Deck 2: Introduction to Algebra

Question 1

How many terms are in the following expression? $(y-5)(2 y+3)-8$

Answer 1

2

Question 2

How many terms are in the following expression? $4 x^{2}+6\left(x^{3}-3\right)$

Answer 2

2

Question 3

How many terms are in the following expression? $(-3 x) 12 y+y^{4}-12 x(-2 y)+x y$

Answer 3

4

Question 4

How many terms are in the following expression? $\frac{3}{4}(x-2)-\frac{1}{3}\left(x^{2}+3\right)$

Question 5

Write the coefficient of each term in the expression: $4 x^{4}-6(2 x)$

Question 6

Write the coefficient of each term. Assume that the letter $x$ is the variable and all other letters are constants.
(a) $\frac{a x^{4}}{4}$
(b) $2 a(5 bx^4)$
(c) $\frac{6 b x^{7}}{2 a c}$

Question 7

Write the coefficient of each term in the expression. Assume that the letter $x$ is the variable and all other letters are constants: $5 a x^{5}+2 x^{2}-k a x$

Question 8

Identify the factors in each of the following expressions.
(a) $16 x y$
(b) $(x+2)(3 y-z)$
(c) $2 x$
(d) $x(y z)$

Question 9

State the degree of each term.
(a) $x^{5} y^{2}$
(b) $14 w x z^{2}$
(c) $-x$

Question 10

State the degree of each expression.
(a) $3 x^{4}+4 y^{6}$
(b) $7 x^{2}+3 x-5$
(c) $-9 x y^{2}+4 y^{3}$

Question 11

Combine as indicated, and simplify: $3 x-4 x+2 y-4 y$

Question 12

Combine as indicated, and simplify: $-5 a+5 a+b+6 b$

Question 13

Combine as indicated, and simplify: $14 x^{2}+2 x+12-4 x+2 x^{2}$

Question 14

Combine as indicated, and simplify: $6 a b+4 b c-2 b c-a b$

Question 15

Find the sum of $4 x+9 p-5 y,-3 p+2 p+3 x$ , and $-4 y+7 p-9 y$ .

Question 16

Find the sum of $5-x^{2}+3 m, 5 x+9-2 x^{2}, 9 m+7+3 x^{2}-x$ , and $15 x^{3}+2 x^{2}-5$ .

Question 17

Add $3 p^{2}-3 a\left(y-z^{2}\right), 9 a\left(y-z^{2}\right)-6 p$ , and $12 p c-7 a\left(y-x^{2}\right)$ .

Question 18

Add $11 a-b+4 a b, 2 a+13 b-6 a b$ , and $-4 a-8 b+2 a b$ .

Question 19

Subtract $10\left(x^{2}-y\right)+20$ from $-5-2\left(x^{2}-y\right)$ .

Question 20

Subtract $x^{3}-3 x^{2}+11 x$ from $4 x^{3}+x^{2}-9$ .

Question 21

Subtract $9 a^{2} b-a b^{2}-3 a b$ from $3 a b^{2}+a^{2} b+4 a b$ .

Question 22

Subtract $5 a-12 b-3 c$ from $10 b-6 c+4 d$ .

Question 23

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: $2(5 x-2)-3$

Question 24

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: $21 a^{2}+2 b^{2}-$ $6\left(a b+3 a^{2}-5 b^{2}\right)$

Question 25

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: $5 p+8 q-4 r-$ $(9 q+6 r)+(30 p-9 q)$

Question 26

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: $-2 c-[(2 a+$ $3 b)-2 b]-[(6 d+b)-3 c]-(10 d+9 a)$

Question 27

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: 2 - 3[2a- $(5-3 x)]+4(3 x-5)$

Question 28

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: $\frac{3}{4}(x-2)$ - $\frac{1}{2}\left(x^{2}+3\right)$

Question 29

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: $3(x-y)+\{5 y-$ $[3 x-(2 x-y)]+4(x-y)\}$

Question 30

Remove the symbols of grouping (i.e., brackets, braces, parentheses) and collect terms: $5(a+b)-$ $\left\{2 a b-\left[2\left(a^{2}-5 a b\right)-3\left(5 a b-5 b^{2}\right)\right]\right\}$

Question 31

The surface area of a cylinder with radius $r$ and perpendicular height $3 r$ is given by $2 \pi\left(r^{2}+3 r^{2}\right)$ . Simplify this expression, keeping $\pi$ in your answer.

Question 32

To maintain proper humidity, a crawl space that is $x$ metres by $2 x$ metres should have $\frac{2}{27} x^{2}(900)+$ $60[2(2 x)+2 x] \mathrm{cm}^{2}$ of ventillation. Simplify this expression. (Use fractions for the coefficients, if necessary.)

Question 33

A simply-supported beam has a uniformly-distributed load. The deflection at the point $x$ metres from the left end of the beam is given by $y=\frac{\omega}{24 k}\left(L^{3} x-2 L x^{3}+x^{4}\right)$ where $L$ is the length of the beam in metres, $\omega$ is the load in $\mathrm{N} / \mathrm{m}$ , and $k$ is a constant. What is the coefficient of $x$ for a 2.00 -metre beam if the load is $600\overline{0} \mathrm{~N} / \mathrm{m}$ and $k$ is $4.00 \times 10^{7}$ ?

Question 34

Multiply: $x \cdot x^{3}$

Question 35

Multiply: $x^{2 a} \cdot x^{a+4}$

Question 36

Multiply: $a^{2} \cdot a^{3} \cdot a^{-4}$

Question 37

Multiply: $\mathrm{c}^{\mathrm{x}+4} \cdot \mathrm{c}^{\mathrm{x}+5}$

Question 38

Divide. Write your answer without a negative exponent: $\frac{x^{4}}{x^{-2}}$

Question 39

Divide. Write your answer without a negative exponent: $\frac{4^{10}}{4^{6}}$

Question 40

Divide: $\frac{x^a}{x^{a-7}}$

Question 41

Divide: $\frac{a^{5-x}}{a^{3+x}}$

Question 42

Simplify: $\left(a^{2}\right)^{-5}$

Question 43

Simplify: $\left(x^{2 m}\right)^{n}$

Question 44

Simplify: $\left(7^{4}\right)^{x+2}$

Question 45

Simplify: $\left(x^{3}\right)^{2 a+5}$

Question 46

Raise to the power indicated: $\left(5 x y^{2}\right)^{2}$

Question 47

Raise to the power indicated: $-\left(\frac{2 b}{a}\right)^{5}$

Question 48

Raise to the power indicated: $\left(4 y^{6}\right)^{-2}$

Question 49

Raise to the power indicated: $\left(\frac{2 x y^{3}}{z^{2}}\right)^{3}$

Question 50

Write with positive exponents only: $\left(\frac{a}{5}\right)^{-2}$

Question 51

Write with positive exponents only: $\left(\frac{-2 x}{y}\right)^{-2}$

Question 52

Write with positive exponents only: $\left(\frac{2 x y^{3}}{3 z^{2}}\right)^{-3}$

Question 53

Write with positive exponents only: $\left(\frac{3 a^{4} b}{5 c^{2} d^{3}}\right)^{-2}$

Question 54

Write with positive exponents only: $3 x^{-5} y+12 y^{-4}$

Question 55

Express without fractions, using negative exponents where needed: $\frac{2}{a}$

Question 56

Express without fractions, using negative exponents where needed: $\frac{a^{-2} b^{3}}{c^{4}}$

Question 57

Express without fractions, using negative exponents where needed: $\frac{2 x y^{-3}}{x^{-2} y^{4}}$

Question 58

Express without fractions, using negative exponents where needed: $\frac{3 a^{4} b^{-1}}{a^{2} b^{-3}}$

Question 59

Evaluate: $\frac{7 a^{2}}{b^{0}}$

Question 60

Evaluate: $\left(3 x-4 y^{2}\right)^{0}$

Question 61

Evaluate: $\frac{x^{3 a} \cdot x^{-4}}{x}$

Question 62

The volume of a cylinder of radius $3 r$ and perpendicular height $4 r$ is given by $\pi(3 r)^{2}(4 r)$ . Simplify this expression.

Question 63

The volume of a cone of radius $2 r$ and perpendicular height $3 r$ is given by $\frac{\pi}{3}(2 r)^{2}(3 r)$ . Simplify this expression.

Question 64

The density of a block is given by $\frac{7.20}{(3 x)(2 x)^{2}} \mathrm{~g} / \mathrm{cm}^{3}$ . Express the density without fractions, using negative exponents where needed.

Question 65

Multiply these monomials, and simplify: $a^{4}(a)$

Question 66

Multiply these monomials, and simplify: $(-5 x)\left(3 x y^{2} z\right)\left(-2 x^{2} z\right)\left(-x y^{3}\right)$

Question 67

Multiply these monomials, and simplify: $\left(4 a^{3}\right)\left(5 a b^{2}\right)\left(a b c^{4}\right)$

Question 68

Multiply the polynomial by the monomial, and simplify: $-15 x y^{2}\left(y^{3}-2 x y+3 x^{2}-x^{2} y\right)$

Question 69

Multiply the polynomial by the monomial, and simplify: $3 a^{2} b\left(a b^{2}-3 a+4 a^{2} b-5 b\right)$

Question 70

Multiply these binomials, and simplify: $(5 a+2 b)(-3 a+b)$

Question 71

Multiply these binomials, and simplify: $\left(y^{2}+13\right)\left(y^{3}-2\right)$

Question 72

Multiply these binomials, and simplify: $\left(7 a b^{2}+3 b^{2}\right)\left(2 a b^{3}-5 a^{2}\right)$

Question 73

Multiply these binomials, and simplify: $\left(2 a^{2} b^{3}-8 m n^{2}\right)\left(a^{2} b^{3}+3 m n^{2}\right)$

Question 74

Multiply the binomial and trinomial, and simplify: $(a-2 b)(3 a+5 b+6)$

Question 75

Multiply the binomial and trinomial, and simplify: $(c-d)\left(c^{2}-2 c d+d^{2}\right)$

Question 76

Multiply the binomial and trinomial, and simplify: $\left(2 x+5 a^{2}\right)\left(4 x^{2}-10 x a^{2}+25 a^{4}\right)$

Question 77

Multiply these binomials, and simplify: $(c-3)(c+5)(c+5)$

Question 78

Multiply these binomials, and simplify: $(x-3 y)(x+3 y)(3 y-2 x)$

Question 79

Multiply these binomials, and simplify: $(3 x+2)(x-2 y)(x+y)$

Question 80

Multiply these binomials, and simplify: $(5 p-1)(p+1)(p-2)(p+2)$