Math Analysis Summer Practice
Math Analysis Summer Practice
Name: ______________
____ 1. Find the value of 5 + 4 × 2 ÷ 6 – 1. a. b. c. d.
16/5 28/3 5 16/3
____ 2. Evaluate 2b(4a -‐ 𝑐 ! ) if a = 5, b = 3/2, and c = 11. a. 303 b. 423 c. -‐6 d.
!!"! !
!!
____ 3. Name the sets of numbers to which ! belongs. a. b. c. d.
Naturals, rationals Rationals, reals Integers, rationals Integers, rationals, reals
!
!
____ 4. Simplify ! (15x – 9) + ! (25x + 5). a. 10x – 2 b.
!"
!"
x -‐ !" !
c. 5x – 2 !
d. !(40x -‐4)
____ 5. Solve each equation for “m” !
23 = 5 -‐ m !
a. b. c. d.
-‐42 -‐12 -‐27 42
____6. | x – 3 | + 10 = 2 a. b. c. d.
{ -‐5} {-‐5,11} {11} Ø
____7. Abby is 4 years younger than her sister. Five years from now, the sum of their ages will be 32. Find Abby’s present age. a. b. c. d.
9 10 13 14
____ 8. 9 ≤ 7 – x ≤ -‐1 a. b. c. d.
{x| -‐2 ≤ x ≤ 8} Ø {x| x ≤ -‐2 or x ≥ 8} {x| x ≤ -‐2}
____ 9. 2|m + 7| > 8 a. b. c. d.
{m| -‐11 < m < -‐3} All real numbers {m| m < -‐13 or m > -‐1} {m| m < -‐11 or m > -‐3}
____10. Find the RANGE of the relation {(-‐2, 3),(-‐1,3), (-‐1,5)} then determine whether the relation is a function. a. b. c. d.
{-‐2, -‐1} function {-‐2, -‐1} not function {3, 5} function {3, 5} not function
____11. Find f(-‐1) if f(t) = t² -‐ 2t -‐2 a. b. c. d.
-‐5 -‐3 1 3
____12. Which is linear? a. b. c. d.
y > x – 2 y = x² y = 3 y² = ½x + 1
____13. Write 3y = -‐1 – 5x in standard form a. 5x + 3y = -‐1 b. -‐5x -‐3y = -‐1 !!
c. y = ! x – 1 d. 3x + 5y -‐1 = 0 ____14. Find the x-‐intercept in the graph 3x -‐2y = 12 a. b. c. d.
4 6 -‐4 -‐6
____15. Find the slope of the line that passes through (2, 6) and (-‐7, 8)
!! !!!
a. b. c. d.
m= !
!! ! !! ! !! ! !! !
! ! !!
____16. What is the slope of a line that is parallel to the graph of 2x + 3y = 5. !
a. !
!
b. -‐! c.
!
! !
d. -‐!
____17. What is the slope of a line that is perpendicular to the graph of 2x + 3y =5 !
a. !
!
b. -‐! c.
!
! !
d. -‐ !
____ 18. Write an equation in slope intercept form for the line that passes !
through (1, -‐2) and has a slope of !. a. y = -‐2 !
b. y = -‐2x + ! !!
c. y = x – 2 ! !
d. y = !x – 2 ____19 Which inequality is being graphed? a. b. c. d.
y ≥ |x| -‐ 5 y ≤ |x| -‐ 5 y > |x| -‐ 5 y < |x| -‐ 5
State whether the system of equations is inconsistent, consistent independent or consistent dependent. ____20. 2x – 3y = 0 4x – 6y = 3 a. inconsistent b. consistent dependent c. consistent independent ____21. 3x – y = 2 x – y = 6 a. inconsistent b. consistent dependent c. consistent independent ____22. 5x + y = 6 3x – y = 10 a. b. c. d.
(-‐2, 4) (2, -‐4) (2, 4) (-‐2, -‐4)
____23. 7x + 2y = -‐1 4x – 3y = -‐13 a. b. c. d.
(1, 3) (-‐1, -‐3) (-‐1, 3) (1, -‐3)
____24. What is the value of “z” in the solution of system of equations? 2x + 3y + z = 9 x – 2y – z = 4 x – 3y + 2z = -‐3 a. b. c. d.
4 1 -‐2 ¾
Solve the matrix equations using ____25. x = a. b. c. d.
2 ¼ ½ 4
2𝑥 + 22 +
5 4 = 2𝑦 2
____26. y = a. b. c. d.
4 12 6 11
Solve the matrix equation for “x” ____27. a. b. c. d.
20 25 1 4
____28. Evaluate using diagonals 1 0 2
4 3 6 a. b. c. d.
−1 5 −2 58 -‐2 12 10
3𝑥 10 + = 𝑦 5−
2𝑦 𝑥
____29. Evaluate using diagonals 2 4 5 a. b. c. d.
−3 0 −1
1 −2 6
-‐38 94 -‐42 114
Find each product 3 ____30. 0 −5
−2 1 4 x 2 1
2 = 1
____31.Find the value of each determinant −6 −4 ____32. Use Cramer’s rule to solve 7x + 5y = -‐8 9x + 2y = 3
𝑎 𝑐
−3 −1
𝑏 = 𝑎𝑑 − 𝑏𝑐 𝑑
Simplify ____33. 𝑥 !! 𝑥 !! 𝑥 ! ____34. (4𝑥 ! 𝑦 ! )! (3𝑥 ! 𝑦²)! ____35.(
!! !! ! ! !! ) !!! ! ! !
____36. 5a²𝑤 ! (𝑎²𝑤 ! -‐ 3𝑎! 𝑤 ! + 9𝑎𝑤 ! ) ____37.
!! ! !!!"! ! !²!!! ! !!"²
Use long division ____38.
!!²!!!!!" !!!
Use synthetic division ____39. (6𝑦 ! + 15𝑦 ! − 28y – 6) ÷ (y +2) Factor ____40. 𝑏 ! − 81 ____41.
! ! !!"!!!" ! ! ! !!!"
