Expressions & Equations
Simplify: 3x + 5x - 2x
What is 6x?
A car travels 150 miles in 3 hours. What is the unit rate in miles per hour?
What is 50 miles per hour?
Find the area of a parallelogram with a base of 10 cm and a height of 6 cm.
What is 60 cm²? (A = base x height = 10 x 6 = 60)
List the sample space for rolling one standard six-sided die.
What is {1, 2, 3, 4, 5, 6}?
A line passes through the points (0, 2) and (4, 10) on a graph. What is the slope of this line?
What is 2? (slope = rise/run = (10-2)/(4-0) = 8/4 = 2)
Are the expressions 4(x + 3) and 4x + 12 equivalent? Justify your answer.
What is yes? 4(x + 3) = 4x + 12 by the distributive property.
A table shows: x: 2, 4, 6, 8 and y: 6, 12, 18, 24. Does this represent a proportional relationship? How do you know?
What is yes? Every y/x ratio equals 3 (constant of proportionality = 3).
Find the circumference of a circle with a radius of 7 cm. Use 3.14 for pi.
What is approximately 43.96 cm? (C = 2πr = 2 x 3.14 x 7 = 43.96)
Find the mean, median, and mode of the following data set: 4, 7, 9, 7, 3, 10, 7
What is mean = 6.71, median = 7, mode = 7?
A table shows: x: 0, 1, 2, 3 and y: -1, 2, 5, 8. Write the equation of this linear relationship in slope-intercept form.
What is y = 3x - 1? (slope = 3, y-intercept = -1)
Solve and graph the inequality: x + 5 > 12
What is x > 7? (Open circle at 7, arrow pointing right)
A graph of a proportional relationship passes through the points (3, 9) and (5, 15). What is the constant of proportionality?
What is 3? (k = y/x = 9/3 = 15/5 = 3)
A composite figure is made of a rectangle (8 ft x 5 ft) with a triangle on top (base 8 ft, height 3 ft). Find the total area.
What is 52 ft²? (Rectangle: 8x5=40; Triangle: 1/2 x 8 x 3=12; Total: 40+12=52)
Class A test scores: 70, 72, 75, 78, 80. Class B test scores: 60, 70, 75, 82, 88. Which class had a higher mean score and which had greater variability?
What is Class B has a higher mean (75 = 75 tied) but greater variability (range of 28 vs. 10)?
Given the mapping: {(1,3), (2,5), (3,5), (4,7)}, is this relation a function? Identify the domain and range.
What is yes, it is a function? Domain: {1, 2, 3, 4}; Range: {3, 5, 7}. Each input has exactly one output.
Maria earns $8 per hour plus a $15 tip. She earned $55 total. Write and solve an equation to find how many hours she worked.
What is 5 hours? 8h + 15 = 55 → 8h = 40 → h = 5
A shirt originally costs $40. It is on sale for 25% off. What is the sale price of the shirt?
What is $30? (25% of 40 = 10; 40 - 10 = 30)
A cylinder has a radius of 4 cm and a height of 10 cm. Find its surface area using the net. Use 3.14 for pi.
What is approximately 351.68 cm²? (SA = 2πr² + 2πrh = 2(3.14)(16) + 2(3.14)(4)(10) = 100.48 + 251.2)
A bag has 4 red, 3 blue, and 3 green marbles. You draw one at random. The theoretical probability of drawing red is 2/5. If you draw 50 times and get red 18 times, what is the experimental probability and how does it compare?
What is 18/50 = 9/25 (0.36)? This is close to but slightly less than the theoretical probability of 2/5 (0.40).
Graph the equation y = -2x + 4. Describe the key features: slope, y-intercept, and one other point on the line.
What is slope = -2, y-intercept = (0, 4)? Another point: (1, 2) or (2, 0). Line falls from left to right.
Simplify: (3/4)x - 2 + (1/2)x + 5. Write in simplest form.
What is (5/4)x + 3?
If 4 pounds of apples cost $6.00, how much would 10 pounds of apples cost? Set up a proportion and solve.
What is $15.00? (4/6 = 10/x → x = 15)
A water storage tank is a cylinder with a radius of 3 m and a height of 8 m. How many cubic meters of water can it hold? Use 3.14 for pi.
What is approximately 226.08 m³? (V = πr²h = 3.14 x 9 x 8 = 226.08)
In a survey of 80 students, 24 prefer math. Using proportional reasoning, how many students out of 500 would you predict prefer math?
What is 150 students? (24/80 = x/500 → 80x = 12000 → x = 150)
A phone plan charges a flat fee of $20 per month plus $0.05 per text. The equation is y = 0.05x + 20. Interpret the slope and y-intercept in context.
What is: the slope (0.05) means the cost increases $0.05 per text sent, and the y-intercept (20) means the base monthly fee is $20 even with no texts?