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Digital SAT Math Practice Questions – Advanced : Equivalent expressions

Digital SAT Math Practice Questions - Advanced : Equivalent expressions - New Syllabus

DSAT MAth Practice questions – all topics

  • Advanced Math Weightage: 35% Questions: 13-15
    • Equivalent expressions
    • Nonlinear equations in one variable and systems of equations in two variables
    • Nonlinear functions

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DSAT MAth and English  – full syllabus practice tests

 Question  Hard

Which of the following expressions is(are) a factor of \(3x^2+20x-63\)?
I. x-9
II. 3x-7
A.I only
B. II only
C.I and II
D. Neither I nor II

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Answer: B

Question Hard

If \(\left(\frac{\sqrt{x^5}}{\sqrt[3]{x^4}}\right) = x^{\frac{a}{b}}\) for all positive values of \(x\), what is the value of \(\frac{a}{b}\)?

A) \(\frac{5}{6}\)

B) \(\frac{6}{7}\)

C) \(\frac{7}{6}\)

D) \(\frac{8}{7}\)

▶️ Desmos

Answer: 7/6, 1.166, 1.167

 Question  Hard

In the expression \(3(2x^2 +px+8)—16x(p+4)\), p is a constant. This expression is equivalent to the expression \(6x^2—155x+24\). What is the value of p?
A3
B.7

C.13

D.155

▶️Answer/Explanation with desmos

Ans: B
To find \(p\), we focus on the coefficient of \(x\).
\(3p-16p-16\cdot4=-155\)

 Question  Hard

Which expression is equivalent to \( \frac{42a}{k} + 42ak \), where \( k > 0 \)?
A \(\frac{84a}{k}\)
B.\(\frac{84ak^2}{k}\)

C.\(\frac{42a}{(k+1)}\)

D.\(\frac{42a(k^2+1)}{k}\)

▶️Answer/Explanation with desmos

Ans: D
\(\frac{42a+42ak^2}{k}=\frac{42a(k^2+1)}{k}\)

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