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Algebra 1 Team Round Answer Sheet + Solutions
1. Since you know that the number consists of four digits, and the first two
digits are odd consecutive numbers you can write down what you know.
1 3 _ _
3 5 _ _
5 7 _ _
7 9 _ _
Then since you know that the third digit is the sum of the first two digits
you could plug in the possible third digit numbers. Since when you add 5
and 7 or 7 and 9 the sum is not a single digit you can exclude those two
possibilities.
1 3 4 _
3 5 8 _
5 7 12 _
7 9 16 _
Finally the sum of the last digit and first digit is equal to two plus the
second digit. Since no numbers are supposed to repeat 3,584 is Abby’s
favorite number.
1 3 4 4
3 5 84
A: The third digit in this number is 8.
B: 3x5=15
C: The last digit is 4.
D: 8x15=120 120-4=116.
2. 3x+7y=421
4y-56=x
First you would move the x over to the left of the equals sign and add the
56 over in the second equation. Then you would multiply the second
equation by three in order to cancel out the x. When you add the two
equations together you are left with:
3x+7y=421
+ -3x+12y=168
19y=589
Then divide 589 by 19 so you find that y is 31.
Once you have discovered what y equals you can plug it back into any
equation to solve for x. 4(31) – 56=68 Thus x is equal to 68.
A: The value of x is 68
B: The value of y is 31
C: 68x31=2108
D: 2108÷31=68 68+68= 136
3.
A.
Plug back in to get y -16+32+16=32
B.
C. 33.3% of 108 is 108/3=36
D. 16
4. A 3/2.
B
-145
C-44.
-44
D
5. For this question you have to use the distance formula. Distance = Rate x
Time. Also you must demonstrate that you are familiar with converting
from hours to minuets and vice versa.
A: Distance / Time = Rate
15 mins/60 mins= .25 hour
240,000m/.25hr = 960,000 mph
B: Distance / Rate = Time
240,000m/60,000mph = 4 hr
C:Distance = Rate x Time 10/60 = 1/6 (1/6)hr x 70,000 mph = 35,000/3
D: 2.4 x 10^5
6. A. Substitute 3 into the g(x) function = 3/2.
B. Substitute 3 into the f(x) function = 27
C. First substitute 1 into the f(x) function =3. Then plug in 3 into the g(x)
function = 3/2
D. First substitute 0 into the g(x) function = 1/3. Then substitute 0 into the
f(x) function = 1. Add those values 1 + 1/3 = 4/3.
7. A. By adding the two equations, x can be found. X = 7/8
B. By substituting the x value, y can be found. Y = 5/16
C. Slopes can be found by rearranging the equation into y = mx + b form.
The slope of the top equation = -½. The slope of the bottom equation = ½,
so the sum is 0.
D. 7/8 * 5/16 +0 = 35/128+0 = 35/128
8. A mode means number that occurs most 86
B. median is the middle value 78
C.(37+53+60+78+86+86+90)/7= 490/7= 70
D. (37+53+60+78+86+86+90+x)/8=65 520=490+x x=30
9. Here we go!
A. 3x-1=-2x+7 5x=8 x=8/5 Then we will use substitution to get the y
coordinate. 3(8/5)-1=19/5. The sum is 27/5.
B. Using midpoint formula, the midpoint is (-9,5), so the product is -45.
C. The change from (-8,11) to (-1,3) is 7 in the x direction, so -1+7 = 6.
The change in the y direction is -8, so 3-8= -5. (6,-5)
D. Using the slope formula, m = -3/7. y-1 = (-3/7)(x+3)
10. A=-12/5 from when you substitute in y = 0 into the equation.
B= 5(-3)+12= -3
C= 5 is the coefficient of the x term in the equation when in slope-intercept
form
D= -1/5 Negative Reciprocal
11. A= 2+3+5+7+11+13+17+19+23+29+31+37= 197
B= 180- (110+40) = 30 → 30=3x+2 → 28/3
C= -7-6-5-4-3-2-1+1+2+3+4+5+6+7= 0
D= Four repeats in a cycle of 4, 6, 4, → 4
12.
A
14
B
C.
D
13
A -7/3. Easiest way is to put it in slope intercept form
B 5/7. To get x intercept set y=0 and solve for x
C y=
. To get this form solve for y
D 3/7. It is the opposite reciprocal to the original slope
14. A=3(1-2) =-3
B=64– (-2)) = 66
C= 1(3+2) +5= 10
D= -2-2+3= -1
6
15
This all numbers up to the one that they ask for.
A: 2,4,6,8,10,12
B: 0,1,2,3,4,5,6,7
C: 4,6,8,9,10,12,14,15,16,18,20
D: 2,3,5,7,11,13,17
16
You have to use order of operations on this problem. Parentheses,
Exponent, Multiply, Divide, Add, Subtract.
Answer=
A: The number in the denominator is 47
B: The number in the numerator is 271
C: The number that is repeated is 7
D: 271 + 7 – 47 = 231