ATITEAS 7 MATH EXAM RECENTLY UPDATED 2023 WITH COMPLETE SOLUTIONS

ATITEAS 7 MATH EXAM RECENTLY UPDATED 2023 WITH COMPLETE SOLUTIONS 1. Simplify the following expression: 2x + 4y - 3x - 2y Solution: 2x - 3x + 4y - 2y = -x + 2y 2. If a recipe calls for 2 1/2 cups of flour, and you want to make 1/2 of the recipe, how much flour do you need? Solution: To make 1/2 of the recipe, you need half the amount of flour, which is: (1/2) x 2 1/2 cups = 1 1/4 cups 3. Solve for x: 2(x + 5) = 12 Solution: First, distribute the 2: 2x + 10 = 12 Then, subtract 10 from both sides: 2x = 2 Finally, divide both sides by 2: x = 1 4. If a pizza has a diameter of 12 inches, what is the circumference of the pizza? Solution: The formula for the circumference of a circle is: C = πd where C is the circumference, d is the diameter, and π is approximately 3.14. So, for a pizza with a diameter of 12 inches, the circumference is: C = πd = 3.14 x 12 = 37.68 inches 5. Find the slope of the line passing through the points (-3, 4) and (1, -2). Solution: The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: slope = (y2 - y1) / (x2 - x1) So, for the given points: slope = (-2 - 4) / (1 - (-3)) = -6/4 = -3/2 6. Simplify the following expression: 3x + 2y + 4x - 3y Solution: Combine like terms: 3x + 4x + 2y - 3y = 7x - y 7. Find the value of x in the following equation: 4(x - 3) = 12 Solution: Divide both sides by 4: x - 3 = 3 Add 3 to both sides: x = 6 8. Solve for x in the following equation: 5x + 7 = 32 Solution: Subtract 7 from both sides: 5x = 25 Divide both sides by 5: x = 5 9. What is the area of a rectangle with a length of 6 meters and a width of 3 meters? Solution: The formula for the area of a rectangle is: A = lw Substituting l = 6 and w = 3: A = 6 x 3 = 18 square meters 10. What is the perimeter of a square with a side length of 4 feet? Solution: The formula for the perimeter of a square is: P = 4s Substituting s = 4: P = 4 x 4 = 16 feet 11. If the ratio of boys to girls in a class is 3:5 and there are 24 girls, how many boys are in the class? Solution: Let the number of boys in the class be x. The ratio of boys to girls is 3:5, so: x/24 = 3/5 Cross-multiply: 5x = 72 Divide both sides by 5: x = 14.4 Since there can't be a fraction of a person, round up to the nearest whole number: x = 15 12. What is the slope-intercept form of the equation of a line that passes through the point (2, 5) with a slope of 3? Solution: The slope-intercept form of the equation of a line is: y = mx + b where m is the slope and b is the y-intercept. Substituting m = 3 and the point (2, 5): 5 = 3(2) + b Simplifying: 5 = 6 + b Subtract 6 from both sides: -1 = b So the equation is: y = 3x - 1 y = -3 So the y-intercept is (0, -3). 13. If a car is traveling at a speed of 60 miles per hour, how many miles will it travel in 2 hours? Solution: Distance = Rate x Time Substituting r = 60 miles per hour and t = 2 hours: Distance = 60 x 2 = 120 miles 14. What is the y-intercept of the line with the equation y = 2x - 3? Solution: The y-intercept is the point where the line intersects the y-axis, which occurs when x = 0. Substituting x = 0: y = 2(0) – 3 Simplifying: 15. If a pizza has a diameter of 12 inches, what is its circumference? Solution: The formula for the circumference of a circle is: C = πd Substituting d = 12 inches and using π ≈ 3.14: C = 3.14 x 12 = 37.68 inches 16. What is the midpoint of the line segment with endpoints (3, 4) and (9, 8)? Solution: The formula for the midpoint of a line segment is: ( (x1 + x2)/2, (y1 + y2)/2 ) Substituting x1 = 3, x2 = 9, y1 = 4, and y2 = 8: ( (3 + 9)/2, (4 + 8)/2 ) = (6, 6) So the midpoint is (6, 6). 17. If a rectangle has a length of 8 inches and a width of 6 inches, what is its perimeter? Solution: The formula for the perimeter of a rectangle is: P = 2l + 2w Substituting l = 8 inches and w = 6 inches: P = 2(8) + 2(6) = 28 inches 18. What is the slope of the line that passes through the points (-3, 5) and (2, -1)? Solution: The formula for the slope of a line is: m = (y2 - y1)/(x2 - x1) Substituting x1 = -3, y1 = 5, x2 = 2, and y2 = -1: m = (-1 - 5)/(2 - (-3)) = -6/5