Practice for the MIDTERM Test
Express each as an algebraic expression:
1. subract 7 from X
2. subtyract X from 7
3. Four times V minus 12
4. Divide X by the product of 25 and Y
5. incease A by the square of B
Substitute the given numbers for the variables and compute the value of each expression. Round your answer to two decimal
places if needed. e = 8 and f = 4
1. 3ef + 9
2. 5f + ef
3. 5e + f(e/4)
4. (10e  6f)/8
5. 12e /(2f + 2)
Perform the operations indicated:
1. 37  (31)
2. (3)(3)(3)
3. 24/(3)
4. (21)/(7)
5. (4)^2
6. (4)^3
7. [6(9+3)]/[7(116)5]
Simplify each expression:
1. 5x  6x  x  8x
2. (5a + 6b) + (4a + 8b)
3. (6R  5R^2)  (4R  8R^2)
4. (12a)(5a^2)
5. 5x^2(x + x^2y)
6. (16y^2)/8y
Solve each equation:
1. m + 7 = 22
2. y  7 = 20
3. 5x = 55
4. (1/2)E = 6
5. 12X  9 = 39
6. 18/(x+7) = 10
7. 4x  7 = x + 14
Solve the following system of equations using substitution:
6x + 5y = 13
3x + 4y = 14
WORD PROBLEMS
1. The area of a triangle is onehalf the product of the base(b)and the height(h). Write the formula for area (A) as an
algebraic sentence. If the base=2x+1 and the height=x+5, write an expression for the area.
2. Use the Pythagorean Theorem to solve the following:
A carpenter is completing the corner of a room/ He wants to make sure his corner is square or 90 degrees. A 6 ft length
is marked on one wall. An 8 ft length is marked on the other wall. What should be the measurement length between the two
marks?
3. Use a proportion to solve the following:
A machine produces 280 pieces in 3.5 hours. How long does it take to produce a run of 720 pieces?
A tank 6 meters high contains 7200 gallons of water when full. How many gallons of water does it contain when the water
is 2 meters high?
4. Use the quadratic formula to solve the following:
One side of a window is four less than the length of the other side. Three times the product of their lengths is 231.
Find both numbers.
(Hint: Use substitution to write a quadratic equation in the form ax^2+bx+c=0. Determine a, b, and c. Substitute these
values into the quadratic formula and solve.)
[b +/ SQRT(b^24ac)]/2a
