Knowledge Check: Chapters 1–5

Write as a whole number using digits: two hundred five thousand, six hundred seventeen.

Find the Least Common Multiple of 18 and 24.

Evaluate $9x + 7$ when $x = 3$.

Simplify by combining like terms: $17a + 9a$.

Simplify: $4 + 10(3 + 9) - 5^2$.

Evaluate $-|x|$ when $x = -2$.

Translate to an algebraic expression and simplify: twenty less than negative 7. Give the simplified value.

Simplify: $-19 - 25$.

Simplify: $(-5)^3$.

Simplify: $31 - 4(3 - 9)$.

Simplify: $-5(-9) \div 15$.

Simplify: $\tfrac{7}{21}$.

Multiply: $\tfrac{2}{5} \cdot \tfrac{1}{3}$.

Simplify: $\tfrac{4}{5} \div \tfrac{9}{20}$.

Add: $\tfrac{2}{3} + \tfrac{3}{4}$.

Subtract: $\tfrac{11}{12} - \tfrac{3}{8}$.

Simplify: $\tfrac{m}{7} + \tfrac{10}{7}$.

Round $677.1348$ to the nearest hundredth.

Convert $1.85$ to a percent. Enter the number of percent.

Simplify: $-5.8 + (-4.7)$.

Simplify: $(0.07)(31.95)$.

Simplify: $\sqrt{64}$.

Write $8.47$ as the ratio of two integers.

Order using < or >. Enter the full inequality: $-1 \_\_ -\tfrac{1}{8}$

Simplify: $-14\left(\tfrac{5}{7}p\right)$.

Simplify: $6x + (-4y) + 9x + 8y$.

A movie lasted $1\tfrac{2}{3}$ hours. How many minutes did it last? (1 hour = 60 minutes)

Jennifer ran 2.8 miles. Convert this length to kilometers. (1 mile = 1.61 kilometers)

Solve: $-8x - 15 + 9x - 1 = -21$.

Solve: $x - 9 = -4$.

Translate into an algebraic equation and then solve: four less than $n$ is 13. Enter the value of $n$.

Solve: $\tfrac{9}{2}c = 144$.

Solve: $\tfrac{2}{3}x = 6$.

Jenna bought a coat on sale for $120, which was $\tfrac{2}{3}$ of the original price. What was the original price of the coat, in dollars?

Solve: $10y = -5y - 60$.

Solve: $9m - 2 - 4m - m = 42 - 8$.

Solve: $5n - 20 = -7n - 80$.

Solve: $-(d - 9) = 23$.

Solve: $2(6x - 5) - 8 = -22$.

Solve: $\tfrac{1}{4}p - \tfrac{1}{3} = \tfrac{1}{2}$.

Solve: $\tfrac{1}{2}(k - 3) = \tfrac{1}{3}(k + 16)$.

Solve: $0.36u + 2.55 = 0.41u + 6.8$.

Link rode his bike at a steady rate of 15 miles per hour for $2\tfrac{1}{2}$ hours. How much distance did he travel, in miles?

Use the formula $A = \tfrac{1}{2}bh$ to find $h$ when $A = 153$ and $b = 18$.

Solve the formula $A = \tfrac{1}{2}bh$ for $h$.

Solve the formula $V = LWH$ for $H$.

Solve the inequality $m + 14 \leq 56$. Enter the solution as a full inequality, e.g. $x > 2$.

Solve the inequality $3c - 10(c - 2) < 5c + 16$. Enter the solution as a full inequality, e.g. $x > 2$.

Translate to an inequality and solve: fifteen more than $n$ is at least 48. Enter the solution as a full inequality for $n$.

Four-fifths of the people on a hike are children. If there are 12 children, what is the total number of people on the hike?

The sum of two consecutive odd integers is $-96$. Find the numbers. Enter them from smallest to largest, separated by commas.

Humberto's hourly pay increased from $16.25 to $17.55. Find the percent increase.

Dotty bought a freezer on sale for $486.50. The original price of the freezer was $695. Find the amount of discount.

Dotty bought a freezer on sale for $486.50. The original price of the freezer was $695. Find the discount rate.

Francie has $4.35 in dimes and quarters. The number of dimes is five more than the number of quarters. How many dimes does she have?

Francie has $4.35 in dimes and quarters. The number of dimes is five more than the number of quarters. How many quarters does she have?

At a concert, $1,600 in tickets were sold. Adult tickets were $9 each and children's tickets were $4 each. If the number of adult tickets was 30 less than twice the number of children's tickets, how many adult tickets were sold?

At a concert, $1,600 in tickets were sold. Adult tickets were $9 each and children's tickets were $4 each. If the number of adult tickets was 30 less than twice the number of children's tickets, how many children's tickets were sold?

The measure of one angle of a triangle is twice the measure of the smallest angle. The measure of the third angle is 14 more than the measure of the smallest angle. Find the measures of all three angles, in degrees, from smallest to largest, separated by commas.

A baseball diamond is really a square with sides of 90 feet. How far is it from home plate to second base? Round to the nearest tenth of a foot.

When Gabe drives from Sacramento to Redding it takes him 2.2 hours. It takes Elsa 2 hours to drive the same distance. Elsa's speed is seven miles per hour faster than Gabe's speed. Find Gabe's speed, in miles per hour.

When Gabe drives from Sacramento to Redding it takes him 2.2 hours. It takes Elsa 2 hours to drive the same distance. Elsa's speed is seven miles per hour faster than Gabe's speed. Find Elsa's speed, in miles per hour.

Two planes leave Dallas at the same time. One heads east at a speed of 428 miles per hour. The other plane heads west at a speed of 382 miles per hour. How many hours will it take them to be 2,025 miles apart?

Julianne has a weekly food budget of $231 for her family. If she plans to budget the same amount for each of the seven days of the week, what is the maximum amount she can spend on food each day?

Chloe has a budget of $800 for costumes for the 18 members of her musical theater group. If all the costumes are the same price, what is the maximum she can spend for each costume?

Find the ordered pair $(x, y)$ solution to the equation $y = -\tfrac{1}{2}x + 3$ when $x = 4$.

Find the ordered pair $(x, y)$ solution to the equation $3x + 2y = 6$ when $y = 0$.

Which of the ordered pairs $(3, 3)$, $(2, 0)$, $(4, -6)$ are solutions to the equation $3x - y = 6$? Enter the solutions separated by commas, in the order given.

Which of the ordered pairs $(0, -1)$, $(3, 1)$, $(-3, -3)$, $(6, 4)$ are solutions to the equation $y = \tfrac{2}{3}x - 1$? Enter the solutions separated by commas, in the order given.

The graph of $y = \tfrac{2}{3}x - 1$ is shown above. One of the ordered pairs $(0, -1)$, $(3, 1)$, $(-3, -3)$, $(6, 4)$ is not a point on the line. Which one?

Find the $x$- and $y$-intercepts of the line $x - y = -1$. Enter them as ordered pairs separated by commas, $x$-intercept first.

Find the $x$-intercept of the graph of the equation $4x - 3y = 12$. Enter it as an ordered pair.

Find the $y$-intercept of the graph of the equation $4x - 3y = 12$. Enter it as an ordered pair.

Find the slope of the line $y = -1$.

A mountain road rises 50 feet for a 500-foot run. What is its slope?

Find the slope of the line between the points $(5, 2)$ and $(-1, -4)$.

Identify the slope of the line $y = \tfrac{5}{3}x - 6$.

Identify the $y$-intercept of the line $y = \tfrac{5}{3}x - 6$. Enter it as an ordered pair.

Identify the slope of the line $4x - 5y = 8$.

Identify the $y$-intercept of the line $4x - 5y = 8$. Enter it as an ordered pair.

Marjorie teaches piano. The equation $P = 35s - 250$ models the relation between her weekly profit, $P$, in dollars, and the number of student lessons, $s$, that she teaches. Find Marjorie's profit for a week when she teaches 20 student lessons.

Find the equation of the line with slope $-\tfrac{3}{4}$ and $y$-intercept $(0, -2)$. Write the equation in slope-intercept form.

Find the equation of the line containing the points $(10, 1)$ and $(6, -1)$. Write the equation in slope-intercept form.

Find the equation of the line perpendicular to the line $y = \tfrac{5}{4}x + 2$, containing the point $(-10, 3)$. Write the equation in slope-intercept form.

Write the inequality shown by the graph above, with the boundary line $y = \tfrac{2}{3}x - 3$. Enter the full inequality.

Write the inequality shown by the shaded region in the graph above, with the boundary line $x - 2y = 6$. Enter the full inequality, using the boundary line as given.

Solve the system of equations by graphing: $3x + y = 6$ and $x + 3y = -6$. Write the solution as an ordered pair $(x, y)$.

Solve the system of equations by graphing: $2x - y = 6$ and $y = 4$. Write the solution as an ordered pair $(x, y)$.

LaVelle is making a pitcher of caffe mocha. For each ounce of chocolate syrup, she uses five ounces of coffee. How many ounces of chocolate syrup does she need to make 48 ounces of caffe mocha?

LaVelle is making a pitcher of caffe mocha. For each ounce of chocolate syrup, she uses five ounces of coffee. How many ounces of coffee does she need to make 48 ounces of caffe mocha?

Solve the system of equations by substitution: $3x - y = -5$ and $y = 2x + 4$. Write the solution as an ordered pair $(x, y)$.

Solve the system of equations by substitution: $x - y = 0$ and $2x + 5y = -14$. Write the solution as an ordered pair $(x, y)$.

The sum of two numbers is 55. One number is 11 less than the other. Find the numbers. Enter them separated by commas, smaller first.

Solve the system of equations: $x + y = -3$ and $x - y = 11$. Write the solution as an ordered pair $(x, y)$.

Solve the system of equations by elimination: $x + y = 12$ and $x - y = -10$. Write the solution as an ordered pair $(x, y)$.

Solve the system of equations by elimination: $3x - 8y = 20$ and $x + 3y = 1$. Write the solution as an ordered pair $(x, y)$.

The sum of two numbers is $-90$. Their difference is 16. Find the numbers. Enter them separated by commas, larger first.

The sum of two numbers is $-24$. One number is 104 less than the other. Find the numbers. Enter them separated by commas, larger first.

Two angles are complementary. The measure of the larger angle is six more than twice the measure of the smaller angle. Find the measure of the smaller angle, in degrees.

Two angles are complementary. The measure of the larger angle is six more than twice the measure of the smaller angle. Find the measure of the larger angle, in degrees.

Kathy left home to walk to the mall, walking quickly at a rate of 4 miles per hour. Her sister Abby left home 15 minutes later and rode her bike to the mall at a rate of 10 miles per hour. How long will it take Abby to catch up to Kathy? Give the time in hours.

Jack has $12,000 to invest and wants to earn 7.5% interest per year. He will put some of the money into a savings account that earns 4% per year and the rest into a CD account that earns 9% per year. How much money, in dollars, should he put into the savings account?

Jack has $12,000 to invest and wants to earn 7.5% interest per year. He will put some of the money into a savings account that earns 4% per year and the rest into a CD account that earns 9% per year. How much money, in dollars, should he put into the CD account?

Liz paid $160 for 28 tickets to take the Brownie troop to the science museum. Children's tickets cost $5 and adult tickets cost $9. How many children's tickets did Liz buy?

Liz paid $160 for 28 tickets to take the Brownie troop to the science museum. Children's tickets cost $5 and adult tickets cost $9. How many adult tickets did Liz buy?