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Algebra 4th Grade
1. For what value of x is the following equation true? 8 =
9+ x
3
2. If the sum of 4 consecutive even integers is 276, what is the largest of those integers?
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3. A mystery number is increased by 6, then tripled, then doubled twice, resulting in the number 168.
What is the mystery number?
4. Write an equation in y = mx + b form for the following table:
x
– 14
–6
0
2
y
– 86
– 62
– 44
– 38
5. What is the next number in this sequence:
10
– 14
18
10
2, 6, 18, 54, _____
6. Ben wanted his Valentine’s Day candy to last as long as possible. On the first day after Valentine’s
Day, he ate half of the candies he had. On the second day, he ate one-fourth of what he had left. On day 3,
he had 24 candies left. How many candies did he start with?
7. If θ = 4 + 5 + 6 + … + 14 + 15, and ψ = 5 + 6 + 7 + … + 15 + 16, what is ψ – θ?
8. If a + b = 15, b + c = 15 and c + d = 15, what is a + d?
9. Abby’s friend says that the number of squares in this sequence is 1, 4, 9, and so the next one should be
16. Abby, on the other hand, says that there are 5 squares in the second figure, and 14 in the third.
According to Abby, how many squares will be in the next figure?
10. If 4♠8 = 2, 3♠9 = 3, 5♠5 = 0 and 7♠11 = 2, what is 6♠16?
Algebra 5th Grade
1. A mystery number is increased by 6, then tripled, then doubled twice, resulting in the number 168.
What is the mystery number?
2. Write an equation in y = mx + b form for the following table:
x
– 14
–6
0
2
y
– 86
– 62
– 44
– 38
3. What is the next number in this sequence:
10
– 14
18
10
2, 6, 18, 54, _____
4. Ben wanted his Valentine’s Day candy to last as long as possible. On the first day after Valentine’s
Day, he ate half of the candies he had. On the second day, he ate one-fourth of what he had left. On day 3,
he had 24 candies left. How many candies did he start with?
5. If θ = 4 + 5 + 6 + … + 14 + 15, and ψ = 5 + 6 + 7 + … + 15 + 16, what is ψ – θ?
6. If a + b = 15, b + c = 15 and c + d = 15, what is a + d?
7. Abby’s friend says that the number of squares in this sequence is 1, 4, 9, and so the next one should be
16. Abby, on the other hand, says that there are 5 squares in the second figure, and 14 in the third.
According to Abby, how many squares will be in the next figure?
8. If 4♠8 = 2, 3♠9 = 3, 5♠5 = 0 and 7♠11 = 2, what is 6♠16?
9. Express 122103 as a base ten number.
10. The first 4 designs are shown below. How many *’s will there be in the 10th figure?
*
**
***
****
****
*****
******
**
*******
********
*****
**********
***
********
******
****
Algebra 6th Grade
1. What is the next number in this sequence:
2, 6, 18, 54, _____
2. Ben wanted his Valentine’s Day candy to last as long as possible. On the first day after Valentine’s
Day, he ate half of the candies he had. On the second day, he ate one-fourth of what he had left. On day 3,
he had 24 candies left. How many candies did he start with?
3. If θ = 4 + 5 + 6 + … + 14 + 15, and ψ = 5 + 6 + 7 + … + 15 + 16, what is ψ – θ?
4. If a + b = 15, b + c = 15 and c + d = 15, what is a + d?
5. Abby’s friend says that the number of squares in this sequence is 1, 4, 9, and so the next one should be
16. Abby, on the other hand, says that there are 5 squares in the second figure, and 14 in the third.
According to Abby, how many squares will be in the next figure?
6. If 4♠8 = 2, 3♠9 = 3, 5♠5 = 0 and 7♠11 = 2, what is 6♠16?
7. Express 122103 as a base ten number.
8. The first 4 designs are shown below. How many *’s will there be in the 10th figure?
*
**
***
****
****
*****
******
**
*******
********
*****
**********
***
********
******
****
9. Xena started with the number googol (1 with a 100 zeros after it). She multiplied it by 8, then added 8
to the result. She then squared that number, and divided what she got by 1 more than a googol. She then
divided by 8, and divided by 8 again, and subtracted a googol from her result. What is her final result?
10. What is the sum of the first 100 odd numbers?
Algebra 7th Grade
1. If θ = 4 + 5 + 6 + … + 14 + 15, and ψ = 5 + 6 + 7 + … + 15 + 16, what is ψ – θ?
2. If a + b = 15, b + c = 15 and c + d = 15, what is a + d?
3. Abby’s friend says that the number of squares in this sequence is 1, 4, 9, and so the next one should be
16. Abby, on the other hand, says that there are 5 squares in the second figure, and 14 in the third.
According to Abby, how many squares will be in the next figure?
4. If 4♠8 = 2, 3♠9 = 3, 5♠5 = 0 and 7♠11 = 2, what is 6♠16?
5. Express 122103 as a base ten number.
6. The first 4 designs are shown below. How many *’s will there be in the 10th figure?
*
**
***
****
****
*****
******
**
*******
********
*****
**********
***
********
******
****
7. Xena started with the number googol (1 with a 100 zeros after it). She multiplied it by 8, then added 8
to the result. She then squared that number, and divided what she got by 1 more than a googol. She then
divided by 8, and divided by 8 again, and subtracted a googol from her result. What is her final result?
8. What is the sum of the first 100 odd numbers?
9. What is the integer value for the infinite square root:
10. |x|3 < 70 has how many integral solutions?
€
6 + 6 + 6 + 6 + ...
Algebra 8th Grade
1. If θ = 4 + 5 + 6 + … + 14 + 15, and ψ = 5 + 6 + 7 + … + 15 + 16, what is ψ – θ?
2. If a + b = 15, b + c = 15 and c + d = 15, what is a + d?
3. Abby’s friend says that the number of squares in this sequence is 1, 4, 9, and so the next one should be
16. Abby, on the other hand, says that there are 5 squares in the second figure, and 14 in the third.
According to Abby, how many squares will be in the next figure?
4. If 4♠8 = 2, 3♠9 = 3, 5♠5 = 0 and 7♠11 = 2, what is 6♠16?
5. Express 122103 as a base ten number.
6. The first 4 designs are shown below. How many *’s will there be in the 10th figure?
*
**
***
****
****
*****
******
**
*******
********
*****
**********
***
********
******
****
7. Xena started with the number googol (1 with a 100 zeros after it). She multiplied it by 8, then added 8
to the result. She then squared that number, and divided what she got by 1 more than a googol. She then
divided by 8, and divided by 8 again, and subtracted a googol from her result. What is her final result?
8. What is the sum of the first 100 odd numbers?
9. What is the integer value for the infinite square root:
10. |x|3 < 70 has how many integral solutions?
€
6 + 6 + 6 + 6 + ...