Math 7 SOL Review

Math 7 SOL Review

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SOL 7.1a Powers of Ten with Negative Exponents

• They never give you a NEGATIVE number

• They give you a number between 0 and 1

• They may be written as a fraction or decimal

Multiple Choice

Which is a true statement?

• A

• B

• C

SOL 7.1b Scientific Notation

• Scientific notation is used to represent very large or very small numbers. 

• A number written in scientific notation is the product of two factors — a decimal greater than or equal to 1 but less than 10, and a power of 10 .

• Numbers can be written in standard form and in scientific notation. Standard Form: 6,800,000,000,000 Scientific Notation: 6.8 × 10¹²

Multiple Choice

Which of the following is correct scientific notation?

• 20.3 x 10⁴

• .203 x 10⁴

• 203 ⁴

• 2.03 x10⁴

Multiple Choice

UNDERSTANDING:

The first number in scientific notation must be...

• between and including 0 and 10

• between and including 1 and 9.9999

• between and including 0 and 9.999

• between and including 1 and 10

SOL 7.1c Compare and Order

• Change ALL percents and fractions to decimals

• Make them all LOOK the same( Add zeros if necessary)

• Ascending- Least to Greatest

• Descending - Greatest to Least

Multiple Choice

Which statement is FALSE?

Multiple Choice

Order the following from least to greatest.

1/2, 2%, 2.1 x 10^-2, 0.20

• 2%, 2.1 x 10^-2, 1/2, 0.20

• 2%, 2.1 x 10^-2, 0.20, 1/2

• 0.20, 1/2, 2%, 2.1 x 10^-2

• 2.1 x 10^-2, 1/2, 0.20, 2%

Compare and Order Numbers in Scientific Notation

• Compare the exponents

• If the exponents are the same, compare the base numbers

• 
  

• 
  

Multiple Choice

Which of the following numbers is the greatest?

• 7.5 x 10⁴

• 5.6 x 10⁵

• 6.1 x 10⁵

• 6.5 x 10⁵

SOL 7.1d Perfect Squares and Square Roots

• A square root of a number is a number which, when multiplied by itself, produces the given number. 

• The square root of a number can be represented geometrically as the length of a side of the square.

Multiple Select

Identify each true statement.

• √36 = 6

• √10 = 100

• 15 = √225

• 128 = √256

• 11 = √121

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Which is a square root of 169?

• 12

• 14

• 13

• 11

SOL 7.1e Absolute Value

• The absolute value of a number is the distance from 0 on the number line regardless of direction. 

• The absolute value of a number will always be positive.

Multiple Choice

Which is a true statement?

• -3.79 = |-3.79|

• 0.5 = |-½|

• -|1.5| = |-1.5|

• |-½| = -0.5

Multiple Choice

What's a way to define absolute value?

• The value of a number

• The opposite of a number

• The distance of a number from zero

• The multiplicative inverse of a number

SOL 7.2 Solve Practical Problems

• Solve practical problems involving addition, subtraction, multiplication, and division with rational numbers expressed as integers, fractions (proper or improper), mixed numbers, decimals, and percents.

• 
  

Multiple Choice

The news reported that 40% of customers lost their electricity during the last storm. If there are 2,600 customers, how many of them lost their electricity?

• 1,040

• 2,560

• 6,500

• 1,560

Multiple Choice

Alana runs laps after school. On Monday she runs 3 1/2 laps, on Tuesday 4 1/3 laps, and on Wednesday 4 1/2 laps. What is the total number of laps Alana has run this week?

• 12 laps

• 13 1/2 laps

• 11 1/2 laps

• 12 1/3 laps

SOL 7.3 Proportions

• A proportion is a statement of equality between two ratios.

• A proportion can be written as a/ b = c/ d

• Solve a proportion by using cross products

• Proportions can be used to represent percent problems as follows: is/of = p/100

Multiple Choice

A map has a scale of 2 cm = 25 km. Two cities are 15 centimeters apart on the map. What is the actual distance between the cities?

• 1.2 km

• 30 km

• 40 km

• 187.5 km

Multiple Choice

Shannon is driving to visit her aunt, who lives 308 miles away. There are about 1.6 kilometers in every mile. About how many kilometers will Shannon travel to get to her aunt's home?

• 184.8

• 192.5

• 309.6

• 492.8

SOL 7.3 Tip

• Tip is an amount you pay for a service in addition to the original price.

• Tip can be found by taking the original amount and multiplying by the percentage of the tip.

Multiple Choice

Lauren went to Buffalo Wild Wings with her friends for dinner. Her total bill was $18.75 and she wanted to leave an 18% tip. How much did Lauren leave for a tip?

• $3.38

• $3.375

• $3.37

• $3.30

SOL 7.3 Sales Tax

• Sales Tax is an amount charged in addition to the original purchase price.

• Sales tax can be found by taking the original amount and multiplying by the percentage of sales tax. 

• Sales Tax is ADDED to the Original price

Multiple Choice

Ralph buys a computer for $675. The sales tax rate is 6%. How much total did Ralph pay for the computer?

• 40.50

• 715.50

• 6.00

• 634.50

SOL 7.3 Discount

• Discount is the amount of money you subtract from the original price of an item.

• Discount can be found by taking the original amount and multiplying by the percentage of the discount.

• Example: Sara decided to buy a pair of shoes that cost $64.00 and were discounted for 25% off. How much did Sara save with the discount? % /100 = 𝑋/ $ total 25 /100 = 𝑋/ 64 100x = 1600 or $64.00 x .25 = $16.00 discount

Multiple Choice

If you receive 25% off an item costing $22.00, how much money do you save?

• $ 5.50

• $ 4.25

• $6.00

• $7.35

SOL 7.4 Surface Area

• A rectangular prism can be represented on a flat surface as a net that contains six rectangles — two that have measures of the length and width of the base, two others that have measures of the length and height, and two others that have measures of the width and height. The surface area of a rectangular prism is the sum of the areas of all six faces. 

• A cylinder can be represented on a flat surface as a net that contains two circles (bases for the cylinder) and one rectangular region whose length is the circumference of the circular base and whose width is the height of the cylinder. The surface area of the cylinder is the area of the two circles and the rectangle.

SOL 7.4 Volume

• The volume of a rectangular prism is computed by multiplying the length, by the width, by the height.

• The volume of a cylinder is computed by multiplying the area of the base by the height of the cylinder

Multiple Choice

 Calculate how much cheese the container can hold.

• 7230.2 m³

• 6621 m³

• 1130.4 m³

• 376.8 m³

Multiple Choice

Calculate the volume.

• 1120 ft²

• 2011 ft²

• 120 ft³

• 1120 ft³

Multiple Choice

What is the surface area of this figure?

• 200 cm ²

• 800 cm ²

• 400 cm ²

• 100 cm ²

Multiple Choice

Surface area is...

• filling in a 3 dimensional shape

• wrapping the outside of a 3 dimensional shape

Multiple Choice

Volume is...

• filling your water bottle with water

• the plastic used to make your water bottle

SOL 7.5 Similar Figures

• Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional. 

• Similarity statements can be used to determine corresponding parts of similar figures

• Set up a PROPPRTION and solve.

Multiple Choice

• F

• G

• H

• J

Multiple Choice

Find side length X.

• 30

• 25

• 15

• 40

SOL 7.6 Quadrilaterals

• A QUADRILATERAL is a closed figure that has four sides, four angles, and four vertices.

• A parallelogram is a quadrilateral whose opposite sides are parallel and opposite angles are congruent.

• A rectangle is a parallelogram with four right angles. The diagonals of a rectangle are the same length and bisect each other.

• A square is a rectangle with four congruent sides whose diagonals are perpendicular. A square is a rhombus with four right angles. 

• A rhombus is a parallelogram with four congruent sides whose diagonals bisect each other and intersect at right angles.

• A trapezoid is a quadrilateral with exactly one pair of parallel sides.

• A trapezoid with congruent, nonparallel sides is called an isosceles trapezoid.

Multiple Choice

Which figure could be placed in the box that would fit all three properties given in the Venn diagram?

• Parallelogram

• Rhombus

• Rectangle

• Square

Multiple Choice

Find the missing angle.

• 30

• 60

• 90

• 120

Multiple Choice

What are the attributes of a square and a rectangle?

• 4 congruent sides and 4 90 degree angles

• exactly one pair of parallel sides

• four congruent sides

• four 90 degree angles

Multiple Choice

Fill in the blank

A square is ________ a rhombus.

• always

• sometimes

• never

Multiple Choice

Name that shape.

• quadrilateral

• quadrilateral, parallelogram

• quadrilateral, rectangle

• quadrilateral, rhombus

Multiple Choice

Name that shape.

• square

• square

  rhombus

• quadrilateral

  parallelogram

  rhombus

• quadrilateral

  parallelogram

  square

SOL 7.7

• A transformation of a figure called the preimage changes the size, shape, or position of the figure to a new figure called the image.

• Translations and reflections do not change the size or shape of a figure (e.g., the preimage and image are congruent figures). Translations and reflections change the position of a figure. 

• A translation is a transformation in which an image is formed by moving every point on the preimage the same distance in the same direction. 

• A reflection is a transformation in which an image is formed by reflecting the preimage over a line called the line of reflection. All corresponding points in the image and preimage are equidistant from the line of reflection.

• The image of a polygon is the resulting polygon after the transformation. The preimage is the polygon before the transformation. 

• A transformation of preimage point A can be denoted as the image Aʹ (read as “A prime”).

Multiple Choice

Translate the triangle down four and right three, then reflect over the x-axis. What is the new location of point C?

• (-2,-6)

• (2,-6)

• (2,6)

• -2,6)

Multiple Choice

If the square in the image is reflected over the x-axis, what would be the new location of point P?

• (4,3)

• (-4,-3)

• (4,-3)

• -4,3)

Multiple Choice

If the triangle in the image is translated up three and five to the right, what would be the location of point C?

• (1,0)

• (5,3)

• (-5,-3)

• (-4,-3)

Multiple Choice

Determine how to translate triangle A'B'C' to triangle ABC.

• right two, down five

• right two, down 9

• left two, down 9

• left two, down 5

SOL 7.8 Theoretical and Experimental Probability

• The theoretical probability of an event is the expected probability and can be determined with a ratio. 

• The experimental probability of an event is determined by carrying out a simulation or an experiment.

• In experimental probability, as the number of trials increases, the experimental probability gets closer to the theoretical probability (Law of Large Numbers).

Multiple Choice

Arianna spins a fair number cube (dice) 80 times. The results are shown in this table. What is the theoretical probability that she rolls a 4? (Write your answer as a fraction. Example: 1/2 or 11/13.)

• 1/6

• 18/80

• 9/40

• 1/20

Multiple Choice

• 2/5

• 1/3

• 12/30

• 3/30

Multiple Choice

A restaurant surveys customers with the following results: 8 pizzas, 12 hamburgers, 14 pastas, and 6 steaks. What is the experimental probability of pizza or steak?

P(pizza or steak)

• 20%

• 65%

• 50%

• 35%

SOL 7.9 Histograms

• A histogram is a form of bar graph in which the categories are consecutive and equal intervals. The length or height of each bar is determined by the number of data elements (frequency) falling into a particular interval. 

• A frequency distribution shows how often an item, a number, or range of numbers occurs. It can be used to construct a histogram.

• A line plot provides an ordered display of all values in a data set and shows the frequency of data on a number line. Line plots are used to show the spread of the data, to include clusters (groups of data points) and gaps (large spaces between data points), and quickly identify the range, mode, and any extreme data values.

• A circle graph is used for categorical and discrete numerical data. Circle graphs are used to show a relationship of the parts to a whole. Every element of the data set is not preserved when representing data in a circle graph.

• A stem and leaf plot is used for discrete numerical data and is used to show frequency of data distribution. A stem and leaf plot displays the entire data set and provides a picture of the distribution of data.

Multiple Choice

3) Mrs. Nelson asks her students how many days this month have they bought school lunch. The line plot displays this data. Which histogram represents this data?

Multiple Choice

1) West Elementary School had a bake sale and a student recorded all the sales that were made in the table shown.

Which histogram represents this data?

Multiple Choice

2) What set of data would be most appropriate to represent in a histogram?

SOL 7.1 Proportional Relationships, Additive Relationships, and Slope

• When two quantities, x and y, vary in such a way that one of them is a constant multiple of the other, the two quantities are “proportional”. A model for that situation is y = mx where m is the slope or rate of change. Slope may also represent the unit rate of a proportional relationship between two quantities, also referred to as the constant of proportionality or the constant ratio of y to x. 

• The relationship between two quantities could be additive (i.e., one quantity is a result of adding a value to the other quantity) or multiplicative (i.e.., one quantity is the result of multiplying the other quantity by a value). 

• Two quantities, x and y, have an additive relationship when a constant value, b, exists where y = x + b, where b  0. An additive relationship is not proportional and its graph does not pass through (0, 0). Note that b can be a positive value or a negative value. When b is negative, the right side of the equation could be written using a subtraction symbol (e.g., if b is −5, then the equation y = x – 5 could be used).

• 
  

• 
  

Multiple Choice

Which equation best describes the relationship in this table?

• y = x - 4

• y = x + 4

• y = 3x

• y = 4x

Multiple Choice

Find the slope of the line that passes through the points (2, 4) and (6, 12)

• 1/2

• -1/2

• 2

• -2

Multiple Choice

Which equation matches the graph?

• y = 2x

• y = ½x

• y = x + 2

• y = x - 2

Multiple Choice

What is the equation for this graph?

• y = 3x

• y = x+3

• y = x-3

• y = -3x

Multiple Choice

The table shows the relationship between x and y. Which could be used to represent the relationship between x and y?

• y = ½x

• y = x+1

• y = x - 1

• y = 2x - 1

Multiple Choice

Which of the following graphs represents y = ⅔x

Multiple Choice

Level 1: What is the y-intercept?

• It is where the line crosses the x-axis.

• It is where a vertical line crosses.

• It is where the line crosses the y-axis.

• It is where the slope crosses the y-axis.

SOL 7.11 Evaluate Algebraic Expressions

• To evaluate an algebraic expression, substitute a given replacement value for a variable and apply the order of operations. For example, if a = 3 and b = -2 then 5a + b can be evaluated as: 5(3) + (-2) = 15 + (-2) = 13 

• Once you have substituted the values you may use your calculator.

Multiple Choice

15) What is the value of the expression

when y = 5 and x = -4 ?

• 71

• 79

• 221

• 229

Multiple Choice

10) Evaluate the expression

when x = 25 and y = -10

• -18

• -12

• 2

• 8

Multiple Choice

7) If n = -3, what is the value of

• -18

• -16

• 12

• 15

SOL 7.12 Write Algebraic Expressions and Equations

• Expressions are mathematical sentences that do not contain an equal sign.

• Equations are mathematical sentences that do have an equal sign.

• Remember the turn around words are THAN and FROM.

Multiple Choice

Which equations means "a number increased by the product of 7 and 12 is 93"?

• $$7x+12=93$$

• $$7x+12x=93$$

• $$\left(x+7\right)\left(12\right)=93$$

• $$x+\left(7\right)\left(12\right)=93$$

Multiple Choice

$$6x-4=32$$  

Which verbal sentence represents the equation above?

• the product of six and a number less than 4 is 32

• the quotient of six and a number, minus four is 32

• six times the difference of x and 4 is 32

• Four less than the product of six and a number is 32

SOL 7.12 Solve Equations

I can solve two-step linear equations in one variable, including practical problems that require the solution of a two-step linear equation in one variable.

Two-Step Equations Tips

• Isolate the variable

• What you do to one side you must do to the other

• Use inverse (opposite) operations to solve

• "Undo" addition/subtraction first, then multiplication/division

• equations can be modeled using colored chips, algebra tiles, or weights on a balance scale

• An equation is a mathematical sentence that states that tow expressions are equal

• Always check your answers!

Multiple Choice

Level 3

Solve for a

• a= -2

• a= -6

• a= 3

• a= 15

Multiple Choice

Level 3

Solve for x

• x = 2

• x = -2

• x = -10

• x = 4

Multiple Choice

What is the equation shown in this picture?

• $$3x=7$$

• $$-3x=-7$$

• $$x-3=-7$$

• $$x+3=7$$

SOL 7.13 Inequalities

• A one-step inequality is defined as an inequality that requires the use of one operation to solve.

• The inverse operation for addition is subtraction, and the inverse operation for multiplication is division.

• When both expressions of an inequality are multiplied or divided by a negative number, the inequality symbol reverses.

• When the solution to an inequality is > or <, it is represented on a graph using an open circle.

• When the solution to an inequality is ≥ or ≤, it is represented on a graph using a closed circle.

Multiple Choice

Which graph matches the inequality?

Multiple Choice

Which inequality matches the graph?

Multiple Choice

Which number is a solution to the inequality?

• -6

• 0

• -9

• 5

Multiple Choice

What is the solution to the inequality?

Multiple Choice

In which of the following inequalities will the inequality symbol be reversed?