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Question 1 of 20 · Scatter plots and two-variable data
A tech reviewer tested 10 phones of the same model. The scatter plot shows how many hours each phone was used and the percent of battery remaining. A trend line has been drawn.
Let x be the hours of use and y the percent of battery remaining. Which equation best represents the trend line?
Hint
Find where the line crosses the vertical axis, then use two clear points on the line to find the slope. Is the line going up or down?
Step-by-step solution
The trend line has the form y = mx + b (slope-intercept form, on the formula sheet).
y-intercept b: the line crosses the vertical axis at (0, 100), so b = 100.
Slope m: use two points where the line crosses gridlines, (5, 60) and (10, 20):
m = \frac{20 - 60}{10 - 5} = \frac{-40}{5} = -8
The slope is negative because the line falls from left to right.
Put them together:
y = -8x + 100
The equation is y = -8x + 100.
Check: Substitute x = 10: -8(10) + 100 = 20 ✓, matching the point (10, 20) on the line.
Tip: Always check the sign of the slope by looking at the graph: falling line, negative slope. Then test your equation with one point you can read from the line. An equation that fails the test is wrong, no matter how close it looks.
Question 2 of 20 · Scale factors and scale drawings
A rectangular store sign has an area of 18 square feet. The owner orders a new sign with the same shape, but every length is 2.5 times as long. What is the area of the new sign?
Hint
Both the length and the width are multiplied by 2.5. What does that do to length × width?
Step-by-step solution
When every length is multiplied by k, the area is multiplied by k^2: k^2 = 2.5^2 = 6.25
New area: 18 \times 6.25 = 112.5\text{ ft}^2
The new sign has an area of 112.5 square feet.
Check: Try a sign 3 ft by 6 ft (area 18 ft²). The new sign is 7.5 ft by 15 ft, and 7.5 \times 15 = 112.5 ft² ✓
Tip: Area is length × width, and both grow by the scale factor, so the area grows by the factor twice (k \times k). When no dimensions are given, picking easy sample numbers is a fast way to check.
Question 3 of 20 · Evaluate polynomials
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Find 6x^2 - 5x + 1 for x = \tfrac{1}{2}. Enter your answer as a number.
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Square the fraction first: \left(\tfrac{1}{2}\right)^2 = \tfrac{1}{4}. You may switch to decimals: \tfrac{1}{2} = 0.5.
Check: the polynomial factors as (2x - 1)(3x - 1). At x = \tfrac{1}{2} the first factor is 2 \cdot \tfrac{1}{2} - 1 = 0, so the product is 0 ✓
Tip: an answer of 0 is allowed. It means x = \tfrac{1}{2} is a zero (root) of the polynomial. Squaring a fraction squares the top and the bottom.
Question 4 of 20 · Rectangular prisms
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A closed jewelry box is a rectangular prism 9\text{ cm} long, 5\text{ cm} wide and 4\text{ cm} tall. Dana wants to cover the whole outside of the box with fabric, with no overlap.
How many square centimeters of fabric does she need?
\text{cm}^2
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Covering the outside means all 6 faces. Use SA = ph + 2B, or add the three different face areas and double the total.
Step-by-step solution
Base (bottom): B = 9 \times 5 = 45\text{ cm}^2.
Perimeter of the base: p = 2(9) + 2(5) = 28\text{ cm}.
Lateral area (the 4 sides): ph = 28 \times 4 = 112\text{ cm}^2.
Top and bottom: 2B = 2 \times 45 = 90\text{ cm}^2.
Tip: A box has three pairs of matching faces. If your total is 101, you counted each face only once — double it.
Question 5 of 20 · Rules of exponents
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Write the value of \dfrac{10^{9}}{10^{6}} as a whole number.
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Both powers have the same base, 10. What do you do with the exponents when you divide?
Step-by-step solution
Quotient rule: \dfrac{a^m}{a^n} = a^{m-n} when the bases are the same.
Here: \dfrac{10^9}{10^6} = 10^{9-6} = 10^3.
10^3 = 10 \times 10 \times 10 = 1{,}000.
Answer: 1,000.
Check:10^9 is one billion (1{,}000{,}000{,}000) and 10^6 is one million (1{,}000{,}000). One billion divided by one million is 1{,}000. ✓
Tip: For powers of ten, the exponent counts zeros. Dividing removes zeros: 9 zeros minus 6 zeros leaves 3 zeros. A common wrong answer is 10^{1.5} (dividing the exponents 9 \div 6) — you subtract, not divide.
Question 6 of 20 · Proportions and unit conversion
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A bag of dog treats weighs 3.5 pounds. How much does the bag weigh in ounces? (1 pound = 16 ounces)
ounces
Type your answer in the box. Fractions like 3/4 are fine.
Hint
An ounce is smaller than a pound. Will the number of ounces be bigger or smaller than 3.5?
Step-by-step solution
Ounces are a smaller unit than pounds, so the number of ounces will be larger. That means multiply.
Multiply by the conversion factor \dfrac{16\text{ oz}}{1\text{ lb}}: 3.5\text{ lb} \times \frac{16\text{ oz}}{1\text{ lb}} = 56\text{ oz}
By hand: 3 \times 16 = 48 and 0.5 \times 16 = 8, so 48 + 8 = 56.
The bag weighs 56 ounces.
Check:56 \div 16 = 3.5 pounds ✓
Tip: Going from a big unit to a small unit, multiply; going from a small unit to a big unit, divide. Dividing here (3.5 \div 16 \approx 0.22) would say a bag of treats weighs less than a quarter of an ounce, which makes no sense.
Question 7 of 20 · Identify functions
No calculatorDrag and drop
The tiles mix equations, word descriptions, ordered pairs and a graph description. Sort them: is y (the output) a function of x (the input)? Three tiles belong in each box.
Function
Not a function
Tap a tile, then tap a box to place it.
Hint
For each tile, try to find one input that could have two different outputs.
Step-by-step solution
y = 0.5x - 3 — a non-vertical line; one y per x → function.
x = y^2 + 1 — at x = 5: y^2 = 4, y = \pm 2 → not a function.
Input: a book's ISBN; output: its number of pages — each ISBN names one edition with one page count → function.
Input: a U.S. state; output: a city in that state — Texas has many cities → not a function.
\{(-1, 0), (0, -1), (1, 0)\} — inputs -1, 0, 1 all different → function (the repeated output 0 is fine).
The vertical line through (4, 0) — the input 4 pairs with every y → not a function.
Answer: Function — y = 0.5x - 3, the ISBN relation, \{(-1, 0), (0, -1), (1, 0)\}. Not a function — x = y^2 + 1, the state → city relation, the vertical line.
Check: Each "not a function" tile has a concrete counterexample: (5, 2) and (5, -2); Texas → Dallas and Austin; (4, 0) and (4, 1) ✓.
Tip: One counterexample is enough to prove "not a function." Proving "function" means every input has one output.
Question 8 of 20 · Compare proportional relationships
Two lemonade recipes mix lemon juice and water in proportional amounts.
Recipe A:j = \tfrac{3}{8}w, where j is cups of lemon juice and w is cups of water.
Recipe B: shown in the table.
Water (w, cups)
4
10
Lemon juice (j, cups)
1.5
3.75
The recipe with more lemon juice per cup of water tastes stronger. Which statement is true?
Hint
Write both unit rates (cups of juice per 1 cup of water) as decimals.
Step-by-step solution
Recipe A: k = \tfrac{3}{8} = 3 \div 8 = 0.375 cup of juice per cup of water.
Recipe B: \tfrac{1.5}{4} = 0.375 and \tfrac{3.75}{10} = 0.375 cup of juice per cup of water.
The two unit rates are equal, so the recipes are equally strong.
Answer: The recipes are equally strong; both use 0.375 cup of juice per cup of water.
Check: Use Recipe A with 10 cups of water: \tfrac{3}{8} \times 10 = 3.75 cups of juice — exactly what Recipe B's table shows ✓.
Tip: Bigger numbers in a table do not mean a bigger rate. Always reduce to "per 1" before you compare.
Question 9 of 20 · Parallel and perpendicular lines
Which equation represents the line that is parallel to y = -\tfrac{1}{2}x + 3 and passes through the point (4, 5)?
Hint
Use the same slope as the given line. Then substitute (4, 5) to find a newy-intercept.
Step-by-step solution
The given slope is -\tfrac{1}{2}. A parallel line has the same slope: y = -\tfrac{1}{2}x + b.
Substitute (4, 5): 5 = -\tfrac{1}{2}(4) + b.
Multiply: 5 = -2 + b.
Add 2: b = 7.
Equation: y = -\tfrac{1}{2}x + 7.
Answer: y = -\tfrac{1}{2}x + 7
Check:-\tfrac{1}{2}(4) + 7 = -2 + 7 = 5 ✓ Same slope as the given line, different intercept (7 \ne 3) ✓
Tip: Keep the slope, change the intercept. If your new line has the same intercept as the old one, you have just rewritten the old line.
Question 10 of 20 · Unit rate as slope
Select all
Select all the relationships that are proportional with a constant of proportionality of 2.5.
Select all that apply.
Hint
For each one, check two things: is it proportional (through the origin, constant \frac{y}{x})? Is \frac{y}{x} equal to 2.5?
Step-by-step solution
A relationship qualifies only if it is proportional (y = kx, graph through the origin) andk = \frac{y}{x} = 2.5.
Test each choice:
y = 2.5x: form y = kx with k = 2.5 ✓
Line through (0, 0) and (4, 10): through the origin, k = \frac{10}{4} = 2.5 ✓
y = 2.5x + 1: the +1 means the line does not pass through the origin → not proportional.
Check: a rectangular trough 2 \times 1.5 \times 10 would hold 30\text{ ft}^3 = 225 gallons. The V-shape is half of that: 112.5 ✓.
Tip: Converting cubic feet to gallons means multiplying by 7.5 (each cubic foot holds 7.5 gallons, so gallons is the bigger number).
Question 13 of 20 · Mean, median, mode, range, weighted average
On a reading test, the 20 students in Class A had a mean score of 78. The 30 students in Class B had a mean score of 88. What is the mean score of all 50 students together?
Hint
The two classes are different sizes, so you cannot just average 78 and 88. Find each class's total points first.
Step-by-step solution
Find each class's total points (mean \times number of students):
\text{Class A: } 20 \times 78 = 1{,}560\text{Class B: } 30 \times 88 = 2{,}640
Add to get the total for all students:
1{,}560 + 2{,}640 = 4{,}200
Divide by the total number of students:
\frac{4{,}200}{50} = 84
The combined mean is 84.
Check: The answer is closer to 88 than to 78, which makes sense because Class B has more students ✓
Tip: To combine groups, never average the averages unless the groups are the same size. Go back to totals: total points \div total people.
Question 14 of 20 · Composite 2-D figures
No calculatorSelect all
Select all of the expressions that give the area, in square feet, of the L-shaped figure.
Select all that apply.
Hint
Try different ways to cut the figure: a vertical cut, a horizontal cut, or the full rectangle minus the missing corner. Evaluate each expression to compare.
Step-by-step solution
The correct area is 12 \times 9 - 5 \times 4 = 108 - 20 = 88 ft². Test each expression:
12 \cdot 9 - 5 \cdot 4 = 108 - 20 = 88 ✓ (whole rectangle minus the 5 by 4 corner)
7 \cdot 9 + 5 \cdot 5 = 63 + 25 = 88 ✓ (vertical cut: left 7 by 9, right 5 by 5)
Tip: Every correct way of splitting a figure gives the same area. If two methods disagree, one of them used a wrong side length.
Question 15 of 20 · Triangles and rectangles: area and perimeter
A farmer fences a rectangular pasture that is 120 feet long and 85 feet wide. Fencing costs $4.50 per foot.
What is the total cost to fence all four sides?
Hint
Find how many feet of fence are needed first. Then think about what one foot costs.
Step-by-step solution
Fencing goes around the edge, so find the perimeter: P = 2(120) + 2(85) = 240 + 170 = 410 ft.
Each foot costs $4.50, so multiply: 410 \times 4.50 = 1{,}845.
The fencing costs $1,845.
Check: estimate 400 \times \$4.50 = \$1{,}800, and the extra 10 ft add \$45: \$1{,}800 + \$45 = \$1{,}845 ✓.
Tip: Two-step cost problems: (1) find the right measurement (perimeter for fence, area for flooring), (2) multiply by the price per unit. Ask yourself which unit the price uses: "per foot" means perimeter; "per square foot" means area.
Question 16 of 20 · Write polynomial expressions from context
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A farmer is building a rectangular pen against the side of a barn, as shown. The barn forms one side, so no fence is needed there. Each side touching the barn is x feet, and the side opposite the barn is (3x - 4) feet.
Write an expression for the total length of fence. How many feet of fence are needed when x = 12?
ft
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Only three sides need fence. Add their lengths, combine like terms, and then substitute.
Step-by-step solution
The fenced sides are: two sides of x feet and one side of (3x - 4) feet. The barn side gets no fence.
Total fence: x + x + (3x - 4) = 5x - 4.
Substitute x = 12: 5(12) - 4 = 60 - 4 = 56.
Answer: 56 feet
Check: At x = 12 the sides are 12 ft, 12 ft and 3(12) - 4 = 32 ft. 12 + 12 + 32 = 56 ft ✓.
Tip: Read carefully which sides need material. A full perimeter would be 2x + 2(3x - 4) = 8x - 8, which would give 88 ft, too much fence.
Question 17 of 20 · Solve linear inequalities
No calculator
Find all numbers x for which \dfrac{x}{-5} < 3.
Hint
x is divided by -5. What is the opposite operation, and what does it do to the inequality sign?
Step-by-step solution
x is divided by -5, so undo it by multiplying both sides by -5.
Multiplying by a negative number reverses the sign: < becomes >.
\frac{x}{-5} \cdot (-5) > 3 \cdot (-5)
Simplify:
x > -15
Answer: x > -15
Check: Try x = 0 (in the set): \frac{0}{-5} = 0 and 0 < 3 ✓. Try x = -20 (not in the set): \frac{-20}{-5} = 4 and 4 < 3 is false ✓. The boundary x = -15 gives 3 < 3, false, so the sign stays strict.
Tip: Undoing a negative denominator is a multiplication by a negative, so it flips the sign exactly like dividing by a negative does.
Question 18 of 20 · Parallel and perpendicular lines
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What is the slope of a line that is perpendicular to the line 5x - 2y = 8? Enter your answer as a decimal or a fraction.
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Solve 5x - 2y = 8 for y to find its slope. Then flip and switch.