Algebra & Linear Equations
Solve for x: 3x + 6 = 15
Skill: Solving one-step linear equations.
Answer: x = 3
A recipe calls for 2 cups sugar for 5 cups flour. If you use 10 cups flour, how much sugar is needed?
Skill: Ratios and proportions. Answer: 4 cups sugar
Find the area of a rectangle with length 8 and width 5.
Skill: Area formula (A = l × w). Answer: 40
Simplify: (x + 2)(x + 3)
Skill: Expanding binomials. Answer: x² + 5x + 6
John is twice as old as Mary. Together, they are 18. How old is Mary?
Skill: Setting up equations. Answer: 6 years old
Simplify: 4(x + 2) = 20
Skill: Distributive property & isolating variable. Answer: x = 3
A student scored 80, 90, and 100 on three tests. What’s the mean score?
Skill: Mean/average calculation. Answer: 90
What is the circumference of a circle with radius 7? (Use π ≈ 3.14)
Skill: Circumference formula (C = 2πr). Answer: ≈ 43.96
Solve: x² = 16
Skill: Square root property. Answer: x = ±4
You buy 3 shirts for $60. What is the cost per shirt?
Skill: Unit rate. Answer: $20 per shirt
If y = 2x + 5, find y when x = 4
Skill: Substitution in linear equations. Answer: y = 13
The ratio of boys to girls in a class is 2:3. If there are 25 students, how many are boys?
Skill: Ratio reasoning. Answer: 10 boys
Find the volume of a cube with side 4.
Skill: Volume formula (V = s³). Answer: 64 cubic units
Find the vertex of y = (x − 3)² + 2
Skill: Vertex form identification. Answer: (3, 2)
A tank fills at 5 gallons/minute. How long to fill 50 gallons?
Skill: Proportional reasoning. Answer: 10 minutes
Find the slope of a line passing through (2, 4) and (6, 8)
Skill: Slope formula (m = Δy/Δx). Answer: m = 1
A car travels 150 miles in 3 hours. What is its average speed?
Skill: Speed = distance/time. Answer: 50 mph
The sum of the angles in a triangle is 180°. If two angles are 50° and 60°, find the third angle.
Skill: Angle sum property. Answer: 70°
If f(x) = 2x + 5, find f(4)
Skill: Function substitution. Answer: 13
You earn $15/hour and work 24 hours. If you spend $60, how much remains?
Skill: Multi-step arithmetic reasoning. Answer: $300
Solve the system: 2x + y = 10 and x − y = 2
Skill: Systems of equations
In a survey, 40% of 250 people preferred brand A. How many people is that?
Skill: Percent of a quantity. Answer: 100 people
Use the Pythagorean theorem to find the hypotenuse of a right triangle with legs 9 and 12.
Skill: a² + b² = c². Answer: 15
Solve for x: x² − 5x + 6 = 0
Skill: Factoring quadratics. Answer: x = 2 or x = 3
A store marks up a $40 item by 25% and then offers a 20% discount. What is the final price?
Skill: Percent increase and decrease. Answer: $40 × 1.25 = $50 → $50 × 0.8 = $40