1i) Find three consecutive integers whose sum is equal to 126.
1g) A car has a gas tank with a 12-gal capacity. The tank is filled with gas priced at $1.20 per gallon, and the total price for the fill-up is $13.44. Was the tank empty before the fill-up? If not, how much gas was in the tank? Work with a friend. Set up the equation(s) and have your friend solve the equation(s).
2i) Find the length of a diagonal of a square whose sides are cm long.
2g) Work with a friend. Together, draw a picture and set up an equation to solve the following: A 17-ft ladder is leaning against your house. The bottom of the ladder is 8 ft from the house. Can you reach the window 14 ft above the ground?
3i) Find the slope and equation of a line that passes through the origin and the point (-3, 3). Check the box next to the correct answer.
a. slope: -1; equation: y = -xb. slope: 2; equation: y = 3x c. slope: 1; equation: y = 2x
3g) Work with a friend. Find the equation of the line that passes through the point (1, 1) and is parallel to the line y = 3x. Give your answer in slope-intercept form.
4i) Simplify . Check the box next to the correct answer.
a. b. c.
4g) Work with a friend. Find the equation of the line that passes through the point (1, 2) and is parallel to the line containing the points (2, 0) and (3,). Find the slope and have your friend write the equation in slope-intercept form.
5i) Rationalize the denominator and simplify . Check the box next to the correct answer.
5g) Work with a friend to find the simplest factored form of the following quotient:
6i) Solve for x. Check the box next to the correct answer.
a. x = 2 b. x = 1c. x = -1
6g) Work with a friend to find the solution for the equation Factor the equation and have your friend find the roots.
7i) Solve for x: . Check the box next to the correct answer.
a. x = 4 or x = -1 b. x = 3 or x = -1 c. x = 2 or x = -2
7g) Work with a friend to solve by factoring: . Check the box next to the answer you both agree is correct.
8i) Solve the equation by completing the square.
8g) The height h, in feet, of a projectile is given by h(t) = -16 t2 +32 t where t is the number of seconds from the beginning of the motion. Work with a group to determine how many seconds after the beginning of the motion the projectile will return to the ground.
9i) Solve for x: . Check the box next to the correct answer.
9g) The difference of the squares of two consecutive numbers is 31. What are these numbers? Work with a group to find the answer.
10i) Solve . Check the box next to the correct answer.
a. -4ib. ±2ic. -3i
10g) Work with a friend to complete the square and solve for t: .
11i) Simplify . Check the box next to the correct answer.
a. 2i - i = ib. c.
11g) Which of the following does equal? Work with a friend and check the box next to the answer you both agree is correct.
a. x b. x2c. 1/x d. 1/x2
12i) Use a quadratic formula to solve for x. Check the box next to the correct answer.
12g) Work with a friend to solve the following: The hypotenuse of a right triangle is 17 cm. One of the right sides is 7 cm shorter than the other. Find the length of each side. Set up the equation and have your friend solve it.
13i) Simplify . Check the box next to the correct answer.
13g) Work with a friend to express the complex number in standard form.
14i) Find the value of y that satisfies the system of equations . Check the box next to the correct answer.
a. y = 9 b. y = 6c. y = 3
14g) Work with a partner to find x and y for the equation . (Hint: )
15i) What is x if ? Check the box next to the correct answer.
a. x = 1b. x = 2c. x = 4
15g) Work with a friend to find the value of a if
16i) Find the vertex of the parabola . Check the box next to the correct answer.
a. (-2, 1)b. (1, -1)c. (1, 1)
16g)Work with a friend to complete the square to graph. Do completion to squares, and have your friend find the vertex, determine whether it opens upward or downward, and sketch the graph.
17i) Check the box next to each correct answer.
17g) Work with a friend to factor .
18i) Find the solution set of and sketch it on a number line.
18g) For which and how many integers is the following true: Its square is less than 5 times itself plus 6? Work with a friend to determine the answer.
19i) How many distinct outcomes for the first 2 places are possible in a race with 5 participants? Check the box next to the correct answer.
a. 10 possibilities for first place; 8 possibilities for second place; total = 80b. 8 possibilities for first place; 6 possibilities for second place; total = 48c. 5 possibilities for first place; 4 possibilities for second place; total = 20
19g) Two dice are rolled. What is the probability that each face will show an even number? Work with a friend to find the answer.
20i) What is the value of ? Check the box next to the correct answer.
a. 4b. 6c. 8
20g) In a class of 25, 10 students have both sisters and brothers, 5 students have sisters only, and 7 students have brothers only. How many students have no siblings at all? Work with a friend to draw a Venn diagram of this information.