POWAY UNIFIED SCHOOL DISTRICT
ALGEBRA 1A-1B
STANDARDS AND EXEMPLARS
SPRING, 2003
NUMBER SENSE
Grade 7 1.0 Students know the properties of, and compute with, rational numbers expressed in a variety of
forms.
2.0 Students use exponents, powers, and roots and use exponents in working with fractions.
1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10)
with approximate numbers using scientific notation.
Write 548,200 in scientific notation
8 3
1 , –.6(3.21)
11 4
Write 7.28 x 104 in standard notation
Write 0.00147 in scientific notation
Write 0.00591 x 108 in standard notation
The radius of the earth’s orbit is 150,000,000,000 meters. What is
this number in scientific notation?
11
a) 1.5 10
b) 1.5 1011
c) 15 10
10
d) 150 10
9
3.6 x 102 =
a) 3.6000
b) 36
c) 360
d) 3,600
1.2* Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimal)
and take positive rational numbers to whole-number powers.
–3[4(6 – 3) – 7 (4 + (–2))]
2 1
2 3
3 4
1 5
1
2 7
13 2
15 3
105
.5
8 1
1
11 4
0.6(3.21)
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The five members of a band are getting new outfits. Shirts cost $12 each, pants cost $29 each,
and boots cost $49 a pair. What is the total cost of the new outfits for all of the members?
a) $90
b) $95
c) $450
d) $500
11 1 1
Simplify:
12 3 4
1 5
a) c)
3 6
3 9
b) d)
4 5
23.065 (10.5)
3(4 +12) + 7(3)
43
2
1
3
0
7
9
3
2
5
1.785 0.0984
(1.23)(4.78)
Write the prime factorization of 72.
Which of the following numerical expressions results in a negative number?
a) (7) + (3)
b) (3) + (7)
c) (3) + (7)
d) (3) + (7) (11)
43 42
a) 45
b) 46
c) 165
d) 166
One hundred is multiplied by a number between 0 and 1. The answer has to be
a) Less than 0.
b) Between 0 and 50 by not 25.
c) Between 0 and 100 but not 50.
d) Between o and 100.
Which is the best estimate of 326 x 279?
a) 900
b) 9,000
c) 90,000
d) 900,000
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The winning number in a contest was less than 50. It was a multiple of 3, 5, and 6. What was
the number?
a) 14
b) 15
c) 30
d) It cannot be determined.
1.3 Convert fractions to decimals and percents and use these representations in estimations,
computations, and applications.
7
Convert to a decimal.
8
5
Convert to a percent.
6
23
is between which two whole numbers?
7
There is a 20% off sale on sweaters. The list price is $25.00. Find the sales price.
If Freya makes 4 of her 5 free throws in a basketball game, what is her free throw shooting
percentage?
a) 20%
b) 40%
c) 80%
d) 90%
Some students attend school 180 of the 365 days in a year. About what part of the year do
they attend school?
a) 18%
b) 50%
c) 75%
d) 180%
A pair of jeans regularly sells for $24.00. They are on sale for 25% off. What is the sale price
of the jeans?
a) $6.00
b) $18.00
c) $20.00
d) $30.00
What is the fractional equivalent of 60%?
1 3
a) c)
6 5
3 2
b) d)
6 3
A CD player regularly sells for $80. It is on sale for 20% off. What is the sale price of the CD
player?
a) $16
b) $60
c) $64
d) $96
1.4* Differentiate between rational and irrational numbers.
Define rational numbers.
Define irrational numbers.
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Label the following numbers with an “R” for rational or an “I” for irrational:
1) 8
9
2)
16
3) 225 25
4) 1.27
5) 1.212112111…
6)
7) g. 9.85
1.5* Know that every rational number is either a terminating or repeating decimal and be able to convert
terminating decimals into reduced fractions.
Convert the following into a decimal:
1
1)
2
5
2)
6
5
3)
11
Convert the following into a fraction:
1) 0.27
2) 1.45
3) 0.2727
1.6 Calculate the percentage of increases and decreases of a quantity.
Calculate the percent of increase:
a. From 1 to 1.2
b. From 3 to 6
c. From 5 to 18
Calculate the percent of decrease:
a) From 1 to 0.8
b) From 14 to 7
c) From 15 to 4
The cost of an afternoon movie ticket last year was $4.00. This year an afternoon movie ticket
cost $5.00. What is the percent of increase of the ticket from last year to this year?
a) 10%
b) 20%
c) 25%
d) 40%
The price of a calculator has decreased from $12.00 to $9.00. What is the percent of
decrease?
a) 3%
b) 25%
c) 33%
d) 75%
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1.7* Solve problems that involve discounts, markups, commissions, and profit and compute simple and
compound interest.
What is 15% of 36?
16 is what percent of 64?
A real estate agent earned 5% commission on a $200,000 house. What is her commission?
If a shirt is on sale for $25 and it originally sold for $30, what is the percent of decrease?
Sally puts $200.00 in a bank account. Each year the account earns 8% simple interest. How
much interest will be earned in three years?
a) $16.00
b) $24.00
c) $48.00
d) $160.00
Sally puts $200 in a bank at 8% interest compounded yearly. How much compound interest will
be earning in 3 years?
** Students need to be able to estimate percents (multiples of ten) without a calculator.
2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents
with a common base.
Simplify:
22
2
1
2
32 34
2 2 3
56
54
62
6 3
102
104
2.2* Add and subtract fractions by using factoring to find common denominators.
Simplify:
2 1
28 49
5 7
63 99
2 4
3 27
Which of the following is the prime factored form of the lowest common denominator of
7 8
?
10 15
a) 5x1
b) 2x3x5
c) 2x5x3x5
d) 10 x 15
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2.3* Multiply, divide, and simplify rational numbers by using exponent rules.
Evaluate for x = 2, y = 3, and z = 5
1) x3
2) y2
3) z2 + y
4) (x3)2
32 33
23 32
3
8 2
=
a) 34
b) 3
6
c) 3
10
d) 3
16
23
25
2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square
integer; for an integer that is not square, determine without a calculator ht two integers between
which its square root lies and explain why.
25
100
169
Find the side of a square with an area of 81 units2.
Determine which two integers the radical is in between:
a) 37
b) 99
c) 12
81
d)
4
The square root of 150 is between
a) 10 and 11
b) 11 and 12
c) 12 and 13
d) 13 and 14
The square of a whole number is between 1,500 and 1,600. The number must be between
a) 30 and 35
b) 35 and 40
c) 40 and 45
d) 45 and 50
2.5* Understand the meaning of the absolute value of a number; interpret the absolute value as the
distance of the number from zero on a number line; and determine the absolute value of real
numbers.
Simplify |–9|, |8 – 3|
True or false?
19 19 4 9 5
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If |x| = 3, what is the value of x?
a) 3 or 0
b) 3 or 3
c) 0 or 3
d) 9 or 9
What is the absolute value of 4?
a) 4
1
b)
4
1
c)
4
d) 4
ALGEBRA AND FUNCTIONSe or inequalities that represent a verbal description (e.g., three less
than a number, half as large as area A).
Grade 7 1.0 Students express quantitative relationships by using algebraic terminology, expressions,
equations, inequalities, and graphs.
2.0 Students interpret and evaluate expressions involving integer powers and simple roots.
1.2 Use the correct order of operations to evaluate algebraic expressions such as 3(2x+5) 2.
If x = 2, y = 3 and z = –1, evaluate:
1) x – 5
2) 3x + 2y – z
3x y
3)
4
4) 8(x – 2y)
5) 3(2x + 5)2
Simplify :
(–5y) + (– 4) + (– x + (2y) – (–7y)
4b – 9b + 7b
3x – 5 + 4 x – 2
2(2x + 1) – 3 (x – 4)
(2x 4)
hk 4
If h =3, and k= 4, then 2
2
a) 6
b) 7
c) 8
d) 10
1.3* Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse,
distributive, associative, commutative) and justify the process used.
Name the property illustrated by each of the following:
1) x(y + y) = x(0)
2) x(y + y) = xy + x(y) Use properties to solve
3) x(y + y) = (y + y)(x) problems.
4) x(y + y) = x(y + y)
1
5) x( y ) x(1)
y
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2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number
powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate
expressions that include exponents.
Simplify:
(x3)4
(3x4)2
(2xy2)(3x4y)
m3m2m6
Simplify: 2x–3
x y
3 3
a) 9xy
b) (xy)6
c) 3xy
d) xxxyyy
X3
X5
x3 y 2
x5 y
Simplify the expression shown below.
(5 x 2 z 2 )(8 xz 3 )
a) 40x 2 z 6
b) 40x3 z 5
c) 40x3 z 6
d) 40x5 z 5
Simplify (6a 4bc)(7 ab3c) .
a) 13a b c
4 3
b) 13a b c
5 4 2
c) 42a 4b3c
d) 42a b c
5 4 2
4x4
a) 2
b) 2x
c) 4x
d) 2 x2
3 x(4 x)
xy(2 xy)
2
2 x(3 x )
10 x 2
5
12 x
15 x 2
EQUATIONS
Grade 7 (Algebra and Functions)
4.0* Students solve simple linear equations and inequalities over the rational numbers.
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4.1* Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret
the solution or solutions in the context from which they arose, and verify the reasonableness of the
results.
2
x=8
3
3x + 1 = –7
4x + 3.24 = 0.72
m
– 18 = 7
3
Solve for x: 2x – 3 = 7
a) 5
b) 2
c) 2
d) 5
A flower shop delivery van traveled these distances during one week: 104.4, 117,8, 92,3, 168,7,
and 225.6 miles. How many gallons of gas were used by the delivery van during this week?
What other information is needed in order information is needed in order to solve this
problem?
a) The average speed traveled in miles per hour
b) The cost of gasoline per gallon
c) The average number of miles per gallon for the van
d) The number of different deliveries the van made
4.2* Solve multi-step problems involving rate, average speed, distance, and time or a direct variation.
2(x + 1) – 3 = 22
6y – 4 + 3y = 19
–3(2w – 1) = 15
5n – 10 = 4n + 2
3
x + 6 = 12x
4
Before each game, the Harbor High Mudcats sell programs for $1.00 per program. To print the
programs, the printer charges $60 plus $0.20 per program. How many programs does the team
have to sell to make a profit of $200?
A) 250 programs
B) 300 programs
C) 325 programs
D) 350 programs
A person drove for 6 hours at an average speed of 45 miles per hour (mph) and for 9 hours at an
average speed of 55 mph. Find the average speed for the entire trip.
A) 50 mph C) 52 mph
B) 51 mph D) 53 mph
d = rt
The diameter of a tree trunk varies directly with the age of the tree. A 45-year-old tree has a
trunk diameter of 18 inches. What is the age of a tree that has a trunk diameter of 20 inches?
a) 47 years
b) 50 years
c) 63 years
d) 90 years
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Stephanie is reading a 456-page book. During the past 7 days, she has read 168 pages. If she
continues reading at the same rate, how many more days will it take her to complete the book?
a) 12
b) 14
c) 19
d) 24
Tina is filling a 45 gallon tub at a rate of 1.5 gallons o water per minute. At this rate, how long
will it take to fill the tub?
a) 30.0 minutes
b) 43.5 minutes
c) 46.5 minutes
d) 67.5 minutes
An airplane flies 678 miles from Seattle to San Francisco. The trip takes an hour and a half.
What is the airplane’s average speed?
a) 402 miles per hour
b) 422 miles per hour
c) 432 miles per hour
d) 452 miles per hour
ALGEBRA 1-2
3.0 Students solve equations and inequalities involving absolute value.
10 |x| + 5 = 11
|2x + 1| = 5
The sum of three consecutive integers is –237. Find the integers.
Assume k is an integer and solve for k:
10 – 2|k| >4
a) {–3, –2, –1, 1, 2, 3}
b) {–3, –2, –1, 0, 1, 2,}
c) {–2, –1, 0, 1, 2} For these types of multiple
d) {–2, –1, 1, 2, 3} choice questions, students
If x is an integer, what is the solution to x 3 1? should be able to work
backwards from the given
a. {3}
answers to determine the
b. {3, 2, 1, 0, 1}
solution.
c. {3}
d. {1, 0, 1, 2, 3}
Assume y is an integer and solve for y.
y2 9
a) {11, 7}
b) {7, 7}
c) {7, 11}
d) {11, 11}
If x is an integer, which of the following is the solution set for 3|x| = 15?
a) {0, 5}
b) {, 5}
c) {5, 0, 5}
d) {0, 45}
4.0* Students simplify expressions prior to solving linear equations and inequalities in one variable,
such as 3(2x 5) + 4( x 2) = 12.
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Solve:
4
x 16
5
1/3 (x – 7) = 5x
¾ (8n – 4) = –2
–3(2 + 3x) = 12
x 3x
22
6 4
6t + 1 = 6t – 8 (no solution)
14 – (2q + 5) = –2q + 9 (identity)
5x + 3 – 2x = 7 – 4x
3 4
2x 1 2x
10 |x| + 5 = 11
|2x + 1| = 5
Which of the following is equivalent to 4(x+5) 3(x +2) = 14 ?
a. 4x + 20 3x 6 = 14
b. 4x + 5 3x + 6 = 14
c. 4x + 5 3x + 2 = 14
d. 4x + 20 3x 2 = 14
The diameter of a tree trunk varies directly with the age of the tree. A 45-year-old tree has a
trunk diameter of 18 inches. What is the age of a tree that has a trunk diameter of 20 inches?
a. 47 years
b. 50 years
c. 63 years
d. 90 years
Solve and graph on a number line inequalities in one variable.
x + 2 ≥ –2
5 – y 2 – 3x
Which of the following is equivalent to 9 3x > 4(2x 1)?
a) 13 11x
c) 10 > 11x
d) 6x >0
Which of the following is equivalent to 3x – (2 –x) 3x 2
b) 1 2x > 3x 5
c) 1 2x 3x 6
d) 1 2x > 3x 7
5.0* Students solve multi-step problems, including word problems, involving linear equations and
linear inequalities in one variable and provide justification for each step.
Solve:
1/3 (x – 7) = 5x
¾ (8n – 4) = –2
–3(2 + 3x) = 12
x 3x
22
6 4
6t + 1 = 6t – 8 (no solution)
14 – (2q + 5) = –2q + 9 (identity)
5x + 3 – 2x = 7 – 4x
3 4
2x 1 2x
The length of a rectangle is 4 more than 3 times its width. If the perimeter is 56 inches, what
is the length of the rectangle?
The two rectangles below have dimensions as shown. Which of the following expressions
represents the area of the shaded region?
a) 3w + 2
b) 3w – 2
c) w + 2
d) w – 2
After examining the equation a = 2b + c2, John stated that a will always be greater than b.
Which of the following is a counter example to John’s statement?
b) b ≤ 0 and c = 0
c) b and c are negative numbers
d) b = 0 and c = any number
e) b > 0 and c –6
2x – y ≤ 3
y > –2x + 1
x≥5
2
The slope of the line shown below is .
3
d
6
What is the value of d?
a. 3
b. 4
c. 6
d. 9
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What is the slope of the line shown in the graph below?
a. 2
1
b.
2
1
c.
2
d. 2
Which scatter plot shows a negative correlation?
What is the y-intercept of the line 2x 3y = 12?
a) (0, 4)
b) (0, 3)
c) (2, 0)
d) (6, 0)
What are the coordinates of the x-intercept of the line 3x + 4y = 12?
a) (0, 3)
b) (3, 0)
c) (0, 4)
d) (4, 0)
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1
Which of the following is the graph of y x 2?
2
7.0* Students verify that a point lies on a line, given an equation of the line. Students are able to
derive linear equations using the point-slope formula.
4
What is the equation of a line that includes the point (9,3) and has a slope of ?
3
3
b) y = 3x –
4
4
c) y = x + 13
3
4
d) y = x + 15
3
1 4
e) y = x
3 3
Is (3,–4) a point on the line 2x + 3y = –4? (yes/no)
Which of the following points lies on the line 4x + 5y = 20?
a. (0, 4)
b. (0, 5)
c. (4, 5)
d. (5, 4)
**Students should be able to transform equations from standard form slope-intercept
form (e.g., write 2x + 3y = 6 in slope intercept form).
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8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are
related. Students are able to find the equation of a line perpendicular to a given line that passes
through a given point.
Give the slope intercept form of the equation of the line that is perpendicular to 4x – 9y = –9
and passes through (– 4,7).
Which equation models a line parallel to y = 3x – 6?
1
a) y = x – 8
3
b) y = 3x – 6
1
c) y = – x + 4
3
d) y = 3x + 1
Give the slope-intercept form of the equation of the line that is parallel to 4x 9y = 9 and
passes through (4, 7).
a. 4x 9y = 79
b. 4x + 9y = 47
c. 9x 4y = 64
d. 9x + 4y = 8
1
What is the slope of a line parallel to the line y x 2?
3
A. 3
1
B.
3
1
C.
3
D. 2
1
What is the slope of a line perpendicular to the line y x 2?
3
a. 3
1
b.
3
1
c.
3
d. 2
Which of the following statements describes parallel lines?
a) Same y-intercept but different slopes
b) Same slope but different y-intercepts
c) Opposite slopes but same y-intercept
d) Opposite slopes but same x-intercept
Which of the following could be the equation of a line parallel to the line y = 4x 7?
1
a) y x7
4
b) y 4x 3
c) y 4 x 3
1
d) y x7
4
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