Math Analysis/trigonometry Readiness Test

27 Questions  I  By Saep on May 27, 2010
Math Analysis/Trigonometry Readiness Test for the Summer Academic Enrichment Program (SAEP)

  
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1.  Simplify:   √50 - √18√ is the square root sign, copy and paste it for your answer
2.  Simplify:     (3 + 3i)/(4 - 2i)                  
3.  Simplify:   1/[ 4√(p4q-12)]remember: just put x3 for x3
4.  Factor  8x3+ 27
5.  Solve   (x + 4)2 = 18
6.  Find the solutions of   4x3 - 6x2 = 0(place commas between multiple answers)
7.  Find the solutions of    √(3x - 2) = 4 - x(place commas between multiple answers)
8.  Solve the inequality    -3 ≤ (2x - 5)/3 < 5
9.  Solve for x:  (4x - 3)/6 + (x/4) = x - 2
10.  Find the discriminant for x2 + x√3x - 1 = 0  and state whether the roots are real or not.(place commas between multiple answers)
11.  Evaluate the function at each specified value of the independent variable and simply: f(x) = x2 + 1         (a)  f(t2)         (b)  f(t + 1)remember: just put x3 for x3(place commas between multiple answers) in order
12.  Suppose z varies directly as the square of x and inversely as y.  If z = 8  when x = 4  and y = 6 , find z when x = 6 and y = 12.
13.  Evaluate the function at each specified value of the independent variable and simplify:  h(x) = 2x + 1, x ≤ - 1 and x2 + 2, x > -1(a) h(-2) (b) h(0)(place commas between multiple answers) in order
14.  Find the zeros of the function algebraically:  f(x) = 3x2 - 16x + 21(place commas between multiple answers)
15.  Find the zeros of the function algebraically:  f(x) = (8x + 3)/(11 - x)(place commas between multiple answers)
16.  Find the inverse function of f informally. Verify the f(f -1(x)) =x and f -1(f(x)) =x.           f(x) = x - 7
17.  Simplify:     (-3a/4x)-2 - (3a/4x)0 + (4x/3a)2remember: just put x3 for x3
18.  Solve:   (x/6) - (x - 3)/3 ≤ (x - 2)/10 - 2
19.  Solve:   3/(x2 - 3x -10)  +  1/(x - 5)  = 1/(x + 2)
20.  Simplify:   √(a/20) + √(4a/5) - 2√(a/45)
21.  Find the real value(s) of k so that kx2 + 6x + 5 has real double root
22.  Solve:    3 -(x + 5) = 9 4x
23.  Solve the equation or inequality  |2x + 5| ≥ 3
24.  If  f(x) = (2x3 + 3x2 - 5x)/(4x2 - 25) , what values must be excluded from the domain?(place commas between multiple answers)
25.  Given f(x) 2x + 1, g(x) = x2  and h(x) = √x evaluate:   (a)  g(h(-2))  (b)  g(f(x))  (place commas between multiple answers)remember: just put x3 for x3
26.  Solve each system of equation for x:   12x - 3y = -9 -4x + y = 3
27.  Find the equation of the line passing through  (2,3) and perpendicular to y = (1/2)x - 1
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