Knowledge Check: Chapters 1–6

Simplify: $5n + 8 + 2n - 1$.

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

Simplify: $16 - 2\left|3(1 - 4) - (8 - 5)\right|$.

Simplify: $\tfrac{180}{204}$.

Simplify: $\tfrac{4}{5} \div \left(-\tfrac{12}{25}\right)$.

Round $28.1458$ to the nearest hundredth.

Simplify: $-8 \div 0.05$.

Simplify: $6(3y - 1) - (5y - 3)$.

Solve: $-5(2x + 1) = 45$.

Solve: $\tfrac{3}{4}x - \tfrac{2}{3} = \tfrac{1}{2}x + \tfrac{5}{6}$.

Three-fourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert?

Winston deposited $3,294 in a bank account with an interest rate of 2.6%. How much simple interest, in dollars, was earned in five years?

Solve $A = \tfrac{1}{2}d_1d_2$ for $d_2$.

The length of a rectangle is 12 centimeters more than its width. The perimeter is 74 centimeters. Find the width.

The length of a rectangle is 12 centimeters more than its width. The perimeter is 74 centimeters. Find the length.

Lenny has $3.69 in pennies, dimes, and quarters. The number of pennies is three more than the number of dimes, and the number of quarters is twice the number of dimes. How many dimes does he have?

Lenny has $3.69 in pennies, dimes, and quarters. The number of pennies is three more than the number of dimes, and the number of quarters is twice the number of dimes. How many quarters does he have?

Marquese is making 10 pounds of trail mix from raisins that cost $3.45 per pound and nuts that cost $7.95 per pound. How many pounds of raisins should he use for the trail mix to cost $6.96 per pound?

Solve the inequality: $3c - 10(c - 2) < 5c + 16$.

Sara has a budget of $1000 for costumes for the 18 members of her musical theater group. What is the most she can spend on each costume, to the nearest cent?

Solve $|2x - 1| = |4x + 3|$. Enter the smaller solution.

Solve $|2x - 1| = |4x + 3|$. Enter the larger solution.

Find the $x$-intercept of $x + 2y = 6$. Write it as an ordered pair.

Find the $y$-intercept of $x + 2y = 6$. Write it as an ordered pair.

Find the slope of the line through $(3,5)$ and $(4,-1)$.

Find an equation of the line with slope $-5$ and $y$-intercept $(0,-3)$.

Find an equation of the line through $(7,1)$ and $(5,0)$.

For $h(y) = 3|y - 1| - 3$, find $h(-4)$.

Solve the system $x - y = 5$ and $x + 2y = -4$. Write the solution as an ordered pair $(x,y)$.

Solve the system $x + 4y = 6$ and $-2x + y = -3$. Write the solution as an ordered pair $(x,y)$.

A bulb garden contains 200 bulbs. The number of tulip bulbs is three times the number of iris bulbs. How many iris bulbs are there?

A bulb garden contains 200 bulbs. The number of tulip bulbs is three times the number of iris bulbs. How many tulip bulbs are there?

Two angles are supplementary, and their measures differ by 58 degrees. Find the larger angle.

Priam has $4.21 in pennies and dimes. The number of dimes is three less than four times the number of pennies. How many pennies does he have?

Priam has $4.21 in pennies and dimes. The number of dimes is three less than four times the number of pennies. How many dimes does he have?

Solve the system $x + y - z = -1$, $2x - y + 2z = 8$, and $-3x + 2y + z = -9$. Write the solution as an ordered triple $(x,y,z)$.

After a baseball game, one family buys four T-shirts, one cap, and one stuffed animal for $135. Another couple buys two T-shirts, one cap, and three stuffed animals for $115. A third couple buys two T-shirts, one cap, and one stuffed animal for $85. What is the cost of one cap?

Use matrices to solve the system $-3x + y + z = -4$, $-x + 2y - 2z = 1$, and $2x - y - z = -1$. Write the solution as an ordered triple $(x,y,z)$.

Use matrices to solve the system $2x - y + 3z = -3$, $-x + 2y - z = 10$, and $x + y + z = 5$. Write the solution as an ordered triple $(x,y,z)$.

Find the value of the determinant $\begin{vmatrix}3 & -2 & -2 \\ 2 & -1 & 4 \\ -1 & 0 & -3\end{vmatrix}$.

Use Cramer's Rule to solve $x - 3y = -9$ and $2x + 5y = 4$. Write the solution as an ordered pair $(x,y)$.

Find the degree of $8y^4 - 3y^2 + 1$.

Subtract: $(10x^2 - 3x + 5) - (4x^2 - 6)$.

Simplify and write with positive exponents: $x^{-3}x^4$.

Simplify and write with positive exponents: $\tfrac{24r^3s}{6r^2s^7}$.

Multiply and write the answer in scientific notation: $(2.4 \times 10^8)(2 \times 10^{-5})$.

Multiply: $(8xy^3)(-6x^4y^6)$.

Multiply: $(m + 3)(7m - 2)$.

Multiply: $(4x - 3)^2$.

Divide: $(15xy^3 - 35x^2y) \div 5xy$.

Factor completely: $80a^2 + 120a^3$.

Factor by grouping: $xy - 8y + 7x - 56$.

Factor completely: $x^2 + 13x + 36$.

Factor completely: $9s^2 - 12s + 4$.

Factor completely: $3x^2 - 75y^2$.

Factor completely: $x^3 + 125$.

Factor completely: $6x^4 - 19x^2 + 15$.

Solve $5a^2 + 26a = 24$. Enter the smaller solution.

Solve $5a^2 + 26a = 24$. Enter the larger solution.

A rectangular placemat has an area of 168 square inches. Its length is two inches longer than its width. Find the width.

A rectangular placemat has an area of 168 square inches. Its length is two inches longer than its width. Find the length.