TSI Math FREE Sample Practice Questions

TSI Math FREE Sample Practice Questions: work through realistic questions in the same format and difficulty as the real test, then check every answer against a full step-by-step solution so you can see where you lost marks and what to review next.

3- C
(f(x) = x, frac{5}{3}⇒ y = x, frac{5}{3}⇒ y+ frac{5}{3}=x)
(f^{-1 }= x+ frac{5}{3})
(f ^{, 1}(5) = 5 +frac{5}{3}=frac{20}{3})

4- C
(cos)( 30^circ = frac{sqrt 3}{2})

5- C

sin(θ=frac{3}{5})⇒ we have following triangle, then:
(c=sqrt {(5^2-3^2 )}=sqrt{(25-9)}=sqrt 16=4)
cos(θ=frac{4}{5})

6- B
(-2x- y = -9)
(5x-2y= 18)
⇒ Multiplication ((, 2)) in first equation
(4x +2y =18)
(5x-2y= 18)
Add two equations together ⇒( 9x =36 ⇒ x= 4) then: (y = 1)

7- C
(|9, (12 ÷ | 2 to 5 |)| = |(9-(12÷|-3|))|=|9-(12÷3)|=|9-4|=|5|=5)

8- D
METHOD ONE
(log_2⁡x = 5)
Apply logarithm rule:(a = log_b⁡(b^a))
(5 = log_2⁡(2^5) = log_2⁡(32))
(log_2⁡x = log_2⁡(32))
When the logs have the same base: (log_b⁡(f(x)) = log_b⁡(g(x))⇒ f(x) = g(x))
then: (x = 32)
METHOD TWO
We know that:
(log_a⁡b=c⇒b=a^c)
(log_2⁡x=5⇒x=2^5=32)

9- D
(frac{x^3}{16})
⇒ reciprocal is : (frac{16}{x^3})

10- A
(f(x) = ln (2x + 1))
(y = ln (2x + 1))
Change variables ( x) and (y: x = ln (2y + 1))
solve: (x = ln (2y + 1))
(y = frac{e^{x}-1}{2}=frac{1}{2}(e^{x}, 1))

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