2007 Cedar Ridge Test Solutions

1. Find the sum of the first 5 composite numbers. Composite Number: least 1 positive divisor, other than itself and 1. Solution: So we know that the first 5 composite numbers are: 4, 6, 8, 9, and 10. Now, add them all together: 4 + 6 + 8 + 9 + 10 = 37 2007 Cedar Ridge Test Solutions 2) If A = the number of sides of an octagon, and B = the number of sides of a decagon, find: AB + B² + A. Solution: So we know that a octagon has 8 sides and a decagon has 10 sides, now just plug them in to your formula: (8)(10) + (10)² + (8) = ? 80 + 100 + 8 = ? A = 188 3) Simplify: Solution: Well, we know that the square root is: A number that, when multiplied by itself, produces another number (It is the reverse of squaring a number). So the square root of 144 is: 12 x 12 = 144 The square root of 25 is: 5 x 5 = 25 And The square root of 49 is: 7 x 7 = 49 Let’s plug in the numbers: 12 - 5 + 7 = 14

2. 4) If 4a = 160 and 6b = 3, find ab. Solution: First thing we need to do is find a and b, so you will need to solve both equations: 4a = 160 6b = 3 Now find:ab a = 160 ÷ 4 b = (40)() a = 40 b =Answer:20 2007 Cedar Ridge Test Solutions 5) Ashli really wants an A in Math. If her test scores were 88, 95, 100, 86, and 92, what must she make on her sixth test for her average to be 93? Solution: To normally to find an average, we have to add the total number of scores together and then divide by the total number of scores. So we know that we have to find the current average of 88, 95, 100, 86, and 92. Step 1 88 + 95 + 100 + 86 + 92 = ? 183 + 100 + 178 = ? Answer = 461 Step 2 If you take 93 and times it by 6 and then minus 461 from that from that product, you will have the percent that Ashli has to make on the next test. Step 3 93 x 6 = 558 558 – 461 = 97 The score that Ashli needs to make on the 6th tests is : 97

3. 6) Find the difference between the greatest common factor(GCF) and the Least Common Multiple (LCM) of 18 and 90. Step 1: Find Least Common Multiple 18: 18,36,54,72,90 90: 90, 180, 270,360,… Definition of LCM The lowest number that can be divided by two or more numbers. It has to be greater or equal to the highest number. Step 2:Find Greatest Common Factors 18: 1,2,3,6,9,18 90: 1,2,3,6,9,10,18,30,45,90 Definition of GCF The largest whole number that can be divided by each of the numbers in a fraction. Has to be equal or lower than the lowest number. 2007 Cedar Ridge Solutions Step3: Find the Difference between LCM and GCF. 90 -18 72 Answer: 72 7) Neal did twice as many sit-ups on Friday as Monday. On Wednesday and Thursday he did equal amounts of sit-ups. He did half as many on Monday as Tuesday. On Wednesday, he decreased his previous number by 5. How many sit-ups did he do from Monday through Friday, if he did ten on Tuesday? Solution: The best way to work this is to chart it: Monday = ½ Tuesday Tuesday = 2 x Monday Wednesday = Tuesday – 5 Thursday = Tuesday - 5 Friday = 2 x Monday So plug in 10 on Tuesday and go from there: Monday = ½(10) 5 Tuesday = 10 10 Wed. = 10 – 5 5 Thursday = 10 – 5 5 Friday = 2 x ½(10) 10 Total for the week: 35

4. 8) Beau bought 2 pounds of cashews at $1.50 a pound. He bought ½ pound of almonds at $1.00 per pound. What was the average cost per pound of nuts? Solution: This is a simple averaging problem. First, find out how many pounds were bought and how much money was spent. Then divide Total money spent by total pounds, this will give you your average of money spent per pound of nuts. 2007 Cedar Ridge Solutions Pounds boughtMoney Spent 2 pounds of Cashews 2 x $1.50 = $3.00 ½ pound of Almonds ½ x $1.00 = $0.50 2.5 pounds of Nuts Total $ Spent = $3.50 $3.50 ÷ 2.5 = $1.40 per pound 9) The length of a rectangle is 3 times its width. The area is 48ft². What is the perimeter of the rectangle? Solution: Plug in the Area Formula to find Your variables for the perimeter. Area = L X W (3W) x W = 48 L X W = 48 ÷ 3 L x W = 16 Remember, L will be the same number as W, because the length is 3 times the width. So that narrow it down to a number times its self. Which the answer is : 4 L = 3 x W Area = 48ft² W

5. 2007 Cedar Ridge Solutions 10)What is the 12th number in the following sequence? 1, 1, 2, 3, 5, 8, 13, ………. So, you will want to look for a pattern to figure out the sequence. Sometimes it will be 2 difference sequence over lapped, or it could be just one. This one is just one with adding: Given Sequence Answer Sequence 0 + 1 = 1 1 + 1 = 2 1 + 2 = 3 2 + 3 = 5 3 + 5 = 8 5 + 8 = 13 8 + 13 = 21 13 + 21 = 34 21 + 34 = 55 34 + 55 = 89 55 + 89 = 144 The 12th number in the sequence is 144 11) What is the probability of rolling a prime number when a fair six-sided number cube is rolled? 6 sides of a die: P: Prime C: Composite N: None 1, 2, 3, 4, 5, 6 N, P, P, C, P, C With Prime Numbers, you get 3 sides: With Composite Numbers, you get 2 sides: With None , you get 1 side: Answer is:

6. 2007 Cedar Ridge Solutions 12) Evaluate: First thing we need to do is change the mixed numbers into improper fractions. Next, flip your division fraction Now, let’s cross divide: 1 1 -- -- 13 5 2 -- 12 And what you are left with is: -- -- -- 2 1 1 1 1 13) The price of a $160 cell phone was reduced by 25%. Later, the sale price was reduced another 25%. What was the final price of the cell phone? Step 1: we need to find the 25% of $160 and then reduce from the $160 160 X .25 800 320 40.00 $160 -$40 $120 Step 2: Now we need to find the 25% of $120 and then reduce that from $120 and that will give us the final price of the cell phone. 120 X .25 600 240 30.00 $120 -$30 $90 Final Price: $90

7. 2007 Cedar Ridge Solutions 14) By how much does exceed the product of 2, 3, and 4? Step 1:Solve: Product: a answer to a multiplication problem (9) + (8) + (16) = ? Answer: 33 Step 3:Now we have to find how much Step 1 exceeds Step 2. Step 2:Now find the product of 2, 3, and 4. 33 -24 9 2 x 3 x 4 = ? 6 x 4 = ? Answer: 24 Answer: 9 15) Simplify: Step 1: We need to find the common dominator for the top fraction equation and solve. = = = Step 2: We need to divide the dominator fraction by the numerator: Remember, you need to flip the dominator fraction over, to cross divide/multiple the fraction. Answer:

8. 2007 Cedar Ridge Solutions 16) Find the area of the figure below. 6 4 6 10 Step 1: We need to separate the two shapes with a dotted line. 6 4 6 2 2 4 6 10 Step 2:Need to find the area of both shapes. Remember Area of a Square is A = S² and Area of a Rectangle is A = L x W Area of Square: A = (6)² = 36 Area of Rectangle: A = (4) x (2) = 8 Add the two areas together to get TOTAL AREA. 36 + 8 = 44 Answer: 44

9. 2007 Cedar Ridge Solutions 17) The time for the first increment was four hundred thousand and three thousand, two hundred fifty hundred – thousandths seconds. The time for the second increment was only three hundred forty-two thousand, fifteen and twenty-five ten thousandths seconds. By how much was the time of the first increment greater? Step 1: Write out first increment. Four Hundred thousand and three thousand, two hundred fifty hundred-thousandths seconds 400,000.03250 Key Note: The word “AND” represents decimal. Step 2: Write out second increment. Three hundred forty-two thousand, fifteen and twenty-five ten thousandths seconds 342,015.0025 Labeling Position after Decimal .0 = Tenths .00 = Hundredths .000 = Thousandths .0000 = Ten Thousandths .00000 = Hundred-Thousandths NOTE: Numbers to the right of the decimal point are read like whole numbers and given a value according to the position of the last number. Step 3: Find the difference between the increments to find how much more the first increment was greater. 400,000.03250 - 342,015.0025 57,985.0350– rounded to the nearest hundredths. Answer: 57,985.03 18) Find the Measurement ofLCRM D C 130° 50° 50° S R M 130° Angle CRM is an interior angle to Angle DRS, which is 50°. Answer: 50°

10. 2007 Cedar Ridge Solutions 19) What is 10% of 70% of 650? Step 1:Find 70% of 650 650 x.70 000 4550 455.00 Step 2:Find 10% of the 70% 455 x.10 000 455 45.50 Answer: 45.50 20) Evaluate: x²y - if x = 4, y = 2 and z = 10 We just need to plug in everything and solve: (4)²(2) - = (16)(2) - = 32 - = = = = 28 Answer: 28

11. 2007 Cedar Ridge Solutions 21) Solve for x: 9(x + 6) = 144 Step 2: Move 54 to the other side of the equation. Remember: What you do to one side, you must do to the other. 9x + 54 = 144 - 54 = -54 9x = 90 Step 1:Multiple 9 by x and 6 9x + (9)6 = 144 9x + 54 = 144 Step 3: Divide 9 by both sides to solve for X = 10 Answer: 10 22) What is the measure of the complement of a 45° angle? Definitions Complementary Angles: Two angles that add up to 90° Formula: 90° - X So we know that formula for a Complementary Angle is 90° - X, so now we plug in our number. 90° - 45° = 45° Supplementary Angles: Two angles that add up to 180° Formula: 180° - x Answer: 45°

12. 2007 Cedar Ridge Solutions 23) Find the sum of the prime factors of 175. Step 1: You need to all the factors of 175. 175 5 5 35 7 All the factors of 175 are: 5,5,7 Step 2:Add all the Prime (prime being the key factor) factors together. 5 + 7 = 12 Answer: 12 24) A regular decagon has a perimeter of 680cm. What is the length of one side? Step 1: We know that to find a perimeter of a polygon, you must use the formula: Measurement of a side X number of sides. So, we are going to do the reverse: divide the total perimeter by the number of sides. This will give us the measurement of one side. Decagon A decagon has 10 sides, and 10 corners. 680 ÷ 10 = 68 Answer: 68

13. 2007 Cedar Ridge Solutions 25) Find the product of the perimeter and area of a rectangle with a length of 25 and a width of 5. Rectangle Formulas Perimeter = 2L + 2W Area = L x W Step 1: Solve for each perimeter and area of the rectangle. Area: 25 x 5 = ? A = 125 Perimeter: 2(25) + 2(5) = ? 50 + 10 = ? P = 60 Step 2: Solve for the product of perimeter and area. P(60) x A(125) = Product 60 x 125 = ? Product = 7,500 Answer: 7,500 Tiebreaker #1) Simplify: 16(3-1) + 25 – (4 + 4)² Step 1: Use the Order of Operations to solve this equation: 16(3-1) + 25 – (4 + 4)² = ? 16(2) + 25 – (8)² = ? 16(2) + 25 – 64 = ? 32+25–64= ? Answer: - 7 Answer: -7

14. 2007 Cedar Ridge Solutions Tiebreaker #2) Brianna’s watch stopped at exactly 4:00. What was the measure of the smaller angle formed by the hour and the minute hands? Step 1: Draw the Watch to show the angle you are looking for: Step 2: You know that a full circle is 360 degrees, so you the formula of : 360 ÷ 12 = 30 degrees for every 5 minutes. 12 1 11 2 10 3 9 8 4 5 7 6 Step 3: You now know that for every 5 minutes it’s 30 degrees, so now times that by 4. 30 x 4 = 120 degrees. Answer: 120° Tiebreaker #3) If two of the angles of a certain triangle are 35° and 15°, what is the measure of the third angle? Step 1: Draw your triangle with the angles. 35° 15° Step 2: You know that the angles in a triangle add up to 180. 15 + 35 + n = 180 50 + n = 180 n = 180 – 50 n = 130 degrees Answer: 130°