Operations with Rational Numbers
Geometry
Two Step equations, Inequalities, Variables on both sides
Probablity
Ratios and Scales
100
What is 8 + (-11)
-3
Explanation if you got it wrong: Remember when you add a positive number with a negative number you have to subtract the larger number by the smaller number and then keep the sign of the larger number. In this case, since 11 >8, the larger number is 11. So we do 11- 8 which equals 3 and since 11 is negative, our answer becomes negative as well. Thus -3 :D
100
What is the area of a rectangle that has a length of 6.3in and a width of 2in?
12.6
Explanation if you got it wrong: Area of rectangle = length * width
100
Solve for x: 2x + 4 = 6
x = 1
Explanation if you got it wrong: Remember when you have equations, inequalities, or anythiing of the sort, you always solve for the variable by doing inverse operations. Also, this is important, you always do the backwards of PEMDAS, or SADMEP, when you move numbers around. So 2x + 4 =6, you do the inverse operation of the addition that is happening to x first, thus you subtract 4 from both sides. Then you have 2x = 2, then its a one step equation, do the inverse operation which is division by 2 on both sides, and you get x= 1
100
What is the theorethical probability of landing on heads when you flip a coin?
50% or 1/2
Explanation if you got it wrong: Since there are two possible outcomes, and we only want one of those outcomes, we have P(heads) =favorable outcomes/ total outcomes = 1/2 or 50% if you convert it into a percent.
100
3 apples cost $1.50, how much does 1 apple cost?
0.50 cents
Explanation if you got it wrong: This is a unit rate problem which means they are asking Cost of apples /total number of apples. Your ratio is 3:1.50 or 3/1.50. If they are asking for the cost of 1 apple your equivalent ratio/fraction is x cost/ 1 apple and then you solve for x or if you do it logically, 3/1.50 :D
200
What is -0.5 * 4
-2
Explanation if you got it wrong: A negative times a positive is always negative and 0.5 * 4 = 2, thus our answer is -2 :D
200
What is the base shape of a triangular prism?
Triangle
Explanation if you got it wrong: The base shape of a prism is the shape that is getting extended. To make it easy though, looking at any prism, they always have an additional name that tells us the base. For example, in trapezoidal prism, the word trapezoidal tells us the base is a trapezoid.
200
Solve for y: -3y ≤ 9
y≥3
Explanation if you got it wrong: Treat inequalties similar to equations with some rules. So if you solved for y by using inverse operations you would divide both sides by the coefficient in front of y which is -3. So you would have y ≤ -3 but now the addiational rule with inequalities is that if you multiply or divide by a negative number like -3, you have to FLIP the sign. Thus your answer is y ≥ -3.
200
B. 3/8
Explanation if you got it wrong: Since there are 3 favorable outcomes and 8 outcomes in total, the probablity is 3/8
200
2 cups of flour make 48 cookies. How many cookies does 3 cups of flour make.
72 cookies
Explanation: ratio is 2 cups : 48 cookies or 2cups /48 cookies. If you simplify it you would get 1 cup:24 cookies or 1 cup/24 cookies . Thus if 1 cup makes 24 cookies, 3 cups makes 72.
300
What is -10/3 - 3/5
-59/15 or -3 and 14/15
Explanation if you got it wrong: This one is hard to explain in writing but read carefully; When you are subtracting a negative number by a positive number, you are really just adding two negative numbers. Thus if you were to rewrite your expression as -10/3 + -3/5, you can just act like you are adding the positive values of those two fractions and then add the negative sign at the end. If you forgot how to add fractions, please review this.
300
What is volume of a rectangular prism that has a length of 3 and 1/2, a width of 4, and a height of 2
28
Explanation if you got it wrong: Volume of a Rectangular Prism =l*w*h
300
Solve for t: -2t + 3 ≥ 9
t≤ -3
Explanation if you got it wrong: This one combines both two step equations and inequaltes with those speical rules from the ones before. You do inverse operations on both sides of the inequality sign following backwards PEMDAS aka SADMEP. Since x is getting added by 3 and multiplied by -2, and you are following SADMEP,addition comes before multiplication, and so the inverse operation is subtracting 3. Thus your inequality is -2t ≥ 6. Then you divide by -2 and get t≥ -3 BUT remember if you divide an inequality by negative numbers you have to FLIP the sign. Thus your answer is t≤-3
300
Mr.Rana spins the spinner 6 times and gets the following outcomes. 2 blue, 1 red, 0 yellow, and 3 green
Which of these are not true?
a) The theoretical probablity of landing on green is 1/4
b) The experimental probablity of landing on green or yellow is 4/6
c) The experimental probablity of landing on blue is 2/6
d)The theoretical probablity of landing on green,yellow, or blue is 3/4
b)The experimental probablity of landing on green or yellow is 4/6
Explanation: Since experimental probablity is favorable outcomes/ total outcomes, and in the experiment we got 3 green and 0 yellows, the amount of favorable outcomes we got were 3, and since we did the experiement 6 times, we have 3/6 as the experimental probabilty.
300
Which is the better buy?
a) 12 pencils for $2
b) 15 pencils for $2.50
c) 19 pencils for $3
c) 19 pencils for $3
Explanation: Find the unit rate for each one. To do so, divide the number of pencils by the cost and the one where you pay the least per pencil is your answer.
400
Using the distributive property, what is the expression -10(3 + 5) after you distribute? Hint: you should have two terms in the expression.
-30 - 50 or -30 + -50
Explanation if you got it wrong: If you forgot what the distributive property is, it is when you have a number outside of parentheses you can "distribute" it into the parentheses by multiplying it by each term inside. For example, in this problem, since -10 is outside next to the parentheses, you can"distribute" it to 3 and 5. Thus it would become -10(3) + -10(5) which is equal to -30 +-50 or -30 -50 :D
400
What is the formula to calculate the surface area of a cube?
6*s2
Explanation if you got it wrong: A cube is made up of 6 equal squares. The area around one of these squares is equal to s2. Now, the surface area is the total sum of the areas of each shape that makes up the 3d shape. Now since the cube is made up of 6 equal squares, all the areas of the squares are s2. Thus, the surface area of the cube is equal to s2+s2+s2+s2+s2+s2 and repeated addition is multiplication we can further simplify it into 6s2
400
3x + 6 = -2x -4
x = -2
Explanation if you got it wrong: When you have variables on both sides of the equal sign, my piece of advice is to pick one side and move your variables to that side. Now on the other side, move all your constants. So for this problem, I am going to pick the left side for my variables, now you can pick any side you want, BUT another piece of advice: if you have a negative variable on one side, you should move that to the other side. So if I want to move my variables to the left side I have to add (because -2x is negative) 2x to both sides which means my equation becomes 5x + 6 = -4, then you move the constant from the left side which is +6 to the right side by doing its inverse operation (subtract 6) to both sides. Thus your new equation is 5x = -10. Then its just a simple one step equation, using inverse operations by dividing by 5 to both sides and you get x = -2 :D
400
What is the difference between theoretical probablity and experimental probablity?
Ans: Theoretical is what is expetected to happen based on math vs Experimental is what actaully happens during an experiment
400
The empire state building is about 1400 ft tall. If I were to use a scale of 1in:70ft to draw a scale drawing. How tall would the scale drawing have to be?
20in tall
Explanation: Since the scale is 1in = 70ft, My proportion is 1in/70ft = x/1400ft, and when you solve for x you would get 20ft.
500
Use PEMDAS: (-102 + 12) * (-1)(3 + ( 1+ 1) * 2)
-784
Explanation if you got it wrong: Be careful when you use PEMDAS. The first thing you should have done is work inside the first parentheses which were (-102 + 12). In there, you should have done -102 first since Exponets come before Addition. So you would have 100 + 12 which then you do the addition so it is 112. Next,you would look at your new expression which is now
112 *(-1)(3 + ( 1+ 1) * 2). Now when you have a number like (-1) you can just ignore it for a bit since all that is doing saying we have to multiply by -1, so you would use PEMDAS again this time since there are parentheses around 3 + ( 1+ 1) * 2, that is what you solve. Using PEMDAS with 3 + ( 1+ 1) * 2, you do the parentheses first which in this case is just 1+1 = 2, so you have 3 + 2 *2 and since M comes before A, you multiply 2*2 before adding 3 which would give you 7 inside that parentheses.Your expression is now looking like 112*-1*7 = -784 :D
500
Ms.Annunziata took Blue Angel for a walk around a circular path. The distance between the path and the center is 3km. What is the distance they walked around the circular path? Remember that pi = 3.14 :)
18.84km
Explanation if you got it wrong: Since the path is circular and the question asked for you to calculate the distance they walked around the circular path which is circumference, you have to use the formula C= 2*∏* r. Since the distance between the path and the center is 3km, your radius(remember the definition of radius) is 3. Therefore, C= 2 * 3.14 * 3 = 18.84km
500
6 - 4x ≤ 10x + 6
x ≤ 0
Explanation:This combines everything from the previous ones in this category. Move the variable to one side and the constant to the other. To do so, you use inverse operations and SADMEP, the opposite of PEMDAS,AND pick a side of the inequality that you want to move the variables and the opposite side gets the constants. Thus if I pick the left side of the inequality for my variables, all the variables on the right side have to move to the left. To do so, I am going to do the inverse operation of the right side variable to both sides of the inequality.In this case, since it is +10x(the plus is invincible),I am going to -10x from both sides. Thus I have 6 - 14x ≤ 6 after I subtract 10x from both sides. Then I will move my constant(s) from the left side to the right, in this case +6 is my constant on the left side. Thus the inverse operation that I do to both sides of the inequality sign is to subtract 6. My new inequality is now -14x≤ 0. Finally, the last step is to divide by -14 to both sides since x is getting multiplied by it. Thus you have x≤ 0.Most importantly,since you divided by a negative number during a inequality, you have to FLIP the sign. Thus your final answer is x≥0
500
Grace is trying to make an outfit that includes a pair of pants, a hat, a t-shirt, and a pair of shoes. She has 3 hats, 6 t-shirts, and 2 pairs of shoes. If she can make 180 different combinations of outfits, how many pairs of pants does she have?
5 pairs of pants
Explanation if you got it wrong: Since She has 3 hats, 6 t-shirts, and 2 pairs of shoes. That is 3*6*2 combinations so far which is equal to 36. Then since there are 180 total combinations, you would divide 180 by 36 and get 5.
500
Quincy measured a house and made a scale drawing. The living room, which is 4 meters long in real life, is 2 millimeters long in the drawing. What is the scale of the drawing?
1 mm = x meters
2 meters