \times 0.10 = $5 (discount); $50 - $5 = 45
What is the mode of the following data set: 2, 5, 7, 5, 9, 2, 5?
5
This brilliant Italian astronomer, physicist, and engineer is often called the "Father of Modern Science" and made significant contributions to our understanding of gravity and motion.
Galileo Galilei
Solve the inequality: 2(3x+1)≤4x−6.
6x+2≤4x−6⟹2x≤−8⟹x≤−4
A right triangle has legs measuring 5 units and 12 units. What is the length of its hypotenuse?
Using Pythagorean Theorem a^2+b^2=c^2: 5^2+12^2=c^2⟹25+144=c&2⟹169=c^2⟹c=13 units.
If you put $1000 in a savings account with a simple interest rate of 3% per year, how much interest would you earn in 2 years?
$1000 \times 0.03 \times 2 = 60
a bag, there are 4 red marbles and 6 blue marbles. What is the probability of picking a red marble?
4/10 or 2/5
Often called the "Father of Geometry," this ancient Greek mathematician wrote "The Elements," a foundational text for geometry.
Euclid
If g(x)=−3x2+x−5, what is the value of g(−2)?
g(−2)=−3(−2)2+(−2)−5=−3(4)−2−5=−12−2−5=−19
A circle has a circumference of 18π cm. What is its area?
C=2πr⟹18π=2πr⟹r=9 cm. Area A=πr2=π(92)=81π square cm.
A 6-pack of soda costs $3.60. A single can costs $0.75. Which is the better deal per can?
6-pack: $3.60 / 6 = 0.60 per can. Single can: $0.75. The 6-pack is the better deal.
What is the mean (average) of the numbers 12, 15, 10, 13, and 20?
(12+15+10+13+20)/5=70/5=14
This British scientist is famous for developing the laws of motion and universal gravitation, and is also credited with co-inventing calculus.
Isaac Newton
Solve the system of equations for x and y: 3x+2y=16 x−3y=−2
(Multiply second eq. by 3: 3x−9y=−6. Subtract from first eq.: (3x+2y)−(3x−9y)=16−(−6)⟹11y=22⟹y=2. Substitute y=2 into x−3y=−2: x−3(2)=−2⟹x−6=−2⟹x=4. So, x=4,y=2)
A square is inscribed in a circle. If the radius of the circle is 5 units, what is the perimeter of the square?
The diagonal of the square is the diameter of the circle, so diagonal d=2×5=10 units. For a square with side s, s2+s2=d2⟹2s2=102⟹2s2=100⟹s2=50⟹s=50=52 units. Perimeter =4s=4×52=202units.
You want to buy a new laptop for $800. You make a down payment of 25% and finance the rest. How much do you need to finance?
$800 \times 0.25 = $200 (down payment); $800 - $200 = 600 (to finance)
A die is rolled. What is the probability of rolling an even number or a number greater than 4?
Even numbers: {2, 4, 6}. Numbers greater than 4: {5, 6}. Union: {2, 4, 5, 6}. Probability: 6/4 or 3/2.
This German mathematician is considered one of the greatest mathematicians of all time, making profound contributions to number theory, algebra, statistics, and many other areas. He has a famous bell-shaped curve named after him.
Carl Friedrich Gauss