Basic rules
Simplify: 3 + 6 ÷ 2 × (4 − 1)
3 + 6 ÷ 2 × 3 = 3 + 9 = 12
Write 0.5 as a fraction
1/2
Write 4,500 in scientific notation.
4.5 × 10³
Simplify √64
Simplify √(9/16)
What shape is the graph of y = x² + bx + c?
A parabola
Simplify: (2x³y²)² ÷ (4x²y⁵)
(4x⁶y⁴)/(4x²y⁵) = x⁴ / y
Simplify: (5/8) ÷ (10/3)
(5/8 × 3/10) = 3/16
Write 0.00052 in scientific notation.
5.2 × 10⁻⁴
Simplify √(9/16)
3/4
Factor completely: x² + 7x + 10
(x + 2)(x + 5)
If 5(x − 2) = 3x + 6, what is x?
5x − 10 = 3x + 6 → x = 8
The ratio of boys to girls is 3:5. If there are 40 students, how many boys are there?
3/8 × 40 = 15 boys
Simplify: (2 × 10³)(3 × 10⁻²)
6 × 10¹
Simplify √(50x²)
5x√2
Solve: x² − 5x + 6 = 0
x = 2 or 3
Simplify: (a⁻³b²)⁻²
a⁶ / b⁴
Convert 0.375 into a simplified fraction
3/8
Simplify: (6 × 10⁵) ÷ (3 × 10⁻²)
2 × 10⁷
Solve for x: √(x + 4) = 5
x = 21
Vertex form of y = x² − 4x + 1
y = (x − 2)² − 3 (vertex (2, −3))
When a number is increased by 20% and then decreased by 20%, is the final result the same as the original number?
No, it’s 0.96 of the original (a 4% decrease).
A car travels 250 miles using 10 gallons of gas. How many miles per gallon is this, and how many gallons for 600 miles?
25 mpg; 600 ÷ 25 = 24 gallons
The distance to a star is 4.2 × 10⁸ km. A spaceship travels 3.5 × 10⁴ km per hour. How long will it take (in hours)?
(4.2 × 10⁸) ÷ (3.5 × 10⁴) = 1.2 × 10⁴ = 12,000 hours
Rationalize the denominator: 3 / (2√5)
(3√5) / 10
Solve using quadratic formula: 2x² − 3x − 5 = 0
x = [3 ± √(9 + 40)] / 4 = [3 ± 7] / 4 → x = 2.5 or −1