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Question 1 of 20 · Dot plots, histograms and box plots
A transit worker recorded how many minutes late each of 13 buses arrived at one stop. Each dot stands for one bus.
The worker learns that the bus that was 8 minutes late had a breakdown, so she removes it from the data. How do the mean and median of the remaining 12 buses compare with the original mean and median?
Hint
Compute both measures before and after. With 12 values, the median is the average of two middle values.
Both the mean and the median decrease (mean 2.08 \to 1.58, median 2 \to 1.5).
Check:1.58 \times 12 \approx 19 ✓, and 6 values lie on each side of 1.5 ✓.
Tip: Removing a value changes the count, so the median can shift too, especially with a small data set. Do not assume the median never moves.
Question 2 of 20 · Graph solutions on a number line
No calculator
Write the graph below as an inequality. Which choice matches it?
Hint
Look at two things: is the circle filled in or hollow, and which way does the shading go?
Step-by-step solution
Boundary: the circle sits at -4.
Circle type: the circle is closed (filled in), so -4 itself is part of the solution. That means the symbol includes "or equal to": \le or \ge.
Direction: the shading and arrow go to the left, toward smaller numbers, so the values are less than-4.
Put it together: less than or equal to -4.
Answer: x \le -4
Check: Pick a shaded number, -6: is -6 \le -4? Yes ✓. Pick an unshaded number, 0: is 0 \le -4? No ✓. The boundary -4 \le -4 is true, matching the closed circle.
Tip: Read a number-line graph in this order: number → circle (closed = \le/\ge, open = </>) → direction (left = less, right = greater).
Question 3 of 20 · Write linear equations from context
At a bake sale, muffins sell for $2.50 each and cookies sell for $1.75 each. The sale brought in exactly $210. Let m be the number of muffins sold and c the number of cookies sold. Which equation models this situation?
Hint
Money from muffins + money from cookies = total money. How do you find the money from m muffins?
Step-by-step solution
Money from muffins: each muffin brings $2.50, so m muffins bring 2.50m dollars.
Money from cookies: each cookie brings $1.75, so c cookies bring 1.75c dollars.
The two amounts together make the total of $210:
2.50m + 1.75c = 210
The equation is 2.50m + 1.75c = 210.
Check: test a possible pair. If 56 muffins and 40 cookies were sold: 2.50(56) + 1.75(40) = 140 + 70 = 210 ✓ — so the equation describes real combinations of sales.
Tip: In a "total value" equation, each price multiplies the number of that item. The right side is a dollar amount, so every term on the left must also be dollars.
A real estate agent earns a 3% commission on the price of each home she sells. She sells a home for $215,000. How much commission does she earn?
$
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Write 3% as a decimal. Be careful: it is not 0.3.
Step-by-step solution
Change the percent to a decimal: 3\% = \frac{3}{100} = 0.03
Multiply by the sale price: 0.03 \times \$215{,}000 = \$6{,}450
By hand: 1\% of 215,000 is 2,150 (move the decimal point two places left). Then 3\% = 3 \times 2{,}150 = 6{,}450.
She earns a commission of $6,450.
Check:\$6{,}450 \div \$215{,}000 = 0.03 = 3\% ✓ Estimate: 3% of about $200,000 is $6,000, close to $6,450 ✓
Tip: Find 1% first by moving the decimal point two places left, then multiply. This mental-math method avoids the most common error, writing 3% as 0.3, which would make the commission $64,500, ten times too big.
Question 5 of 20 · Counting, combinations and permutations
Fill in
A radio DJ has 14 requested songs. She has time to play 3 of them, one after another, and the order she plays them in matters to her. No song is played twice.
How many different song lineups are possible?
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Does the order matter? Count the choices for the first song, then the second, then the third.
Step-by-step solution
Order matters (a lineup), and no song is played twice, so this is a permutation: {}_{14}P_3.
Tip: On the TI-30XS: 14, prb, choose nPr, 3, enter gives 2,184. Use nPr when order matters and nCr when it doesn't (here nCr would give only 364).
Question 6 of 20 · Write polynomial expressions from context
No calculator
A rectangular dog run is x feet wide. Its length is 6 feet more than 3 times its width.
Which expression represents the area of the dog run, in square feet?
Hint
Write the length in terms of x first. Then use area = length × width and distribute.
Step-by-step solution
Width = x.
"6 more than 3 times the width": length = 3x + 6.
Area = \text{length} \times \text{width} = x(3x + 6).
Distribute x to both terms: x \cdot 3x = 3x^2 and x \cdot 6 = 6x.
Area = 3x^2 + 6x.
Answer: 3x^2 + 6x square feet
Check: If x = 4, the run is 4 ft by 3(4) + 6 = 18 ft, so area = 72 ft². Expression: 3(16) + 6(4) = 48 + 24 = 72 ✓.
Tip: Area uses multiplication, so expect an x^2 term when both sides contain x. An answer with only x terms is probably a perimeter.
Question 7 of 20 · Line from two points
An electric company charges a monthly service fee plus a fixed price for each kilowatt-hour (kWh) used. One month a customer used 400 kWh and paid $68.60. The next month she used 650 kWh and paid $102.85.
What is the monthly service fee?
Hint
Find the price per kWh from the two months. Then remove the energy charges from either bill.
Step-by-step solution
Points (k, C): (400, 68.60) and (650, 102.85).
Price per kWh (slope): m = \dfrac{102.85 - 68.60}{650 - 400} = \dfrac{34.25}{250} = 0.137 dollars per kWh.
Energy charge for 400 kWh: 0.137 \times 400 = 54.80.
The largest acceptable diameter is the upper endpoint, 0.379 (the \le sign includes it).
Answer: 0.379 inch.
Check:\lvert 0.379 - 0.375 \rvert = 0.004 \le 0.004 ✓. Anything bigger, like 0.3791, is more than 0.004 away.
Tip: Line up decimal places when adding: 0.375 + 0.004 changes only the thousandths digit. Adding 0.04 by mistake gives 0.415, ten times too much tolerance.
Question 9 of 20 · Dot plots, histograms and box plots
Fill in
The box plot summarizes the wait times of patients at a walk-in clinic on one Saturday.
What is the range of the wait times?
minutes
Type your answer in the box. Fractions like 3/4 are fine.
Hint
The range uses the two ends of the whiskers.
Step-by-step solution
Range = maximum − minimum. On a box plot these are the ends of the whiskers.
Minimum (left end): 5 minutes. Maximum (right end): 52 minutes.
Subtract:
52 - 5 = 47
The range is 47 minutes.
Check: Add back: 5 + 47 = 52 ✓. Do not confuse this with the interquartile range, 30 - 12 = 18, which uses the edges of the box.
Tip: Range = whisker end − whisker end. IQR = box edge − box edge. Saying it this way helps you pick the right two numbers fast.
Question 10 of 20 · Compare proportional relationships
Maya's bike ride is shown on the graph. Leo rides at a constant speed of 15 miles per hour.
If both ride at their constant speeds for 2 hours, how many more miles does Leo ride than Maya?
Hint
Look closely at the units on the horizontal axis. Are they hours?
Step-by-step solution
Read a point on Maya's line: (30, 6) means 6 miles in 30 minutes.
Convert to miles per hour: 30 minutes is half an hour, so in 60 minutes she rides 6 \times 2 = 12 miles. Maya's speed is 12 mph. (Or: \frac{6}{30} = 0.2 mile per minute, and 0.2 \times 60 = 12 mph.)
Check: Leo: 15 \times 2 = 30 miles. Maya: 12 \times 2 = 24 miles (the graph confirms 12 miles at 60 minutes). 30 - 24 = 6 ✓
Tip: Before comparing, make the units identical — here, both in miles per hour. Graph axes in minutes are a classic GED trap.
Question 11 of 20 · Graph solutions on a number line
No calculator
A roller coaster requires riders to be at least 48 inches tall. Which graph shows all the heights h, in inches, of people who may ride?
Hint
Translate "at least 48" into an inequality symbol first. Is a person who is exactly 48 inches tall allowed to ride?
Step-by-step solution
"At least 48" means 48 or more. A rider who is exactly 48 inches tall is allowed, and anyone taller is too:
h \ge 48
Circle:\ge includes 48, so the circle at 48 is closed.
Direction: "or more" means the shading goes to the right.
Graph A has a closed circle at 48 with shading to the right.
Answer: Graph A
Check: A 50-inch rider (50 \ge 48 ✓) is in the shaded part of A. A 46-inch child (46 \ge 48 is false) is not shaded ✓. A child of exactly 48 inches can ride, and the closed circle shows that ✓.
Tip: Learn the phrase pairs: at least / no less than / minimum → \ge; at most / no more than / maximum → \le; more than / over → >; less than / under / below → <.
Question 12 of 20 · Solve linear inequalities
No calculator
Which inequality is the solution of 5 - 2x > 11?
Hint
First move the 5. Then look closely at the sign of the number multiplying x.
Step-by-step solution
Subtract 5 from both sides (the 5 is positive, so subtract it):
5 - 2x - 5 > 11 - 5 \quad\Rightarrow\quad -2x > 6
Divide both sides by -2. Dividing by a negative reverses the sign, so > becomes <:
x < \frac{6}{-2}
Simplify:
x < -3
Answer: x < -3
Check: Try x = -4: 5 - 2(-4) = 5 + 8 = 13 and 13 > 11 ✓. Try x = 0: 5 > 11 is false ✓, so values to the right of -3 really are excluded.
Tip: The term -2x carries its minus sign with it. Treat it as "-2 times x", which is why the last step is a division by -2.
Question 13 of 20 · Compare functions in different forms
Two taxi companies charge a starting fee plus a fixed amount per mile.
Taxi A:C(m) = 2.50 + 1.75m, where C is the cost in dollars for m miles.
Taxi B: shown in the table.
Miles
2
4
6
Cost ($)
8.00
12.00
16.00
Which statement is true?
Hint
For Taxi B, find the cost per mile from the change in cost over the change in miles. Then work back to 0 miles to find its starting fee.
Step-by-step solution
Taxi A: starting fee $2.50 (the constant), cost per mile $1.75 (the coefficient of m).
Taxi B's cost per mile: \frac{12 - 8}{4 - 2} = \frac{4}{2} = \text{\textdollar}2.00 per mile.
Taxi B's starting fee: from 2 miles back to 0 miles, subtract 2 \times 2.00 = 4: 8.00 - 4.00 = \text{\textdollar}4.00. So B(m) = 4 + 2m.
Compare: fee $4.00 > $2.50 and per mile $2.00 > $1.75.
Answer: Taxi B has both the higher starting fee and the higher cost per mile.
Check:B(6) = 4 + 2(6) = 16 ✓ matches the table.
Tip:8 \div 2 = 4 is not the cost per mile, because the cost includes a starting fee. Use the change in cost over the change in miles.
Question 14 of 20 · Composite 2-D figures
No calculatorDrop-down
Lena is cutting the front panel of a birdhouse from a board. The panel is a rectangle with a triangle on top.
The area of the panel, in square inches, is + .
Choose an answer from each menu.
Hint
One blank is the rectangle and one is the triangle. Which formula has a one-half in it?
Step-by-step solution
The panel splits into a rectangle (bottom) and a triangle (top) along the dashed line.
Rectangle: 9 in wide and 6 in tall, so its area is 9 \cdot 6 = 54\text{ in}^2.
Triangle: its base is the top of the rectangle, 9 in, and its height is the dashed 4 in. Area \tfrac{1}{2} \cdot 9 \cdot 4 = 18\text{ in}^2.
Check: the whole panel fits in a 9 \times 10 box (90 in²). The two empty triangles beside the roof are \tfrac{1}{2} \cdot 4.5 \cdot 4 = 9 each: 90 - 9 - 9 = 72 ✓.
Tip: The triangle's height is measured from its own base (the top of the rectangle) to the peak, not from the ground. Always keep the \tfrac{1}{2} for a triangle piece.
Question 15 of 20 · Mean, median, mode, range, weighted average
A small bakery has 8 employees. Their hourly wages have a mean of $17.25, a median of $16.80, and a range of $6.40. The owner gives every employee a raise of $1.50 per hour.
Which statement about the new wages is true?
Hint
Imagine sliding every wage up by the same amount. Which measures slide up too, and which stay the same?
Step-by-step solution
Mean: if every value goes up by $1.50, the total goes up by 8 \times 1.50 = 12 and the count stays 8. The mean goes up by 12 \div 8 = \$1.50: new mean \$18.75.
Median: the order of the wages does not change, so the middle value(s) each go up by $1.50: new median \$18.30.
Range: the highest and lowest wages both go up by $1.50, so their difference stays the same: still \$6.40.
The mean and median each increase by $1.50, and the range stays $6.40.
Check: Try a tiny example: wages $10, $12, $16 (mean 12.67, median 12, range 6). Add $1.50: $11.50, $13.50, $17.50 (mean 14.17, median 13.50, range 6). Mean and median up $1.50, range unchanged ✓
Tip: Adding the same number to every value shifts the center (mean, median, mode) by that number but leaves the spread (range) unchanged. Multiplying every value by a number changes both.
Question 16 of 20 · Evaluate linear and quadratic functions
Fill in
A worker on a roof accidentally drops a hammer. The hammer's height above the ground, in feet, t seconds after it is dropped is
h(t) = 144 - 16t^2
After how many seconds does the hammer hit the ground?
seconds
Type your answer in the box. Fractions like 3/4 are fine.
Hint
"Hits the ground" means the height is 0. Solve 144 - 16t^2 = 0. Can time be negative here?
Step-by-step solution
On the ground, the height is 0, so set h(t) = 0: 144 - 16t^2 = 0.
Add 16t^2 to both sides: 144 = 16t^2.
Divide by 16: t^2 = 9.
Square root: t = 3 or t = -3.
Time after the drop cannot be negative, so reject t = -3.
Answer: 3 seconds
Check:h(3) = 144 - 16(9) = 144 - 144 = 0 ✓ and h(0) = 144 ft is the roof height, which makes sense.
Tip: In word problems, solve completely and then ask whether each solution makes sense. Algebra gives \pm 3, but only the positive time fits the situation. Do not answer 9 — that is t^2, not t.
Question 17 of 20 · Order fractions and decimals, including on a number line
No calculator
A pharmacy technician weighs four tablets. Their masses, in grams, are shown.
Tablet
Mass (g)
A
0.35
B
0.305
C
0.3
D
0.351
Which tablet is the heaviest?
Hint
Give every mass the same number of decimal places by adding zeros at the end, then compare digit by digit from the left.
Step-by-step solution
Write every mass with 3 decimal places: 0.350, 0.305, 0.300, 0.351.
All the tenths digits are 3, so look at the hundredths digits: 5, 0, 0, 5. Tablets A and D are still tied with 5.
Compare A and D at the thousandths place: 0 vs 1. D has the larger digit.
Full order from least to greatest: 0.300 < 0.305 < 0.350 < 0.351.
The heaviest is Tablet D (0.351 g).
Check:0.351 - 0.350 = 0.001 > 0, so D is heavier than A by one thousandth of a gram. ✓
Tip: Do not stop comparing when two numbers look tied. 0.35 and 0.351 match for two places; the third place decides it.
Question 18 of 20 · Absolute value and distance on a number line
No calculatorFill in
Plot -9.5 and -2 on a number line. How many units apart are they?
units
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Both numbers are on the same side of zero. Subtract the two numbers and take the absolute value.
Step-by-step solution
Distance on a number line: d = \lvert b - a \rvert.
Substitute a = -9.5 and b = -2: d = \lvert -2 - (-9.5) \rvert.
Subtracting a negative is adding: -2 + 9.5 = 7.5.
\lvert 7.5 \rvert = 7.5.
Answer: 7.5 units.
Check: both numbers are left of zero, so the distance is the difference of their distances from zero: 9.5 - 2 = 7.5. ✓ Counting the other way gives the same result: \lvert -9.5 - (-2) \rvert = \lvert -7.5 \rvert = 7.5.
Tip: Same side of zero → subtract the sizes. Opposite sides → add them. Adding here (9.5 + 2 = 11.5) is the most common mistake.
Question 19 of 20 · Factor polynomials
Dana factored x^2 - 2x - 15. Her work is shown.
Step 1: I need two numbers whose product is -15 and whose sum is -2.
Step 2: The numbers are 3 and -5.
Step 3: So x^2 - 2x - 15 = (x - 3)(x + 5).
Which statement is true?
Hint
Check each step. Then multiply Dana's final answer back out and compare.
Step-by-step solution
Step 1 states the correct rule for x^2 + bx + c: product = c = -15, sum = b = -2 ✓.
Step 2:3 \cdot (-5) = -15 ✓ and 3 + (-5) = -2 ✓. The numbers are right.
Step 3: the numbers 3 and -5 go into the factors with their own signs: (x + 3)(x - 5). Dana wrote (x - 3)(x + 5), flipping both signs.
Multiply her answer: (x - 3)(x + 5) = x^2 + 5x - 3x - 15 = x^2 + 2x - 15. That has +2x, not -2x.
Answer: The first error is in Step 3; the correct factorization is (x + 3)(x - 5).