Midterm Review Minute to Win It
1. Rewrite the following expression in exponential form: 5 𝑥 9
𝑥 9 5
2. If 2 3 𝑥 =5, what is the value of x to the nearest tenth.
X=15.6
3. The table below represents the function 𝑓 𝑥 =2 𝑥 2 +3 3. The table below represents the function 𝑓 𝑥 =2 𝑥 2 +3. What is the value of f(x) when x= 3? x -1 1 2 F(x) 5 3 11
f(x)=21
4. What is the solution to the following system of equations -4x-5y-x=18 -2x-5y-2z=12 -2x+5y+2z=4
(-4, 0, -2)
5. Luke throws a soccer ball into the air 5. Luke throws a soccer ball into the air. The function ℎ 𝑡 =−16 𝑡 2 +45𝑡 can be used to determine the height in feet, h, of the ball after t seconds. What will the height of the ball after 2.5 seconds?
12.5 feet
6. Simplify 𝑖 25
i
7. If f(x)= (3x+9)(x-1) what are the zeros of the polynomial?
x= -3 and x=1
8. Factor the following equation 𝑦=125 𝑎 3 −8 8. Factor the following equation 𝑦=125 𝑎 3 −8 *Hint: difference of cubes
(5𝑎−2)(25 𝑎 2 +10𝑎+4)
Factor the following equation 𝑦=6 𝑥 2 +𝑥−2 *Hint bottoms up
(3x+2)(2x-1)
10. Solve for x to nearest tenth 4 𝑥 3 =188
X=6.9
11. Solve for x 3= 𝑥−8
X=17
12. Use the graph to find x when f(x)=3.
X=2
13. Use the given functions to find f(2) 𝑓 𝑥 =−5𝑥+2 𝑔 𝑥 = 𝑥−4 2
F(2)=8
14. Simplify (4+2i)(7-i)
30+10i
15.Simplify the following expression 𝑥 2 −36 6𝑥−18 / 𝑥 2 +8𝑥+12 12
2 𝑥−6 𝑥+2 𝑥−3
16. Use the Quadratic Formula to find the zeros of the following polynomial. Nearest hundredth 𝑓 𝑥 =4 𝑥 2 +9𝑥−5
X=.46 and x=-2.71
17. Is the following function even, odd or neither? 𝑦=3 𝑥 3 −5 𝑥 2 +𝑥−8
Neither
18. Name the parent function and describe the transformations 𝑦=− 𝑥+3
Square root Reflected over y Left 3
19. For the polynomial f(x)=− 𝑥 7 −2 𝑥 3 +5𝑥−1 describe f(x) as x approaches ∞
Negative infinity
20. Write the polynomial in factored form with the correct multiplicity
𝑦=𝑎 𝑥+3 𝑥−2 2 (𝑥-5)
21. Write an equation for the graph
y=lx-4l +1
22. Find the inverse y= 𝑥−10
𝑓 −1 = 𝑥 2 +10
23. Solve the following system of equations 𝑦= 𝑥 2 −6𝑥+3 𝑦=2𝑥−13
(4,-5)
24. Use synthetic division to divide 3x3 – 2x2 + 3x – 4 by x – 3
3 𝑥 2 +7𝑥+24+ 68 𝑥−3
25. Name the parent function and describe the transformations 𝑦=2 𝑥−1 2 −5
Quadratic Stretched by 2 Right 1 Down 5
26. You are offered two different sales jobs 26. You are offered two different sales jobs. Company A offers a straight commission of 5% of the sales. Company B offers a salary of $510 per week plus 1% of the sales. How much would you need to sell in a week in order Company A’s offer to be at least as good as Company B’s offer?
P=.05s P=510+.01s $12,750 in sales
27. Is the following function even, odd, or neither.
Odd
28. Find the inverse for 𝑦= 𝑥 2 −7
𝑓 −1 = 𝑥+7
29. f(x)=2x-3 g(x)= 𝑥 2 +2 Find f(g(x))
𝑓 𝑔 𝑥 =2 𝑥 2 +1
30. f(x)=2x-3 g(x)= 𝑥 2 −3𝑥+2 Find f(g(-1))
f(g(-1))=9