Santa Cruz County Math Contest
Grades 7 & 8 INDIVIDUAL
1. Solve |2x -4|
1. -1<x<5
< 6
2. Solve 3x = 4y – 6 for y.
2. y = 3/4x + 3/2
3. Half of a third of a number is 18.
3. 108
4.
Simplify
What is the number?
0 3 0
-4
3
5. What is the value of the expression:
5. 1/7
4. -9/4
1/7 x 2/5 + 1/7 x 3/5?
6. If 180% of a number is equal to 210% of 54, what is the number?
6. 63
7.
Solve for a: 2(a) + 2 + 3(a) + 3 = 40
7. a = 7
8. You fill a jug with water to ½ of its capacity. You then remove 1/3 of the water. You are left
with 0.5 gallons of water. What is the capacity of the jug in gallons?
8. 3 gallons
9.
Solve for x when 4x = the reciprocal of 1
x3
9. X = 2
10. Evaluate (2/3)3
10. 8/27
11. What is the difference between 5/6 and its reciprocal?
11. 11/30
12. Replace letters with correct digits.
MATH + ATH + TH + H = 2010
12. M = 1
A =4
T= 7
H=0
13. How many integers satisfy?
l 2x – 5l < 9
13. 8
14. The sum of three consecutive integers is 21, find the middle integer.
14. 7
15. Evaluate
16. Evaluate:
16. 12x
1 + 1 + 1_
x y xy
15. x + y + 1
xy
or x/xy + y/xy + 1/xy
[(x + 1)2 + (x + 2)2 +(x + 3)2] – [(x2 + 12) + (x2 + 22) + (x2 + 32)]
17. The total value of 2x nickels and x dimes is $.60 when x = what number?
17. x = 3
18. The graph of which equation is parallel to the graph of 2x + y = -3
A) 2x + y = 3
B) 2 x + 4 y = 6
C) 2 x – y = 3
D) x + 2y = -3
18. A
19.
Evaluate |x| + |-x|
19. 2 lxl
20. Express as a simple fraction.
______1__________
2 + __1____
2+
21. If |a-3| + |b -4| = 0, find a2 – b2.
21. -7
½
20. 5/12
22. Assume a = 5 and b = 7, find the value of: a7b-8(a-4b5)2
22. 49/5
23. If x2 < 16, what is the sum of all the positive integers that satisfy the inequality?
23. 10
24. If my mom is 38 and my dad is 44, after how many years will the sum of their ages equal 100?
24. 9 years
25. Factor: 6a2 + 7ab – 10b2
25. (6a-5b) (a+2b)