Practice Problems

Math Practice Problems : 

Math Practice Problems Let’s re-review how to work these problems from the practice test located at: http://www.cde.ca.gov/ta/tg/sr/documents/cstrtqmath4.pdf A man stopped someone on a street in New York City and asked her, “Excuse me, but can you tell me how to get to Carnegie Hall?” She smiled and replied, “Practice, practice, practice.”

More Study Guides : 

More Study Guides NOTE: All students worked each of the 96 problems in this practice packet. The 18 problems contained in this online Study Guide are the ones that more than just a few students answered incorrectly. Therefore, these problems are the ones that most students needed to review. Some students may not need any extra review. Some will need to review more than these 18 problems. You can find more of these Study Guides at this web site by searching the site for “bellaonline.” (Leave off the quotation marks in your search.)

Number Line & Fractions : 

Number Line & Fractions Strategy: order and compare Convert fraction to decimal or find common denominators to compare as fractions. Convert fraction to decimal = what decimal? If you cannot remember the decimal equivalent for a fraction, then you need to calculate it, like this: 2 ÷ 3 = 0.6 falls between .5 and .75, so B is the correct answer. #20. = 0.6

Add Decimal Numbers : 

Add Decimal Numbers Strategy: add in a column The answer is D. #24. Remember: line up the decimal points when you add or subtract.

Round Decimal to Whole Number : 

Round Decimal to Whole Number Strategy: use rounding rules. 205.83 is a whole number and a decimal. “…the nearest whole number” means round to the ONES place. 205.83 Apply the Rounding Rules: The 8 pushes the 5 up. The 5 becomes a 6. The numbers to the right turn into 0. 206.00 The answer is C.

Factors : 

Factors Strategy: look for the number whose only factors are “1” and the number itself. Remember: In multiplication, the numbers being multiplied are called factors. Use this information to answer the question. Choices A, B, and C are NOT true because each number in them has other factors besides “1” and the number itself: 8 has factors of 2 x 4, and 2 x 2 x 2. 9 has factors of 3 x 3. 10 has factors of 2 x 5. Choice D, however, contains the number 11, which doesn’t have any other factors besides “1” and 11. So, D is the correct answer.

Prime Numbers : 

Prime Numbers Strategy: Know the definition of a prime number and apply the definition. Prime numbers are all of the whole numbers that have only two factors: “1” and itself. (Other vocabulary: factors are numbers being multiplied.) The orange-shaded numbers are the prime numbers between 1 and 30. The numbers 4, 8, and 9 are NOT prime numbers because they have factors besides “1” and the number itself. So, A, C, and D do NOT contain prime numbers: 4 = 2 x 2 C. 8 = 4 x 2, and 2 x 2 x 2 9 = 3 x 3 Choice B. contains the prime number 5, because the only factors of 5 are “1” and 5 itself: 5 = 1 x 5. No other factors exist.

Expression and Word Problem : 

Expression and Word Problem Strategy: draw a picture and pick the choice that matches the picture. Based upon the picture, the total number of gumballs must equal 7 x 8 = 56. C is the only answer choice that equals 56.

Equation for AREA of a Rectangle : 

Equation for AREA of a Rectangle Strategy: know the equation and apply it to the answer choices. You know that the equation for Area is this: A = l x w The picture shows you the length and the width. Plug these values into the equation: A = 9 x 45 or A = 45 x9 Choice B is the only one that matches this equation.

Solve an equation with 2 variables. : 

Solve an equation with 2 variables. Strategy: plug in the X value, and calculate the Y value. Usually, an equation with 2 variables has an infinite number of solutions (ordered pairs). Normally, you draw a function table and list about 3 ordered pairs so that you can graph the line. However, if the problem gives you an X value, then all you do is plug X into the equation, and calculate the value of Y. It’s as if the problem is asking you to figure out the matching Y value to complete that ordered pair. y = 6x – 3 (there is an invisible multiplication sign between the 6 and the variable x) y = 6 x 2 – 3 (work from left to right to perform the calculations) y = 12 – 3 y = 9 Therefore, B is the answer.

The “Commutative” Property of Multiplication : 

The “Commutative” Property of Multiplication Strategy: recognize the Commutative Property of Multiplication. In this problem, you just need to realize that the variable “a” MUST equal 21. 21 x 7 = 7 x a (“a” is the variable; a must be equal to 21) The variable “a” must be equal to 21. “21” is the only choice that keeps the equation in balance (the left and the right sides are equal. ) Therefore, D is the answer to this problem. NOTE: In other problems similar to this one, the answer might be more difficult to recognize. For example, another answer to this problem could be “3 x 7” because 3 x 7 also equals 21. Commutative property: When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example 4 * 2 = 2 * 4

The “Associative” Property of Multiplication : 

The “Associative” Property of Multiplication Strategy: Recognize the Associative Property of Multiplication. It’s almost identical to the Commutative Property. Associative Property: When three or more numbers are multiplied, the product is the same regardless of the order of multiplication. For example (2 * 3) * 4 = 2 * (3 * 4) This problem uses a box instead of a variable. 2 x ? X 5 = 2 x 6 x 5 The answer must be equal to 6, to keep the equality in balance (to keep the left and right sides equal). What answer choice equals 6? B is the only choice that equals 6.

Find the AREA : 

Find the AREA Strategy: circle the key words that tell you what to calculate. The key words in this problem are: square, 12 feet, cover the entire garden. These words tell you to calculate the AREA (not the perimeter). Because the garden is a square shape, then all sides are equal length. Just plug 12 into the equation for Area, like this: A = l x w A = 12 x 12 A = 144 feet2

Compare Area and Perimeter of 2 rectangles : 

Compare Area and Perimeter of 2 rectangles Problems #72, 73, and 74 require you to calculate the area and perimeter of two rectangles. Strategy: calculate and compare the Area and Perimeter of each rectangle. Figure 1: A = 4 x 15 = 60 units2 P = 15 + 15 + 4 + 4 = 38 units Figure 2: A = 3 x 20 = 60 units2 P = 20 + 20 + 3 + 3 = 46 units Now compare. A is the correct choice.

Find the AREA of a tricky shape. : 

Find the AREA of a tricky shape. Strategy: split the tricky shape into simple shapes. Then do the calculations. Do you now see that the shape is really just 3 squares? Calculate the AREA of each square, Then add them to find the TOTAL AREA of the whole shape. Like this: 3x3=9 in.2 (the Area of ONE square) 9 + 9 + 9 = 27 in.2 (Total Area) C is the correct choice.

Measure the length of a line segment : 

Measure the length of a line segment #79 is similar to #78 and #80. Each problem describes a horizontal or vertical line segment, and then asks you to measure the length of it. In this problem, the line segment is vertical, which means that the X value remains the same in all of the coordinate points: The X value in Point S is 5, and the X value in Point F is also 5. Therefore, you measure the length of the segment by subtracting the Y values, like this: Y value in Point S is 8, Y value in Point F is 1 Subtract 8 - 1 D is the correct answer.

Parts of a Circle : 

Parts of a Circle Strategy: know the parts of a circle. The diameter is a line segment that cuts the circle in half. The radius is any segment that starts in the center and connects to any point along the outside of the circle. For example, segment OB and segment OA are examples of a radius. The perimeter of a circle is just like the perimeter of any shape. An arc is a section of the perimeter. D is the correct answer.

2 Types of Symmetry : 

2 Types of Symmetry http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/4_Line_Symmetry/index.html One type of symmetry is called line symmetry. This concept is fairly easy to remember. The other type is called rotational symmetry. This concept is more challenging. http://www.mystery-productions.com/hyper/Hypermedia_1999/BENTON/index.htm A is the correct answer. To review line symmetry, click this link: To review rotational symmetry, click this link: To review these concepts online, click on a link below.

4 Types of Triangles : 

4 Types of Triangles Strategy: know the defining characteristics of the 4 types of triangles. Isosceles: 2 sides are equal Right: it contains a right angle (90° angle) Equilateral: all 3 sides are equal Scalene: No sides are equal isosceles right equilateral scalene C is the answer.

Probability (predicting) : 

Probability (predicting) Strategy: match key words and probabilities. Key words and the matching probabilities are: Never = 0 chances Not likely = between 0 and half of the total Equally likely = exactly half Likely = between half and all Always = all of the chances This problem asks you for “most likely,” which is somewhere between Likely and Always. To solve this problem, add up all of the marbles. They = 26. Yellow marbles are the biggest fraction of the total (9/26, or 9 out of 26). (The other colors are 4/26, 5/26, and 8/26.) So, yellow marbles are “most likely.” Therefore, D is the correct answer.