Numbers and operations
Functions
Geometry and Measurement
Statistics and Probability
Algebra
100
Here is a students work on several multiplication problems:
For which of the following problems is this student most likely to get the correct solution, even though he is using an incorrect algorithm?
A
58 x 22
B
16 x 24
C
31 x 23
D
141 x 32
31x23. This is the answer because if you look at the students work sample you can see they were doing the multiplication wrong. To solve this problem you must find the correct answer then do the same way the student did it.
100
There are 15 students for every teacher. Let t represent the number of teachers and let s represent the number of students. Which of the following equations is correct?
A. t=s+15
B. s=t+15
C. t=15s
D. s=15t
D. s=15t 15 teachers for ever student is represent by 15t
100
The polygon depicted below is drawn on dot paper, with the dots spaced 1 unit apart. What is the perimeter of the polygon?
A. 18+√‾2 units
B. 18+2√‾2 units
C. 18 units
D. 20 units
B. Make rectangles and squares out of units to make it easier to count.
100
Four children randomly line up, single file. What is the probability that they are in height order, with the shortest child in front? All of the children are different heights.
A. 1/4
B. 1/256
C. 1/16
D. 1/24
D. The number of ways for the children to line up is 4!=4×3×2×1=244!=4×3×2×1=24 -- there are 4 choices for who is first in line, then 3 for who is second, etc. Only one of these lines has the children in the order specified. For more information on how to solve look up combinations and permutations.
100
Here is a number trick:
1) Pick a whole number
2) Double your number.
3) Add 20 to the above result.
4) Multiply the above by 5
5) Subtract 100
6) Divide by 10
The result is always the number that you started with! Suppose you start by picking N. Which of the equations below best demonstrates that the result after Step 6 is also N?
A. N∗2+20∗5−100÷10=N
B. ((2∗N+20)∗5−100)÷10=N
C.(N+N+20)∗5−100÷10=N
D. (((N÷10)−100)∗5+20)∗2=N
B.
200
The expression 83⋅2-10 is equal to which of the following?
A. 2
B. 1/2
C.16
D. 1/16
B. 1/2 . First you gotta convert 83 into (23)3. Next multiply your exponents together to get 29x2-10 the next step is to add the exponents together to get 2-1. Anytime you have a negative exponent look at it as 1/n so thats where 1/2 came from
200
A publisher prints a series of books with covers made of identical material and using the same thickness of paper for each page. The covers of the book together are 0.4 cm thick, and 125 pieces of the paper used together are 1 cm thick.
The publisher uses a linear function to determine the total thickness, T(n) of a book made with n sheets of paper. What are the slope and intercept of T(n)?
A. Intercept = 0.4 cm, Slope = 125 cm/page
B. Intercept =0.4 cm, Slope = 1/125cm/page
C. Intercept = 125 cm, Slope = 0.4 cm
D. Intercept = 1/125cm, Slope = 0.4 pages/cm
B. Intercept =0.4 cm, Slope = 1/125cm/page
The intercept is how thick the book would be with no pages in it. The slope is how much 1 extra page adds to the thickness of the book.
200
What is the mathematical name of the three-dimensional polyhedron depicted below?
A. Tetrahedron
B. Triangular Prism
C. Triangular Pyramid
D. Trigon
B.
200
At a school fundraising event, people can buy a ticket to spin a spinner like the one below. The region that the spinner lands in tells which, if any, prize the person wins.
If 240 people buy tickets to spin the spinner, what is the best estimate of the number of keychains that will be given away?
A.40
B. 80
C. 100
D. 120
B. The probability of getting a keychain is 1/3, and so about 1/3 of the time the spinner will win.
200
Here is a student€™s work solving an equation:
x−4=−2x+6
x−4+4=−2x+6+4
x=−2x+10
x−2x=10
x=10
Which of the following statements is true?
A. The student‘s solution is correct.
B. The student did not correctly use properties of equality.
C. The student did not correctly use the distributive property.
D. The student did not correctly use the commutative property.
B. After x=−2x+10, the student subtracted 2x on the left and added 2x on the right.
300
Which of the following is equivalent to 3/4−1/8+2/8×1/2?
A. 7/16
B.1/2
C. 3/4
D. 3/16
3/4. Follow PEMDAS
300
Which of the following is the equation of a linear function?
A. y=x2+2x+7
B. y=22
C. y=15/x
D. y=x+(x+4)
D. This is a linear function, y=2x+4, it's graph is a straight line with slope 2 and y-intercept 4.
300
Which of the following is not possible?
A. An equiangular triangle that is not equilateral.
B. An equiangular quadrilateral that is not equilateral.
C. An equilateral quadrilateral that is not equiangular.
D. An equiangular hexagon that is not equilateral.
A.
300
The first histogram shows the average life expectancies for women in different countries in Africa in 1998; the second histogram gives similar data for Europe:
How much bigger is the range of the data for Africa than the range of the data for Europe?
A. 0 years
B. 12 years
C. 18 years
D. 42 years
C. It's a little hard to read the graph, but it doesn't matter if you're consistent. It looks like the range for Africa is 80-38= 42 years and for Europe is 88-64 = 24; 42-24=18.
300
Use the solution procedure below to answer the question that follows:
(x+3)2=10
(x+3)(x+3)=10
x2+9=10
x2+9−9=10−9
x2=1
x=1 or x=−1
Which of the following is incorrect in the procedure shown above?
A. The commutative property is used incorrectly.
B. The associative property is used incorrectly.
C. Order of operations is done incorrectly.
D. The distributive property is used incorrectly.
D. (x+3)(x+3)=x(x+3)+3(x+3)(x+3)(x+3)=x(x+3)+3(x+3)=x2+3x+3x+9.
400
A solution requires 4 ml of saline for every 7 ml of medicine. How much saline would be required for 50 ml of medicine?
A.28 4/7 ml
B. 28 1/4 ml
C. 28 1/7 ml
D. 87.5 ml
A. 28 2/7. set up a proportion. 4/7 x x/50
400
The equation F=9/5C+32 is used to convert a temperature measured in Celsius to the equivalent Farentheit temperature.
A patient's temperature increased by 1.5° Celcius. By how many degrees Fahrenheit did her temperature increase?
A. 1.5°
B. 1.8°
C. 2.7°
D. Not enough information.
c. Each degree increase in Celsius corresponds to a 9/5=1.8 degree increase in Fahrenheit. Thus the increase is 1.8+0.9=2.7.
400
Which of the following nets will not fold into a cube?
A
B
C
D
B.
400
The table below gives the result of a survey at a college, asking students whether they were residents or commuters:
Based on the above data, what is the probability that a randomly chosen commuter student is a junior or a senior?
A. 34/43
B. 34/71
C. 34/147
D. 71/147
A. 34/43
400
Some children explored the diagonals in 2 x 2 squares on pages of a calendar (where all four squares have numbers in them). They conjectured that the sum of the diagonals is always equal; in the example below, 8+16=9+15.
Which of the equations below could best be used to explain why the children€™s conjecture is correct?
A. 8x+16x=9x+15x
B. x+(x+2)=(x+1)+(x+1)
C. x+(x+8)=(x+1)+(x+7)
D. x+8+16=x+9+15
C. x is the number in the top left square, x+8 is one below and to the right, x+1 is to the right of x, and x+7 is below x.
500
Here is a method that a student used for subtraction:
Which of the following is correct?
A. The student used a method that worked for this problem and can be generalized to any subtraction problem.
B. The student used a method that worked for this problem and that will work for any subtraction problem that only requires one regrouping; it will not work if more regrouping is required.
C. The student used a method that worked for this problem and will work for all three-digit subtraction problems, but will not work for larger problems.
D. The student used a method that does not work. The student made two mistakes that cancelled each other out and was lucky to get the right answer for this problem.
A. Try using this method to do another subtraction problem and it would still work.
500
Use the graph below to answer the question that follows:
The graph above represents the equation 3x+Ay=B, where A and B are integers. What are the values of A and B?
A. A=−2,B=6
B. A=2,B=6
C. A=−1.5,B=−3
D. A=2,B=−3
A. Plug in (2,0) to get B=6, then plug in (0,-3) to get A=-2.
500
In the triangle below, line segment AC≅AD≅DE and m∠CAD=100 degrees. What is m∠DAE?
A. 20
B. 25
C. 30
D.40
A. Angles ACD and ADC are congruent since they are base angles of an isosceles triangle. Since the angles of a triangle sum to 180, they sum to 80, and they are 40 deg each. Thus angle ADE is 140 deg, since it makes a straight line with angle ADC. Angles DAE and DEA are base angles of an isosceles triangle and thus congruent-- they sum to 40 deg, so are 20 deg each.
500
The chart below gives percentiles for the number of sit-ups that boys of various ages can do in 60 seconds (source , June 24, 2011)
Which of the following statements can be inferred from the above chart?
A. 95% of 12 year old boys can do 56 sit-ups in 60 seconds.
B. At most 25% of 7 year old boys can do 19 or more sit-ups in 60 seconds.
C. Half of all 13 year old boys can do less than 41 sit-ups in 60 seconds and half can do more than 41 sit-ups in 60 seconds.
D. At least 75% of 16 year old boys can only do 51 or fewer sit-ups in 60 seconds.
D. The "at least" is necessary due to duplicates. Suppose the data were 10, 20, 51, 51. The 75th percentile is 51, but 100% of the boys can only do 51 or fewer situps
500
Taxicab fares in Boston (Spring 2012) are $2.60 for the first 1/7 of a mile or less and $0.40 for each 1/7 of a mile after that.
Let d represent the distance a passenger travels in miles (with d>17). Which of the following expressions represents the total fare?
A. $2.60+$0.40d
B. $2.60+$0.40(d/7)
C. $2.20+$2.80d
D. $2.60+$2.80d
c. You can think of the fare as $2.20 to enter the cab, and then $0.40 for each 1/7 of a mile, including the first 1/7 of a mile (or $2.80 per mile).
Alternatively, you pay $2.60 for the first 1/7 of a mile, and then $2.80 per mile for d-1/7 miles. The total is 2.60+2.80(d-1/7) = 2.60+ 2.80d -.40 = 2.20+2.80d.