Precalculus Module 1-A Worksheet 1 Flashcards

Flashcards for Precalculus Module 1-A Worksheet 1

What is the goal when performing operations on expressions?

Write each expression as either a fraction in simplest form or a decimal number.

How do you simplify algebraic expressions?

Simplify each expression by expanding and combining like terms.

How should simple and compound inequalities be expressed?

Represent the inequality on a number line and in interval notation.

What types of answers are expected when solving equations?

A whole number, a fraction in simplest form, or a decimal number.

How do you solve an equation for a specified expression?

Use algebra to isolate the specified expression.

What do you need to determine when solving equations?

Determine if the equation has zero, one, or infinitely many solutions and solve if applicable.

How should basic word problems be approached?

Write an equation with a variable to represent the problem and solve it.

What is the formula relating distance, rate, and time?

Distance equals rate multiplied by time (D = RT).

What is 2/3 - 4/5?

-2/15

What is -4 * 3/7?

-12/7

What is 1/4 + 3/2?

7/4

What is -8/5 divided by 2/3?

-12/5

What is 100 * 8.7?

870

What is 52.3 / 10?

5.23

What is 3(2x - 4) + 5 simplified?

6x - 7

What is (x + 2)(2x - 5) + 7 simplified?

2x^2 - x - 3

What is -3(x - 1)(x + 5) + 6x simplified?

-3x^2 - 6x + 15

What is (3x + 1)(x - 5) + √3 simplified?

3x^2 - 14x - 5 + √3

What is an example of Simple inequalities?

x ≤ 5

What is an example of Simple inequalities with negative number?

x > −7

What is an example of Compound inequalities?

x < −3 or x ≥ 2

What is another example of Compound inequalities, that could be written as 5 < x < 8?

x > 5 and x < 8

What is another example of Compound inequalities?

x < 4 and x ≤ 7

What is another example of Compound inequalities with negative numbers?

x > −5 or x ≥ −1

What is another example of Compound inequalities?

x ≥ 3 and x ≤ 0

What is another example of Compound inequalities with negative numbers?

x ≥ −4 or x < 1

Solve for x: 3x + 11 = −8

x = -19/3

Solve for y: 2y − 9 = −5

y = 2

Solve for (x + y + z): 4(x + y + z) + 3 = −21

x + y + z = -6

Solve for log(6x): 2 log(6x) − 7 = 3

log(6x) = 5

Solve for sin(x): −8 sin(x) − 7 = −3

sin(x) = 1/2

Solve for x: 2/(x − 4) = 4/3

x = -2

Solve for w: 1/(2w) + 5 = 1/(3w) + 7

w = -12

Solve for y: (y − 4)/6 − 2 = y/2

y = -18

Solve for x: (x − 3)/100 − 2 = 6.4

x = 844

Solve for w: 10w − 8.2 = −1

w = 0.72

How many solutions does −4(4x + 5) = −6 − 2(8x + 7) have?

Infinitely many solutions

Solve 8 − (3x + 5) = −5 + 2(x + 1) for x

x = 6/5

How many solutions does 2x + 4(x − 1) = 3(2x + 1) + 1 have?

No solution

How many solutions does −2(4x + 3) = 5(1 − x) − 3x have?

No solution

Solve 3(2x − 4) = 2(2x + 4) − 14 for x

x = 1

A desk and a chair cost $51 together. The chair cost $12 less than the desk. How much did the desk cost?

$31.50

Sara is three times the age of Ashley. Their combined ages are 52. How old is Sara?

39 years old

On a recent night, there were 43 more adult tickets sold than student tickets, for a total of 209 tickets. How many student tickets were sold?

83 student tickets

Sam’s gas tank is 1/3 full. After she adds 5 gallons, the tank is 3/4 full. How many gallons can the tank hold?

12 gallons

Antonio’s piggy bank is 4/5 full of quarters. After he removes 24 quarters, the bank is 1/2 full. How many quarters can fit in the bank?

80 quarters

Two trains leave the same station at the same time, one traveling north at 40 mph and the other south at 50 mph. How long does it take for them to be 270 miles apart?

3 hours

Alicia ran 8 mph for the first part of the race, then increased her speed to 12 mph for the second part. If the race was 21 miles long and Alicia finished in 2 hours, how far did she run at the faster pace?

15 miles

A car passes a landmark on a highway traveling at a constant rate of 60 kilometers per hour. One hour later, a second car passes the same landmark traveling in the same direction at 100 kilometers per hour. How many hours after the second car passes the landmark will it overtake the first car?

1.5 hours

A car passes a landmark on a highway traveling at a constant rate of 60 kilometers per hour. One hour later, a second car passes the same landmark traveling in the same direction at 100 kilometers per hour. How far did the cars travel, from the landmark to the passing point?

250 kilometers