Grade 9 · Algebra & functions

Literal equations (SAT) practice

Literal equations (SAT) is a grade 9 math skill aligned to Common Core standard HSA.CED.A.4: rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 literal equations (sat) problems our math games drill.

CCSS HSA.CED.A.410 questions in the bank
Sample questions

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Question 1easy

The simple interest formula is I=PrtI = Prt, where II is interest, PP is principal, rr is rate, and tt is time. Which equation correctly expresses rr in terms of II, PP, and tt?

Divide both sides of I=PrtI = Prt by PtPt: r=IPtr = \dfrac{I}{Pt}.

Question 2medium

The equation y=mx+by = mx + b is in slope-intercept form. Which equation correctly expresses xx in terms of yy, mm, and bb?

Subtract bb from both sides: yb=mxy - b = mx. Divide by mm: x=ybmx = \dfrac{y - b}{m}.

Question 3medium

The perimeter formula for a rectangle is P=2l+2wP = 2l + 2w. Which equation correctly expresses ww in terms of PP and ll?

Subtract 2l2l from both sides: P2l=2wP - 2l = 2w. Divide by 22: w=P2l2w = \dfrac{P - 2l}{2}.

Question 4medium

The equation ax+b=cax + b = c relates values aa, bb, cc, and xx. Which equation correctly expresses xx in terms of aa, bb, and cc?

Subtract bb from both sides: ax=cbax = c - b. Divide by aa: x=cbax = \dfrac{c - b}{a}.

Question 5medium

The volume formula for a rectangular prism is V=lwhV = lwh. Which equation correctly expresses hh in terms of VV, ll, and ww?

Divide both sides of V=lwhV = lwh by lwlw: h=Vlwh = \dfrac{V}{lw}.

Question 6medium

The mean of bb and cc is aa, so a=b+c2a = \dfrac{b + c}{2}. Which equation correctly expresses cc in terms of aa and bb?

Multiply both sides by 22: 2a=b+c2a = b + c. Subtract bb from both sides: c=2abc = 2a - b.

Question 7hard

The formula F=95C+32F = \dfrac{9}{5}C + 32 converts a Celsius temperature CC to Fahrenheit FF. Which equation correctly expresses CC in terms of FF?

Subtract 3232 from both sides: F32=95CF - 32 = \dfrac{9}{5}C. Multiply both sides by 59\dfrac{5}{9}: C=59(F32)C = \dfrac{5}{9}(F - 32).

Question 8hard

The point-slope form of a line is yk=m(xh)y - k = m(x - h). Which equation correctly expresses xx in terms of yy, kk, mm, and hh?

Divide both sides by mm: ykm=xh\dfrac{y - k}{m} = x - h. Add hh to both sides: x=ykm+hx = \dfrac{y - k}{m} + h.

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