ATITEAS 7 MATH EXAM RECENTLY UPDATED 2023 WITH
COMPLETE SOLUTIONS
1. Simplify the following expression:
2x + 4y - 3x - 2y
Solution:
2x - 3x + 4y -
... [Show More] 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 [Show Less]