Michigan Secondary Math Advanced
Exam Practice Questions And Correct
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Rationale 2026 Q&A| Instant Download
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1. What is the derivative of f(x)=3x4−5x2+7x−4f(x)=3x^4-5x^2+7x-
4f(x)=3x4−5x2+7x−4?
A. 12x3−10x+712x^3-10x+712x3−10x+7
B. 12x3−10x+712x^3-10x+712x3−10x+7
C. 12x4−10x+712x^4-10x+712x4−10x+7
D. 12x3−5x+712x^3-5x+712x3−5x+7
The derivative of a polynomial is found by applying the power rule to
each term, resulting in 12x3−10x+712x^3-10x+712x3−10x+7.
2. Solve the equation 2x=162^{x}=162x=16.
A. 2
B. 4
C. 4
D. 8
Since 16=2416=2^416=24, solving 2x=162^x=162x=16 yields
x=4x=4x=4.
3. What is the solution to 34x=9\frac{3}{4}x=943x=9?
A. 9
B. 12
C. 12
D. 18
Multiplying both sides by 43\frac{4}{3}34 gives x=12x=12x=12.
,4. What is the value of sin(90∘)\sin(90^\circ)sin(90∘)?
A. 0
B. .5
C. 1
D. 2/2\sqrt{2}/22/2
In the unit circle, sin(90∘)=1\sin(90^\circ)=1sin(90∘)=1.
5. Simplify (x2−9)/(x−3)(x^2-9)/(x-3)(x2−9)/(x−3) for x≠3x\neq3x =3.
A. x+3x+3x+3
B. x+3x+3x+3
C. x−3x-3x−3
D. x2+3x^2+3x2+3
Factoring (x2−9)(x^2-9)(x2−9) yields (x−3)(x+3)(x-3)(x+3)(x−3)(x+3),
canceling gives x+3x+3x+3.
6. What are the zeros of x2−5x+6=0x^2-5x+6=0x2−5x+6=0?
A. 1 and 6
B. 2 and 3
C. -2 and -3
D. 5 and 6
Solving the quadratic by factoring gives roots at x=2x=2x=2 and
x=3x=3x=3.
7. What is the sum of the interior angles of a triangle?
A. 180
B. 180
C. 360
D. 90
The interior angles of any triangle sum to 180 degrees.
8. What is the value of log10(100)\log_{10}(100)log10(100)?
A. 1
B. 2
C. 3
D. 4
Because 100=102100=10^2100=102,
log10(100)=2\log_{10}(100)=2log10(100)=2.
9. If f(x)=x2+3f(x)=x^2+3f(x)=x2+3 and g(x)=2x−1g(x)=2x-1g(x)=2x−1,
what is f(g(x))f(g(x))f(g(x))?
, A. 4x2+14x^2+14x2+1
B. (2x−1)2+3 (2x-1)^2+3(2x−1)2+3
C. 2x2−1+32x^2-1+32x2−1+3
D. x2+6x+4x^2+6x+4x2+6x+4
Function composition places g(x)g(x)g(x) into fff, yielding
(2x−1)2+3(2x-1)^2+3(2x−1)2+3.
10. What is the distance between (0,0)(0,0)(0,0) and (3,4)(3,4)(3,4)?
A. 5
B. 5
C. 13\sqrt{13}13
D. 7
Using the distance formula yields (3−0)2+(4−0)2=9+16=5\sqrt{(3-
0)^2+(4-0)^2}=\sqrt{9+16}=5(3−0)2+(4−0)2=9+16=5.
11. What is the equation of a line with slope 2 passing through
(1,3)?
A. y=2x+1y=2x+1y=2x+1
B. y=2x+1y=2x+1y=2x+1
C. y=2x−1y=2x-1y=2x−1
D. y=2x+3y=2x+3y=2x+3
Using point-slope form and simplifying gives y=2x+1y=2x+1y=2x+1.
12. What is ddx(lnx)\frac{d}{dx}(\ln x)dxd(lnx)?
A. lnx2\ln x^2lnx2
B. 1x\frac{1}{x}x1
C. xlnxx\ln xxlnx
D. 1
The derivative of the natural log function is 1/x1/x1/x.
13. Simplify 50\sqrt{50}50.
A. 525\sqrt{2}52
B. 525\sqrt{2}52
C. 25225\sqrt{2}252
D. 10510\sqrt{5}105
Breaking 50 into 25⋅225\cdot225⋅2 and simplifying gives
525\sqrt{2}52.
14. What is the midpoint of (2,8) and (6,4)?
A. (4,6)
Exam Practice Questions And Correct
Answers (Verified Answers) Plus
Rationale 2026 Q&A| Instant Download
1. What is the derivative of f(x)=3x4−5x2+7x−4f(x)=3x^4-5x^2+7x-
4f(x)=3x4−5x2+7x−4?
A. 12x3−10x+712x^3-10x+712x3−10x+7
B. 12x3−10x+712x^3-10x+712x3−10x+7
C. 12x4−10x+712x^4-10x+712x4−10x+7
D. 12x3−5x+712x^3-5x+712x3−5x+7
The derivative of a polynomial is found by applying the power rule to
each term, resulting in 12x3−10x+712x^3-10x+712x3−10x+7.
2. Solve the equation 2x=162^{x}=162x=16.
A. 2
B. 4
C. 4
D. 8
Since 16=2416=2^416=24, solving 2x=162^x=162x=16 yields
x=4x=4x=4.
3. What is the solution to 34x=9\frac{3}{4}x=943x=9?
A. 9
B. 12
C. 12
D. 18
Multiplying both sides by 43\frac{4}{3}34 gives x=12x=12x=12.
,4. What is the value of sin(90∘)\sin(90^\circ)sin(90∘)?
A. 0
B. .5
C. 1
D. 2/2\sqrt{2}/22/2
In the unit circle, sin(90∘)=1\sin(90^\circ)=1sin(90∘)=1.
5. Simplify (x2−9)/(x−3)(x^2-9)/(x-3)(x2−9)/(x−3) for x≠3x\neq3x =3.
A. x+3x+3x+3
B. x+3x+3x+3
C. x−3x-3x−3
D. x2+3x^2+3x2+3
Factoring (x2−9)(x^2-9)(x2−9) yields (x−3)(x+3)(x-3)(x+3)(x−3)(x+3),
canceling gives x+3x+3x+3.
6. What are the zeros of x2−5x+6=0x^2-5x+6=0x2−5x+6=0?
A. 1 and 6
B. 2 and 3
C. -2 and -3
D. 5 and 6
Solving the quadratic by factoring gives roots at x=2x=2x=2 and
x=3x=3x=3.
7. What is the sum of the interior angles of a triangle?
A. 180
B. 180
C. 360
D. 90
The interior angles of any triangle sum to 180 degrees.
8. What is the value of log10(100)\log_{10}(100)log10(100)?
A. 1
B. 2
C. 3
D. 4
Because 100=102100=10^2100=102,
log10(100)=2\log_{10}(100)=2log10(100)=2.
9. If f(x)=x2+3f(x)=x^2+3f(x)=x2+3 and g(x)=2x−1g(x)=2x-1g(x)=2x−1,
what is f(g(x))f(g(x))f(g(x))?
, A. 4x2+14x^2+14x2+1
B. (2x−1)2+3 (2x-1)^2+3(2x−1)2+3
C. 2x2−1+32x^2-1+32x2−1+3
D. x2+6x+4x^2+6x+4x2+6x+4
Function composition places g(x)g(x)g(x) into fff, yielding
(2x−1)2+3(2x-1)^2+3(2x−1)2+3.
10. What is the distance between (0,0)(0,0)(0,0) and (3,4)(3,4)(3,4)?
A. 5
B. 5
C. 13\sqrt{13}13
D. 7
Using the distance formula yields (3−0)2+(4−0)2=9+16=5\sqrt{(3-
0)^2+(4-0)^2}=\sqrt{9+16}=5(3−0)2+(4−0)2=9+16=5.
11. What is the equation of a line with slope 2 passing through
(1,3)?
A. y=2x+1y=2x+1y=2x+1
B. y=2x+1y=2x+1y=2x+1
C. y=2x−1y=2x-1y=2x−1
D. y=2x+3y=2x+3y=2x+3
Using point-slope form and simplifying gives y=2x+1y=2x+1y=2x+1.
12. What is ddx(lnx)\frac{d}{dx}(\ln x)dxd(lnx)?
A. lnx2\ln x^2lnx2
B. 1x\frac{1}{x}x1
C. xlnxx\ln xxlnx
D. 1
The derivative of the natural log function is 1/x1/x1/x.
13. Simplify 50\sqrt{50}50.
A. 525\sqrt{2}52
B. 525\sqrt{2}52
C. 25225\sqrt{2}252
D. 10510\sqrt{5}105
Breaking 50 into 25⋅225\cdot225⋅2 and simplifying gives
525\sqrt{2}52.
14. What is the midpoint of (2,8) and (6,4)?
A. (4,6)
