A full-length, test-day-style GED Mathematical Reasoning practice exam: 46 questions modeled on the real blueprint, split into a no-calculator section (the first 5 questions) and a calculator section (the remaining 41), with a provided formula sheet. It covers the complete range of tested skills -- number sense and operations, ratios, proportions, and percents, geometry and measurement, data and statistics, and the full sweep of algebra (expressions, equations, inequalities, functions, and graphs) -- at an easy-to-hard difficulty spread. Every question includes a worked explanation and a pro tip. Use the lessons to learn the exam rules (115 minutes, scored 100-200, 145 to pass) and the formula sheet before you start, then take the 46 questions as one timed rehearsal.

Before you begin — exam rules & formula sheet

### 1. The Real GED Math Test: Format & Rules

This exam is built to feel like the real GED® Mathematical Reasoning test. Here is exactly what you are walking into:

- 46 questions in 115 minutes (1 hour and 55 minutes). That is just over 2 minutes per question on average.
- The test comes in two parts, and this practice exam follows the same order:
- Part 1 -- Questions 1-5: NO CALCULATOR. These are kept friendly on purpose: clean numbers, basic operations, and number sense you can do by hand.
- Part 2 -- Questions 6-46: CALCULATOR ALLOWED. On the real test you get an on-screen TI-30XS calculator (or your own approved one). Everything from percents to algebra to geometry lives here.
- You may not go back to Part 1 once you start Part 2 on the real test, so finish the no-calculator questions before moving on.
- A formula sheet is provided (see the next lesson) -- you do not have to memorize area and volume formulas.

Scoring: each GED® test is scored from 100 to 200, and you need 145 to pass. There is no penalty for wrong answers, so never leave a question blank -- always guess.

Quick Check

How many questions are on the GED® Mathematical Reasoning test?

It is 46 questions in 115 minutes.

### 2. The Formula Sheet You Get

On test day the GED® gives you a formula sheet. You do not need to memorize these -- but you do need to know which formula to grab. The most-used ones:

Area

- Rectangle: \(A = lw\)
- Triangle: \(A = \tfrac{1}{2}bh\)
- Circle: \(A = \pi r^2\)
- Trapezoid: \(A = \tfrac{1}{2}(b_1 + b_2)h\)

Perimeter / Circumference

- Rectangle: \(P = 2l + 2w\)
- Circle: \(C = 2\pi r = \pi d\)

Volume

- Box (rectangular prism): \(V = lwh\)
- Cylinder: \(V = \pi r^2 h\)
- Cone: \(V = \tfrac{1}{3}\pi r^2 h\)
- Sphere: \(V = \tfrac{4}{3}\pi r^3\)

Algebra & Geometry

- Pythagorean theorem: \(a^2 + b^2 = c^2\)
- Slope: \(m = \dfrac{y_2 - y_1}{x_2 - x_1}\)
- Slope-intercept line: \(y = mx + b\)
- Quadratic formula: \(x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Percent & rate ideas to keep in your head

- Percent change \(= \dfrac{\text{new} - \text{old}}{\text{old}}\)
- Distance \(= \text{rate} \times \text{time}\)

Reading a problem, picking the right formula, and substituting the numbers in.
Quick Check

Which formula gives the volume of a cylinder? Write it using pi, r, and h.

Volume of a cylinder is pi times r squared times the height.

### 3. Pacing & Strategy for Test Day

You have the math skills -- this lesson is about using your time well across 46 questions.

Pacing. A little over 2 minutes per question. If one stalls you, lock in your best guess, flag it, and move on. Coming back with a fresh eye is faster than grinding.

Backsolve. When the answer choices are numbers, plug them into the problem instead of doing all the algebra -- start with a middle value and adjust.

Estimate first. A quick estimate kills obviously-wrong choices and catches calculator typos (a decimal in the wrong place).

Mind the units. Length is plain units, area is square units, volume is cubic units. Re-read the last line of the question so you answer what's actually asked (price vs. discount, area vs. perimeter).

Never leave a blank. No penalty for wrong answers -- eliminate what you can, then guess.

Part 1 first. Get the 5 no-calculator questions done before you touch Part 2; you can't return to them.

Quick Check

About how many minutes do you have per question on the GED® Math test? Answer with a number.

115 minutes for 46 questions is just over 2 minutes each.

## Part 1 — Questions 1–5No calculator

Q1 Easy

No-calculator section. Simplify using order of operations: \(3 + 4 \times 2^2\).

- \(19\)

- \(28\)

- \(49\)

- \(22\)

Explanation

Powers first: \(2^2 = 4\). Then multiply: \(4 \times 4 = 16\). Then add: \(3 + 16 = 19\). The trap 28 does \((3+4)\times 4\), adding before multiplying. Pro tip: remember PEMDAS -- exponents and multiplication come before addition.

Q2 Easy

No-calculator section. What is \(\dfrac{3}{4} - \dfrac{1}{2}\)?

- \(\frac{1}{4}\)

- \(\frac{1}{2}\)

- \(\frac{2}{2}\)

- \(\frac{1}{8}\)

Explanation

Use a common denominator of 4: \(\frac{1}{2} = \frac{2}{4}\), so \(\frac{3}{4} - \frac{2}{4} = \frac{1}{4}\). The trap \(\frac{1}{8}\) subtracts tops and multiplies bottoms. Pro tip: you can only add or subtract fractions once the denominators match.

Q3 Medium

No-calculator section. Evaluate: \(-5 + (-3) \times 2\).

- \(-11\)

- \(-16\)

- \(4\)

- \(-1\)

Explanation

Multiply first: \((-3)\times 2 = -6\). Then add: \(-5 + (-6) = -11\). The trap \(-16\) does \((-5 + -3)\times 2\), adding before multiplying. Pro tip: multiplication comes before addition, even with negatives.

Q4 Medium

No-calculator section. Simplify: \(2^3 \times 2^2\).

- \(32\)

- \(64\)

- \(16\)

- \(12\)

Explanation

When you multiply powers with the same base, add the exponents: \(2^{3+2} = 2^5 = 32\). You can also check: \(8 \times 4 = 32\). The trap 64 multiplies the exponents \((2^6)\). Pro tip: same base and multiplying -> add the exponents.

Q5 Medium

No-calculator section. Between which two whole numbers does \(\sqrt{50}\) fall?

- Between 7 and 8

- Between 6 and 7

- Between 8 and 9

- Between 24 and 26

Explanation

\(7^2 = 49\) and \(8^2 = 64\). Since 50 is just above 49, \(\sqrt{50}\) is a little more than 7, so it sits between 7 and 8. The trap 'between 24 and 26' halves 50. Pro tip: to estimate a square root, find the two perfect squares it lands between.

## Part 2 — Questions 6–46Calculator allowed

Q6 Easy

Calculator section. What is \(20\%\) of \(150\)?

- \(30\)

- \(3\)

- \(300\)

- \(7.5\)

Explanation

\(20\% = 0.20\), and \(0.20 \times 150 = 30\). The trap 3 misplaces the decimal \((0.02 \times 150)\). Pro tip: 'percent of' means multiply, after turning the percent into a decimal.

Q7 Medium

An \$80 pair of shoes is marked \(25\%\) off. What is the sale price?

- \$60

- \$20

- \$55

- \$100

Explanation

The discount is \(0.25 \times 80 = \$20\), so the price is \(80 - 20 = \$60\). The trap \$20 gives only the discount, not the new price. Pro tip: 25% off means you pay 75%: \(0.75 \times 80 = 60\).

Q8 Medium

A price rises from \$40 to \$50. What is the percent increase?

- \(25\%\)

- \(20\%\)

- \(10\%\)

- \(125\%\)

Explanation

Percent change \(= \frac{\text{new}-\text{old}}{\text{old}} = \frac{50-40}{40} = \frac{10}{40} = 0.25 = 25\%\). The trap 20% divides by the new value (50). Pro tip: for percent change, always divide by the ORIGINAL amount.

Q9 Medium

\(12\) is what percent of \(48\)?

- \(25\%\)

- \(4\%\)

- \(40\%\)

- \(36\%\)

Explanation

\(\frac{12}{48} = 0.25 = 25\%\). The trap 4% comes from \(48 \div 12\) read backwards. Pro tip: 'what percent of' means part divided by whole, then times 100.

Q10 Medium

A \$50 item has an \(8\%\) sales tax added. What is the total cost?

- \$54.00

- \$58.00

- \$50.08

- \$4.00

Explanation

The tax is \(0.08 \times 50 = \$4\), so the total is \(50 + 4 = \$54\). The trap \$4 is only the tax. Pro tip: adding 8% tax is the same as multiplying by 1.08: \(1.08 \times 50 = 54\).

Q11 Medium

Two numbers are in the ratio \(3:5\) and add up to \(40\). What is the smaller number?

- \(15\)

- \(24\)

- \(8\)

- \(5\)

Explanation

The ratio has \(3 + 5 = 8\) parts, so each part is \(40 \div 8 = 5\). The smaller number is \(3 \times 5 = 15\). The trap 24 is the larger number \((5 \times 5 - 1)\)? No -- 24 is \(3\times 8\), mixing up the steps. Pro tip: add the ratio numbers to find the size of one part first.

Q12 Medium

Solve the proportion \(\dfrac{4}{10} = \dfrac{x}{25}\).

- \(x = 10\)

- \(x = 62.5\)

- \(x = 16\)

- \(x = 100\)

Explanation

Cross-multiply: \(10x = 4 \times 25 = 100\), so \(x = 10\). The trap 62.5 cross-multiplies the wrong pair. Pro tip: \(\frac{4}{10}\) is the same as \(0.4\), and \(0.4 \times 25 = 10\).

Q13 Easy

A car travels \(240\) miles in \(4\) hours. What is its average speed?

- \(60\) mph

- \(960\) mph

- \(236\) mph

- \(40\) mph

Explanation

Speed \(= \frac{\text{distance}}{\text{time}} = \frac{240}{4} = 60\) mph. The trap 960 multiplies instead of dividing. Pro tip: 'per hour' means divide the distance by the number of hours.

Q14 Easy

A train travels at \(65\) miles per hour for \(3\) hours. How far does it go?

- \(195\) miles

- \(68\) miles

- \(21.7\) miles

- \(62\) miles

Explanation

Distance \(= \text{rate} \times \text{time} = 65 \times 3 = 195\) miles. The trap 21.7 divides instead of multiplying. Pro tip: distance equals rate times time -- when you know the speed and the hours, multiply.

Q15 Medium

On a map, \(1\) inch represents \(50\) miles. How many miles apart are two towns that are \(3.5\) inches apart on the map?

- \(175\) miles

- \(53.5\) miles

- \(14.3\) miles

- \(142.9\) miles

Explanation

Each inch is 50 miles, so \(3.5 \times 50 = 175\) miles. The trap 14.3 divides \(50 \div 3.5\). Pro tip: set up a proportion, \(\frac{1\text{ in}}{50\text{ mi}} = \frac{3.5\text{ in}}{x}\), and keep inches across from inches.

Q16 Easy

What is the mean (average) of \(12,\ 15,\ 18,\ 21,\ 24\)?

- \(18\)

- \(21\)

- \(90\)

- \(15\)

Explanation

Add them: \(12+15+18+21+24 = 90\). Divide by 5: \(90 \div 5 = 18\). The trap 90 forgets to divide. Pro tip: mean = total divided by how many values there are.

Q17 Medium

What is the median of \(3,\ 8,\ 2,\ 10,\ 6,\ 5\)?

- \(5.5\)

- \(6\)

- \(5\)

- \(8\)

Explanation

Sort first: \(2, 3, 5, 6, 8, 10\). With an even count, average the two middle values: \(\frac{5+6}{2} = 5.5\). The trap 5 or 6 picks just one middle value. Pro tip: always sort the list, and average the middle two when there's an even number of values.

Q18 Easy

For the data set \(4,\ 7,\ 7,\ 9,\ 12\), what is the range?

- \(8\)

- \(7\)

- \(5\)

- \(12\)

Explanation

Range \(= \text{largest} - \text{smallest} = 12 - 4 = 8\). The trap 7 is the mode (the most frequent value), not the range. Pro tip: range measures spread -- subtract the smallest value from the largest.

Q19 Medium

A spinner has \(8\) equal sections, \(3\) of them red. What is the probability of landing on red?

- \(\frac{3}{8}\)

- \(\frac{3}{5}\)

- \(\frac{5}{8}\)

- \(\frac{1}{3}\)

Explanation

Probability \(= \frac{\text{favorable}}{\text{total}} = \frac{3}{8}\). The trap \(\frac{3}{5}\) compares red to non-red instead of to the total. Pro tip: probability is the wanted count over the TOTAL count.

Q20 Medium

Use the scatter plot below.

A scatter plot of points rising from lower-left to upper-right

What kind of relationship does the scatter plot show between the two variables?

- A positive (increasing) relationship

- A negative (decreasing) relationship

- No relationship at all

- A perfectly horizontal relationship

Explanation

The points rise from lower-left to upper-right, so as one variable increases the other tends to increase -- a positive relationship. The trap 'negative' describes points that fall. Pro tip: up-to-the-right is positive; down-to-the-right is negative.

Q21 Easy

Use the rectangle below.

A rectangle with a length and a width labeled

A rectangle is \(12\) cm long and \(7\) cm wide. What is its area?

- \(84\ \text{cm}^2\)

- \(38\ \text{cm}^2\)

- \(19\ \text{cm}^2\)

- \(42\ \text{cm}^2\)

Explanation

Area \(= l \times w = 12 \times 7 = 84\ \text{cm}^2\). The trap 38 is the perimeter \((2\times12 + 2\times7)\). Pro tip: area multiplies the sides and uses square units; perimeter adds them.

Q22 Easy

What is the area of a triangle with a base of \(14\) cm and a height of \(9\) cm?

- \(63\ \text{cm}^2\)

- \(126\ \text{cm}^2\)

- \(23\ \text{cm}^2\)

- \(46\ \text{cm}^2\)

Explanation

\(A = \frac{1}{2}bh = \frac{1}{2}(14)(9) = 63\ \text{cm}^2\). The trap 126 forgets the \(\frac{1}{2}\). Pro tip: every triangle area starts with one-half of base times height.

Q23 Medium

What is the area of a circle with a radius of \(5\) cm? Use \(\pi \approx 3.14\).

- \(78.5\ \text{cm}^2\)

- \(31.4\ \text{cm}^2\)

- \(15.7\ \text{cm}^2\)

- \(25\ \text{cm}^2\)

Explanation

\(A = \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5\ \text{cm}^2\). The trap 31.4 finds the circumference \((2\pi r)\) instead. Pro tip: area uses \(r^2\); circumference uses \(2\pi r\) -- don't mix them up.

Q24 Medium

What is the circumference of a circle with a radius of \(7\) cm? Use \(\pi \approx 3.14\).

- \(\approx 44\ \text{cm}\)

- \(\approx 153.9\ \text{cm}\)

- \(\approx 22\ \text{cm}\)

- \(\approx 14\ \text{cm}\)

Explanation

\(C = 2\pi r = 2 \times 3.14 \times 7 = 43.96 \approx 44\) cm. The trap 153.9 is the area \((\pi r^2)\). Pro tip: circumference is a length \((2\pi r)\); area is a region \((\pi r^2)\).

Q25 Easy

Use the box below.

A rectangular box with length, width, and height labeled

What is the volume of a box measuring \(5 \times 4 \times 3\)?

- \(60\)

- \(12\)

- \(47\)

- \(23\)

Explanation

Volume multiplies all three dimensions: \(5 \times 4 \times 3 = 60\). The trap 12 multiplies only two of them. Pro tip: volume uses all three sides and cubic units.

Q26 Hard

A cylinder has a radius of \(3\) cm and a height of \(10\) cm. What is its volume? Use \(\pi \approx 3.14\).

- \(\approx 282.6\ \text{cm}^3\)

- \(\approx 94.2\ \text{cm}^3\)

- \(\approx 188.4\ \text{cm}^3\)

- \(\approx 90\ \text{cm}^3\)

Explanation

\(V = \pi r^2 h = 3.14 \times 3^2 \times 10 = 3.14 \times 9 \times 10 = 282.6\ \text{cm}^3\). The trap 188.4 uses \(2r\) instead of \(r^2\) \((2\pi r h)\). Pro tip: square the radius first, then multiply by the height and \(\pi\).

Q27 Medium

Use the right triangle below.

A right triangle with two legs and a hypotenuse

The two legs of a right triangle are \(6\) and \(8\). How long is the hypotenuse?

- \(10\)

- \(14\)

- \(100\)

- \(48\)

Explanation

\(c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10\). The trap 14 just adds the legs; 100 forgets the square root. Pro tip: 6-8-10 is the 3-4-5 triple doubled.

Q28 Hard

A right triangle has a hypotenuse of \(13\) and one leg of \(5\). How long is the other leg?

- \(12\)

- \(18\)

- \(8\)

- \(\sqrt{194}\)

Explanation

Use \(a^2 + b^2 = c^2\): \(5^2 + b^2 = 13^2\), so \(b^2 = 169 - 25 = 144\) and \(b = 12\). The trap \(\sqrt{194}\) adds the squares instead of subtracting. Pro tip: when you know the hypotenuse, subtract the known leg's square from the hypotenuse's square.

Q29 Hard

Use the similar rectangles below.

A small rectangle and a larger, same-shaped rectangle

A small rectangle is \(4\) by \(6\). A larger, similar rectangle has a width of \(10\) (matching the \(4\) side). What is its length?

- \(15\)

- \(12\)

- \(8.5\)

- \(9.6\)

Explanation

The scale factor is \(10 \div 4 = 2.5\), so the length is \(6 \times 2.5 = 15\). The trap 12 adds the difference \((6 + 6)\) instead of scaling. Pro tip: similar shapes scale by multiplying every side by the same factor.

Q30 Easy

Use the coordinate plane below.

The four quadrants of the coordinate plane

In which quadrant does the point \((-3,\ 5)\) lie?

- Quadrant II

- Quadrant I

- Quadrant III

- Quadrant IV

Explanation

A negative x and a positive y put the point in the upper-left, Quadrant II. The trap Quadrant III needs both coordinates negative. Pro tip: quadrants go counter-clockwise starting from the upper-right (I), so (-, +) is II.

Q31 Medium

What is the slope of the line through the points \((1,\ 2)\) and \((4,\ 11)\)?

- \(3\)

- \(\frac{1}{3}\)

- \(9\)

- \(13\)

Explanation

Slope \(= \frac{y_2 - y_1}{x_2 - x_1} = \frac{11 - 2}{4 - 1} = \frac{9}{3} = 3\). The trap \(\frac{1}{3}\) flips the fraction (run over rise). Pro tip: slope is rise over run -- change in y on top.

Q32 Easy

Simplify: \(3x + 5 - x + 2\).

- \(2x + 7\)

- \(4x + 7\)

- \(2x + 3\)

- \(9x\)

Explanation

Combine like terms: \(3x - x = 2x\) and \(5 + 2 = 7\), giving \(2x + 7\). The trap \(4x+7\) adds the x-terms instead of subtracting. Pro tip: only combine terms that share the same variable.

Q33 Easy

Use the distributive property to simplify: \(4(2x - 3)\).

- \(8x - 12\)

- \(8x - 3\)

- \(6x - 12\)

- \(2x - 12\)

Explanation

Multiply 4 by both terms: \(4 \times 2x = 8x\) and \(4 \times (-3) = -12\), giving \(8x - 12\). The trap \(8x - 3\) forgets to distribute to the \(-3\). Pro tip: the outside number multiplies EVERY term inside the parentheses.

Q34 Medium

Evaluate \(3x^2 - 2x\) when \(x = 4\).

- \(40\)

- \(16\)

- \(56\)

- \(136\)

Explanation

\(3(4)^2 - 2(4) = 3(16) - 8 = 48 - 8 = 40\). The trap 136 squares \(3 \times 4\) first \(((12)^2 - 8)\). Pro tip: do the exponent before the multiplication -- square the 4, then multiply by 3.

Q35 Easy

Solve for \(x\): \(5x - 7 = 18\).

- \(x = 5\)

- \(x = 25\)

- \(x = 2.2\)

- \(x = 11\)

Explanation

Add 7: \(5x = 25\). Divide by 5: \(x = 5\). The trap 25 stops before dividing. Pro tip: undo the subtraction first, then undo the multiplication.

Q36 Medium

Solve for \(x\): \(\dfrac{x}{3} + 4 = 9\).

- \(x = 15\)

- \(x = 39\)

- \(x = 1.67\)

- \(x = 5\)

Explanation

Subtract 4: \(\frac{x}{3} = 5\). Multiply by 3: \(x = 15\). The trap 39 multiplies before subtracting \((9 \times 3 + ...)\). Pro tip: clear the \(+4\) first, then multiply both sides by 3 to undo the division.

Q37 Medium

Solve for \(x\): \(3x + 4 = x + 12\).

- \(x = 4\)

- \(x = 8\)

- \(x = 2\)

- \(x = 16\)

Explanation

Subtract \(x\) from both sides: \(2x + 4 = 12\). Subtract 4: \(2x = 8\). Divide by 2: \(x = 4\). The trap 8 stops before dividing. Pro tip: collect the variables on one side first, then solve the simpler equation.

Q38 Medium

A phone plan costs \$40 per month plus \$0.10 per text. What is the cost in a month with \(100\) texts?

- \$50

- \$140

- \$4{,}040

- \$50.10

Explanation

The texts cost \(0.10 \times 100 = \$10\), plus the \$40 base: \(40 + 10 = \$50\). The trap \$140 treats each text as \$1. Pro tip: build the expression \(40 + 0.10t\), then substitute \(t = 100\).

Q39 Medium

Use the number line idea below.

A number line showing the solution to an inequality

Solve the inequality \(3x - 2 > 10\).

- \(x > 4\)

- \(x < 4\)

- \(x > 2.67\)

- \(x > 12\)

Explanation

Add 2: \(3x > 12\). Divide by 3: \(x > 4\). The sign stays the same because 3 is positive. The trap \(x < 4\) flips the sign for no reason. Pro tip: only flip the inequality when you multiply or divide by a NEGATIVE number.

Q40 Hard

Solve the inequality \(-2x + 1 < 9\).

- \(x > -4\)

- \(x < -4\)

- \(x > 4\)

- \(x < 4\)

Explanation

Subtract 1: \(-2x < 8\). Now divide by \(-2\) and FLIP the sign: \(x > -4\). The trap \(x < -4\) forgets to flip. Pro tip: dividing or multiplying an inequality by a negative number always reverses the direction of the sign.

Q41 Hard

Solve: \(x^2 + 5x + 6 = 0\).

- \(x = -2\) or \(x = -3\)

- \(x = 2\) or \(x = 3\)

- \(x = -1\) or \(x = -6\)

- \(x = 1\) or \(x = 6\)

Explanation

Factor into \((x+2)(x+3) = 0\), so \(x = -2\) or \(x = -3\). The trap \(x = 2, 3\) forgets the signs flip when you solve each factor. Pro tip: find two numbers that multiply to 6 and add to 5 (that's 2 and 3), then change their signs.

Q42 Hard

Solve the system: \(x + y = 10\) and \(x - y = 4\).

- \(x = 7,\ y = 3\)

- \(x = 3,\ y = 7\)

- \(x = 6,\ y = 4\)

- \(x = 5,\ y = 5\)

Explanation

Add the two equations: \(2x = 14\), so \(x = 7\). Then \(7 + y = 10\) gives \(y = 3\). The trap \(x=3, y=7\) swaps the two values. Pro tip: adding the equations cancels \(y\) and solves for \(x\) in one step.

Q43 Easy

If \(f(x) = 2x + 3\), what is \(f(5)\)?

- \(13\)

- \(10\)

- \(16\)

- \(25\)

Explanation

Substitute \(x = 5\): \(f(5) = 2(5) + 3 = 10 + 3 = 13\). The trap 10 forgets to add the 3. Pro tip: \(f(5)\) means replace every \(x\) with 5, then simplify.

Q44 Medium

Use the line below.

A straight line shown with its table of values

A line has a slope of \(3\) and crosses the y-axis at \(-2\). What is its equation?

- \(y = 3x - 2\)

- \(y = -2x + 3\)

- \(y = 3x + 2\)

- \(y = -2x - 3\)

Explanation

Slope-intercept form is \(y = mx + b\), with \(m = 3\) (slope) and \(b = -2\) (y-intercept), giving \(y = 3x - 2\). The trap \(y = -2x + 3\) swaps the slope and intercept. Pro tip: in \(y = mx + b\), \(m\) multiplies \(x\) and \(b\) stands alone.

Q45 Hard

A colony of bacteria triples every hour. If it starts with \(5\) bacteria, how many are there after \(2\) hours?

- \(45\)

- \(30\)

- \(15\)

- \(10\)

Explanation

Tripling twice: \(5 \times 3 \times 3 = 5 \times 9 = 45\). The trap 30 multiplies \(5 \times 3 \times 2\), treating it as repeated addition. Pro tip: 'triples each hour' means multiply by 3 for each hour -- it grows exponentially, \(5 \times 3^2\).

Q46 Medium

What is the slope of the line that passes through \((2,\ 1)\) and \((6,\ 9)\)?

- \(2\)

- \(\frac{1}{2}\)

- \(4\)

- \(8\)

Explanation

Slope \(= \frac{9 - 1}{6 - 2} = \frac{8}{4} = 2\). The trap 8 uses only the change in y and forgets to divide by the change in x. Pro tip: slope is rise over run -- divide the y-change by the x-change.