Ratios & Proportions
A 6-ft person casts an 18-ft shadow while a car casts a 12-ft shadow. How tall is the car?
4 ft.
What percent is 0.02?
2%.
Simplify: 5(2a^2 - 3a + 1) - (a^2 + 4a - 6).
9a^2 - 19a + 11.
Area formula for a rectangle with length l and width w.
A = lw.
What is the mean of 2, 2, 4, 4, 5?
Mean = (2+2+4+4+5)/5 = 17/5 = 3.4.
If a scale drawing uses 1 in = 2 yd, how many yards does a 40-inch drawing represent?
80 yd.
What is 80% of 60?
48.
Solve: -2(x + 6) + 3x = 4 - x.
x = 8.
Using the Pythagorean theorem, find the hypotenuse c when legs are 8 and 15.
c = 17.
Define range and give the range for the set {3, 7, 12, 7, 9}.
Range = max - min = 12 - 3 = 9.
Solve for x: 3/4 = x/20.
x = 15.
A tent is first marked down 20%, then another 10% off the sale price. The final price is $144. What was the original price?
Original price $200.
Simplify and combine: (2(x+4))/3 - (x-5)/4. Give final answer as a single fraction.
(5x + 47)/12.
Area of a triangle with base 10 and height 6.
A = 1/2 × 10 × 6 = 30.
Given points (1,3) and (3,7), find the slope of the line through them and write the equation in y = mx + b form.
Slope m = (7-3)/(3-1) = 4/2 = 2. Use point (1,3): y - 3 = 2(x - 1) → y = 2x + 1.
Anne walks 7.5 km in 3 trips and 12.5 km in 5 trips. Find the unit rate (km per trip) and write an equation y = mx that models distance y as a function of trips x.
Unit rate 2.5 km/trip; equation y = 2.5x.
An item marked up 150% from cost has selling price $125. What was the original cost?
Cost = 125 / (1 + 1.5) = 125 / 2.5 = $50.
Solve for n: (1/6)(n + 7) + (1/2)(2n - 8) = -4.
n = -1.
Find the volume of a prism with base area B = 12 cm^2 and height h = 5 cm.
V = Bh = 12 × 5 = 60 cm^3.
Explain how to identify whether a scatter plot shows positive, negative, or no correlation. Give a one-sentence example for each.
Positive: points trend upward (e.g., more study hours → higher scores). Negative: trend downward (e.g., more absences → lower grades). No correlation: points scattered with no clear trend.
Two similar triangles have corresponding sides 8 and 12. If the longer triangle has a side 30 corresponding to 12, what is the matching side length for 8? Show scale-factor work.
Scale factor = 30/12 = 2.5, so matching side = 8 × 2.5 = 20.
A $500 loan accrues simple interest at 3% per year. How much interest is earned in 3 years? Show the formula used.
I = Prt = 500 × 0.03 × 3 = $45.
Find three consecutive integers where three times the middle equals four more than the sum of the first and third. Show let statement and solve.
Let x be first integer. Equation: 3(x+1) = (x + x+2) + 4 → x = 3; integers 3,4,5.
A composite figure is made of a rectangle 10 by 6 and a semicircle of radius 3 attached to one 6-unit side. Find its area (use π ≈ 3.14). Show work.
Rectangle area = 60. Semicircle area = (1/2)πr^2 = 0.5 × 3.14 × 9 = 14.13. Total ≈ 74.13 square units.
Use the Pythagorean Theorem to find the distance between points A(-3,4) and B(6,-2). Show the calculation.
Distance = sqrt[(6 - (-3))^2 + (-2 - 4)^2] = sqrt[9^2 + (-6)^2] = sqrt[81 + 36] = sqrt[117] ≈ 10.816.