Show:
Expressions and Equations
Ratios and Proportional Relationships
Number System
Geometry
Statistics and Probability
100
Simplify. (2)(18) ÷ (–2 + 5)( –1)
What is -12
100
The average rate of hair growth is 2.5 centimeters every 2 months. At that rate, how many months will it take to grow 22.5 centimeters of hair?
What is 18 months
100
A bicycle training wheel has a radius of 3 inches. The bicycle wheel has a radius of 10 inches. Approximately how much smaller, in square inches, is the area of the training wheel than the area of the regular wheel?
285.74 square inches because the area of the wheel is 314 square inches and the area of the training wheel is 28.26 square inches, resulting in a difference of 285.74 square inches.
100
A gym teacher at Jackson High School wants the school to have a new team sport: soccer, lacrosse, or rugby. She will take a survey to determine which of those sports most students prefer. Which population would provide a random sampling for the gym teacher to use? A. all students at the school who are sixteen years old B. all students who buy lunch at the school on Friday C. half of the students who play on team sports at the school D. every third student arriving at school
D. every third student arriving at school
200
Which expression is equivalent to –7(y – 2)? A. –7y – 2 B. –7y + 2 C. –7y – 14 D. –7y + 14
What is D. -7y + 14
200
During cooking, chicken loses 10% of its weight due to water loss. In order to obtain 1,170 grams of cooked chicken, how many grams of uncooked chicken must be used?
What is 1,300 grams. It is found by dividing 1,170 by 0.90.
200
What is the product? -8(7 - 3.2)
What is -30.4
200
The complementary angle of 59 degrees is?
What is 31 degrees.
200
A bag contains 14 blue marbles and 14 purple marbles. What is the likelihood of randomly drawing a purple marble? A. certain B. likely C. neither unlikely nor likely D. not likely
The correct answer is choice (C) neither unlikely nor likely. The number of each color of marbles is equal, so each color is equally likely to be chosen.
300
Consider the expression 6r – r + 8(15 – r) + 23 – 6. Part A: Is –3r + 137 equivalent to the given expression? Part B: Explain how you determined whether the expressions are or are not equivalent.
Part A: yes Part B: Part B: I combined like terms in the given expression. The result was the expression in Part A. I also substituted the same value for the variable into both expressions and it always resulted in the same answer.
300
A satellite is 18 meters wide. A model of it was built with a scale of 1 centimeter:3 meters. How wide is the model?
What is 6 centimeters
300
What is the value of 4.2(46 – 65)?
What is -79.8
300
The supplementary angle of 78 degrees is?
What is 102 degrees.
300
A number cube with faces numbered 1 to 6 is rolled 15 times. In theory, how many times would you expect to roll a number less than 5?
10. For each roll, there is a 4 out of 6 chance of rolling a number less than 5, and 4/6 x 15 = 60/6 = 10
400
The sum of a number, n, and 8 is multiplied by –4, and the result is –12. What is the number?
What is -5
400
In three weeks, Raj's favorite store is having a sale on jeans. All jeans will be 50% off regular price. Raj also has a coupon that will give him 30% off his total purchase. "Yay, 80% off!" he exclaims. He wants to buy one pair of jeans that is regularly $50, one pair that is regularly $30, and one pair that is regularly $20. Raj calculated how much money, to the nearest dollar, he will need for his jeans and plans to save the same amount each of the next three weeks until he has enough for the jeans. His calculations are shown below: Regular price total: 50 + 30 + 20 = 100 I will pay 100% - 80% = 20% of the price. Total price after the discount = 100 x 0.20 = $20 Raj thinks he needs to save about $7 each week to have enough money in 3 weeks' time. Raj made a mistake when calculating how much money he will need to buy the jeans. Describe his mistake. Then, figure out how much he will need for the jeans and decide on a new savings plan. About how much will Raj need to save each week to be able to afford his jeans.
Raj added the percentages and took 80% off the regular price of the jeans. You can't just add the percentages. The amounts you're taking 50% off of aren't the same amounts you're taking 30% off of. Raj needs to first take 50% off the regular price of each item and then take 30% off that total. Take 50% off the regular price for each pair: 50% off of 50 =0.5 x 50 = 25 The discounted price is 50 - 25 = 25 50% off of 30 = 0.5 x 30 = 15 The discounted price is 30 - 15 = 15 50% off of 20 = 0.5 x 20 =10 The discounted price is 20 - 10 = 10 The discounted total is 25 + 15 + 10 = 50 Now take 30% off that total: 50 x 0.30 = 15 The final price is 50 - 15 = $35 Since Raj has 3 weeks to save, divide 35 by 3. 35/3 = 11.6 repeating Raj needs to save about $12 each week to have enough money to buy his jeans.
400
A football team loses 5 yards on each of 3 consecutive plays. Part A: What signed number represents the team’s total loss of yards on the 3 plays? Part B: Explain how you found your answer.
Part A: -15 yards Part B: I multiplied 3 times negative 5. I used a number line to show the multiplication by starting at 0 and moving 5 places to the left 3 times.
400
Use your own words to explain how to find the circumference of a circle if you know the radius or diameter of the circle.
If you know the radius of the circle, double it to find the diameter then multiply that number by 3.14.
400
Listed below are the quiz scores for randomly selected students in two seventh-grade classes. Class A: 99, 75, 84, 70, 86, 80 Class B: 85, 83, 87, 90, 85, 82 Part A: Based on the samples, which class generally has higher quiz scores? Part B: Use measures of center and/or variability to justify your answer.
Part A: Class B Part B: Class B has a higher mean score and a smaller range than Class A. Therefore, in general, Class B has higher scores.
500
Julie works Sunday, Monday, and Wednesday for 10 hours each day. On Tuesday, Thursday, and Friday, she works 7 hours each day. She does not work on Saturday. Her weekly total earnings are $612. Part A: What is her hourly rate of pay? $__________ Part B: Julie’s manager proposes a new pay rate. The manager says Julie can get paid twice her hourly rate for working any hours over 8 in a day. What would be her weekly earnings using this method of payment? Explain how you found her total earnings using this method. $__________ Part C: Julie thinks she can earn more money if she is paid 1 1/2 times her hourly rate for any hours over 40 in her weekly total. Which method of payment, Julie’s or her manager’s, would give Julie higher weekly earnings? Explain your reasoning.
Part A: 12 Part B: 684 [Manager’s method] Julie works a total of 51 hours a week. On 3 days she works more than 8 hours. On each of those days, she works for 10 hours, which makes a total of 6 extra hours each week. Twice her hourly rate is 24, so she would earn 144 dollars extra each week. She would earn 12 per hour for the other 45 hours, for a total of 540 dollars. So her weekly total is the sum of 540 and 144, which is 684. Part C: Manager’s method. Since Julie works 51 hours a week, then she works 11 extra hours and would earn 18 dollars per hour for each of those extra hours, for a total of 198 dollars. She would earn 12 per hour for her regular 40 hours, for a total of 480. So her weekly total is the sum of 480 and 198, which is 678.
500
The selling price of a house dropped from $250,000 to $210,000 over a period of 5 years. Part A: By what percent did the selling price decrease? Part B: Explain how you found your answer. Part C: By what percent does the price need to increase in order to return to its original value of $250,000? Part D: Explain how you found your answer.
Part A: 16% Part B: I subtracted the new price from the original price and divided the difference by the original price. Then I multiplied the decimal product by 100 and removed the negative sign to write the percent decrease. Part C: approximately 19% Part D: I divided the difference in the two prices by the new price. Then I multiplied the decimal product by 100 to write the percent increase.
500
During one week, Sheila made several changes to her bank account. She made four withdrawals of $40 each from an ATM. She also used her check card for a $156 purchase. Then she deposited her paycheck of $375. By how much did the amount in her bank account change during that week?
What is a $59 increase
500
A circular dining room table has a radius of 3 feet. If each person sitting at the table needs about 2 feet of space, how any people will fit at the table?
What is about 9 people. You should find the circumference of a table with a radius of 3 feet, and then divide by 2 feet per person.
500
The six sides of a number cube are labeled 1, 2, 3, 4, 5, and 6. You flip a coin and roll the number cube. In theory, what is the probability that the coin lands on heads and you roll a number greater than 4?
1/6 because there are 12 possible outcomes: 2/6 numbers are greater than 4 on the number cube. There is a 1/2 chance that a coin will land on heads. Therefore the probability is 2/12 (2/6 x 1/2) which is equivalent to 1/6.