This companion book to Thinkwell's online Honors Algebra 1 course includes the warm-up exercises for each lesson.
#1 Write the phrase as an algebraic expression. the quotient of a number and 12
#2 Write the number using an exponent and the given base. 25, base 5
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#1 Evaluate the expression for k = 3. (−5) k
#2 Find
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#1 John is 4 inches taller than David, who is k inches tall. Write an expression for John's height in inches.
#2 Simplify the expression. 19 − 5[5 − (−5) 3 ]
#3 Find the union and intersection of the pair of sets. A is the set of prime number factors of 15. B is the set of prime number factors of 18.
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#1 Simplify.
7 y + 3(2 − y ) + y
#2 Evaluate the expression for x = −2. −4(5 + 2 x )
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#1 Solve and check.
2 + 6 x + 8 − x = 0
#2 Simplify.
−3|−6 + 2|
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#1 Solve and check.
#2 Solve the equation. 9| y − 4| = 27
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#1 Solve the equation.
5(2 x + 3) − 8 x = 10 + 2 x − 3
#2 After 6 months the simple interest earned annually on an investment of $5000 was $907. Find the interest rate to the nearest tenth of a percent.
#3 A computer was purchased for $550. The wholesale cost was $440. What percentage was the markup?
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#1 Dillon is a waiter. He waits on a table of 4 whose bill comes to $59.75. If Dillon receives a 15% tip, approximately how much will he receive?
.
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#1 Lilie raised $475 for her softball team’s fundraiser. She wants to raise at least $755. Write and solve an inequality to determine how much more money Lilie must raise to reach her goal. Let d represent the amount of money in dollars Lilie must raise to reach her goal.
.
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Solve each inequality and graph the solutions. #1 −10 h ≥ −25 #2 |x + 2 | > 7
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#1 Generate ordered pairs for the function for x = −2, −1, 0, 1, and 2. Graph the ordered pairs and describe the pattern. y = x + 2
.
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#1 Express the relation as a table and a graph. {(−2, 4), (−1, 2), (0, 0), (1, −2), (2, −4)}
.
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#2 Give the domain and range of the relation.
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#1 Graph.
x + y = 2
#2 Determine a relationship between the x - and y -values. Write an equation to describe this relationship.
1 2 3 4
x
−2 −4 −6 −8
y
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#1 Graph.
y = −2 x + 1
.
#2 The value of y varies directly with x , and y = −18 when x = 12. Find y when x = 60.
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#1 Write an equation in slope-intercept form for the line that passes through (−3, 1) and is perpendicular to the line y = 3( x + 1) + 2.
.
#2 Write an equation in slope-intercept form for the line that passes through (0, −4) and is parallel to the line 2 y = 3 x + 4.
.
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#1 Graph both lines on the same coordinate plane.
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#1 Solve the system by graphing.
#2 Tell whether the ordered pair is a solution of the given system.
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#1 Solve
for a .
#2 Solve the inequality and graph the solutions. Then write the solutions as a compound inequality. | x − 6| − 10 < 1
#3 Find the 21st term of the arithmetic sequence. a 1 = 8.5, d = 3.5
#4 Use the distance formula to find the distance, to the nearest tenth, from D (4, −3) to E (−1, 5).
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#5 Write the equation −5 x + 10 y = 20 in slope-intercept form. Then graph the line described by the equation.
#6 Graph the given system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions.
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#1 Evaluate the expression.
#2 Simplify the expression. 21 p + 9 q 2 + 10 p − q 2
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#1 Simplify. 7 y + 3(2 − y ) + 6 y
#2 Tell whether the ordered pair (−1, −4) is a solution of the system.
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#1 Simplify. (2 3 + 1) 0 − 5 −2 + 5
#2 Write the polynomial − x 3 + 10 x − 4 x 5 + 3 x 2 + 7 x 4 + 14 in standard form. Then give the leading coefficient, the degree, and the number of terms. Standard form: Leading coefficient: Degree: Number of terms:
#3 Multiply. (6x + 5y) 2
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#1 Multiply. a. −5 y 2 (6 y − 1)
b. ( r + 7)( r − 3)
c. ( x − 11) 2
d. (5 m + 2 n )( m + 4 n )
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#1 Factor. a. 12 y 3 + 33 y 2 − 6 y
b. r 2 + r − 90
c. 3 x 2 − 11 x + 6
d. 6 x 2 + 19 x + 15
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#1 For g ( x ) = − x 2 + 9, find g ( x ) when x = −2 and when x = 5.
#2 Tell whether the function y = 3 x + 1 is linear. If so, graph the function.
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#1 Find the axis of symmetry and the vertex of the graph of y = 7 x 2 − 28 x + 29.
#2 Compare the graph of g ( x ) = −4 x 2 + 7 with the graph of f ( x ) = x 2 . Then graph both functions.
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#1 A golfer hits the golf ball. The quadratic function y = −16 x 2 + 80 x gives the time x seconds when the golf ball is at height 0 feet. How long does it take for the golf ball to return to the ground?
#2 Use the Zero Product Property to solve the equation ( x – 4)( x + 5) = –18.
#3 Solve the equation 64 x 2 − 144 = −23 by using square roots.
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#1 Complete the square for x 2 – 14 x + ? to form a perfect square trinomial.
#2 Solve 3 x 2 + 6 x + 1 = 0 by using the Quadratic Formula. If necessary, round to the nearest hundredth.
#3 Determine the number of solutions of the equation 9 h 2 − 12 h + 4 = 0 by using the discriminant.
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#1 Simplify.
#2 Factor the polynomial by grouping. 8 x 3 − x 2 − 16 x + 2
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#1 An experiment consists of spinning a spinner. Use the results in the table to find the experimental probability that the spinner does not land on red. Express your answer as a fraction in simplest form.
Outcome
Frequency
red
9
purple
10
yellow
11
#2 A bag contains hair ribbons for a spirit rally. The bag contains 4 black ribbons and 16 green ribbons. Lilie selects a ribbon at random, then Eleanor selects a ribbon at random from the remaining ribbons. What is the probability that Lilie selects a black ribbon and Eleanor selects a green ribbon?
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#1 On which day(s) was the sale of toy cars more than that of toy trains?
#2 The daily high temperatures in degrees Fahrenheit in a city for May 1–14 are given. Use the data to make a stem-and-leaf plot.
90 91 93 97 84 86 84 84 79 82 84 73 88 91 Daily High Temperatures (°F)
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#1 Out of 75 peaches in a basket, 9 are rotten. What is the experimental probability that a peach chosen at random is a good one? If there are 600 peaches in a basket, how many of them are likely to be good?
#2 The probability distribution for a game is shown in the table below. Outcome 0 points 1 point 2 points 5 points Probability 1/4 3/8 1/4 1/8 What is the probability of getting more than 1 point if the game is played one time?
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#1 Write a compound interest function to model the following situation. Then, find the balance after the given number of years. $14,000 invested at a rate of 6% compounded monthly; 8 years
#2 A radioactive isotope has a half-life of 7 hours. Find the amount of the isotope left from a 360-milligram sample after 35 hours. If necessary, round your answer to the nearest thousandth.
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#1 Find the domain of the square-root function.
#2 Simplify. Assume all variables represent positive numbers.
#3 Solve the equation. Check your answer.
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#1 A playground is in the shape of a rectangle. The length of the rectangle is three times its width. The area of the playground is 19,500 square feet. What is the length of the playground? Round
to the nearest foot. Hint: Use A = bh .
w
3 w
#2 The record numbers of consecutive days with no precipitation in eleven cities in Texas are 67, 50, 57, 52, 43, 65, 48, 66, 86, 62, and 53. Draw a box-and-whisker plot for this data.
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#1 Determine whether the relationship is an inverse variation or not. Explain.
x y 2 45 3 30 5 18
#2 Write and graph the inverse variation in which y = 8 when x = 2.
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#3 Find the asymptotes of the rational function and graph.
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#1 Divide. Simplify your answer.
#2 Divide using long division. (9 x 2 + 3 x 3 + 8) ÷ ( x − 2)
#3 Solve. Check for extraneous solutions.
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