1.
Solve for \(x\): \(x + 9 = 14\)
A3
B4
C5
D6
Subtract 9 from both sides.
Explanation
\(x = 14 - 9 = 5\).
Questions
100
A
Algebra
Linear equations, inequalities, systems, and functions
35 Questions
2.
Solve for \(x\): \(3x = 21\)
A6
B7
C8
D9
Divide both sides by 3.
Explanation
\(x = 21/3 = 7\).
3.
Solve for \(x\): \(2x - 5 = 11\)
A7
B8
C9
D10
Add 5, then divide by 2.
Explanation
\(2x=16\), so \(x=8\).
4.
Solve for \(x\): \(\dfrac{x}{4} + 3 = 10\)
A21
B24
C28
D32
Isolate \(x/4\) first.
Explanation
\(x/4 = 7\), so \(x = 28\).
5.
If \(5x - 3 = 3x + 9\), what is \(x\)?
A3
B4
C5
D6
Move variable terms to one side.
Explanation
\(2x = 12\), so \(x = 6\).
6.
What is the slope of the line \(y = 3x - 7\)?
A-7
B3
C7
D-3
Slope-intercept form is \(y=mx+b\).
Explanation
Here \(m = 3\).
7.
What is the \(y\)-intercept of \(y = -2x + 6\)?
A-2
B2
C6
D-6
The \(y\)-intercept is the constant \(b\).
Explanation
When \(x=0\), \(y=6\).
8.
Solve the inequality: \(2x + 1 > 9\)
A\(x>3\)
B\(x>4\)
C\(x<4\)
D\(x>5\)
Isolate \(x\) as with an equation.
Explanation
\(2x>8\Rightarrow x>4\).
9.
Which point lies on the line \(y = 4x - 1\)?
A(1, 3)
B(2, 6)
C(0, -1)
D(1, 5)
Plug each point's \(x\) into the equation.
Explanation
At \(x=0\): \(y=4(0)-1=-1\), matching \((0,-1)\).
10.
If \(f(x) = 2x + 5\), what is \(f(3)\)?
A8
B9
C10
D11
Substitute \(x=3\) into \(f(x)\).
Explanation
\(f(3)=2(3)+5=11\).
11.
Solve for \(x\): \(\dfrac{2x+3}{5} = 7\)
A14
B15
C16
D17
Multiply both sides by 5 first.
Explanation
\(2x+3=35\Rightarrow 2x=32\Rightarrow x=16\).
12.
A line passes through \((0,4)\) and \((2,10)\). What is its slope?
A2
B3
C4
D6
Slope \(= \Delta y/\Delta x\).
Explanation
\((10-4)/(2-0)=6/2=3\).
13.
Solve for \(x\): \(|x - 4| = 9\)
A\(x=5\) only
B\(x=13\) only
C\(x=13\) or \(x=-5\)
D\(x=5\) or \(x=-13\)
Split into two cases: \(x-4=9\) and \(x-4=-9\).
Explanation
\(x=13\) or \(x=-5\).
14.
If \(3(x-2) = 2x + 1\), what is \(x\)?
A5
B6
C7
D8
Distribute the 3 first.
Explanation
\(3x-6=2x+1\Rightarrow x=7\).
15.
What is the solution to the system \(y=2x+1\) and \(y=x+4\)?
A(2,5)
B(3,7)
C(4,9)
D(1,3)
Set the two expressions for \(y\) equal.
Explanation
\(2x+1=x+4\Rightarrow x=3\), then \(y=7\).
16.
Solve for \(x\): \(\dfrac{1}{2}x - 3 = \dfrac{1}{4}x\)
A8
B10
C12
D14
Clear fractions by multiplying by 4.
Explanation
\(2x-12=x\Rightarrow x=12\).
17.
Solve for \(x\): \(4x + 7 = 2(x + 9)\)
A4.5
B5
C5.5
D6
Distribute the right side first.
Explanation
\(4x+7=2x+18 \Rightarrow 2x=11 \Rightarrow x=5.5\).
18.
If \(2x + 3y = 12\) and \(y = 2\), what is \(x\)?
A2
B3
C4
D5
Substitute \(y=2\) then solve for \(x\).
Explanation
\(2x+6=12\Rightarrow x=3\).
19.
Which value of \(x\) satisfies both \(x > 2\) and \(x < 5\)?
A1
B2
C4
D5
Find the value inside both intervals.
Explanation
Only \(4\) lies strictly between 2 and 5.
20.
Solve the system: \(x+y=10\), \(x-y=2\). What is \(x\)?
A4
B5
C6
D7
Add the two equations to eliminate \(y\).
Explanation
\(2x=12\Rightarrow x=6\).
21.
If \(f(x) = 3x - 2\) and \(f(a) = 13\), what is \(a\)?
A4
B5
C6
D7
Set \(3a-2=13\) and solve.
Explanation
\(3a=15\Rightarrow a=5\).
22.
Solve for \(x\): \(\dfrac{3}{x} = \dfrac{9}{12}\) (assume \(x\neq 0\))
A3
B4
C5
D6
Cross-multiply.
Explanation
\(9x=36\Rightarrow x=4\).
23.
Which system of equations has no solution?
A\(y=2x+1,\ y=2x-3\)
B\(y=2x+1,\ y=x+1\)
C\(y=2x+1,\ y=3x+1\)
D\(y=2x+1,\ y=-2x+1\)
No solution occurs when lines are parallel but not identical.
Explanation
Both have slope 2 but different \(y\)-intercepts, so they never intersect.
24.
Solve for \(x\): \(|2x + 1| = 7\)
A\(x=3\) or \(x=-4\)
B\(x=3\) or \(x=-3\)
C\(x=4\) or \(x=-3\)
D\(x=4\) or \(x=-4\)
Split into \(2x+1=7\) and \(2x+1=-7\).
Explanation
\(x=3\) or \(x=-4\).
25.
The equation \(3x - 2y = 12\) is graphed. What is its \(x\)-intercept?
A3
B4
C6
D12
Set \(y=0\) and solve for \(x\).
Explanation
\(3x=12\Rightarrow x=4\).
26.
If \(2(x+3) - 5 = 3x - 7\), what is \(x\)?
A6
B7
C8
D9
Expand the left side, then isolate \(x\).
Explanation
\(2x+1=3x-7\Rightarrow x=8\).
27.
For the linear function \(g\), \(g(0)=5\) and \(g(2)=13\). What is the slope of \(g\)?
A2
B3
C4
D5
Slope \(=\dfrac{g(2)-g(0)}{2-0}\).
Explanation
\((13-5)/2=4\).
28.
Solve the system: \(4x + y = 10\) and \(2x + y = 4\). What is \(x\)?
A1
B2
C3
D4
Subtract the second equation from the first.
Explanation
\(2x = 6 \Rightarrow x = 3\).
29.
If \(\dfrac{x+2}{3} = \dfrac{x-1}{2}\), what is \(x\)?
A5
B6
C7
D8
Cross-multiply to clear denominators.
Explanation
\(2(x+2)=3(x-1)\Rightarrow 2x+4=3x-3\Rightarrow x=7\).
30.
A line has slope \(-\dfrac{2}{3}\) and passes through \((3, 1)\). What is its \(y\)-intercept?
A1
B2
C3
D4
Use point-slope form: \(y-1=- frac23(x-3)\).
Explanation
At \(x=0\): \(y=1-\tfrac23(-3)=1+2=3\).
31.
If \(3x + 2y = 16\) and \(x = 2y\), what is the value of \(y\)?
A1
B2
C3
D4
Substitute \(x=2y\) into the first equation.
Explanation
\(6y+2y=16\Rightarrow 8y=16\Rightarrow y=2\).
32.
For what value of \(x\) is the equation \(\dfrac{4}{x-2} = \dfrac{2}{x-5}\) true (\(x\neq2,5\))?
A6
B7
C8
D9
Cross-multiply and solve the linear equation.
Explanation
\(4(x-5)=2(x-2)\Rightarrow 4x-20=2x-4\Rightarrow x=8\).
33.
A system of two linear equations has infinitely many solutions. If one equation is \(6x-9y=18\), which could be the other?
A\(2x-3y=6\)
B\(2x-3y=9\)
C\(3x-9y=18\)
D\(6x-9y=9\)
Infinitely many solutions require the same line, i.e., a scalar multiple.
Explanation
Dividing the given equation by 3 gives \(2x-3y=6\), the same line.
34.
If \(-3 \le 2x - 1 \le 5\), what is the range of \(x\)?
A\(-1\le x\le 3\)
B\(-2\le x\le 3\)
C\(-1\le x\le 2\)
D\(0\le x\le3\)
Add 1 to all parts, then divide by 2.
Explanation
\(-2\le 2x\le 6 \Rightarrow -1\le x\le 3\).
35.
A theater sells adult tickets for \$12 and child tickets for \$8. If 100 tickets were sold for a total of \$1000, how many adult tickets were sold?
A40
B45
C50
D60
Let \(a\) = adult tickets; set up \(12a+8(100-a)=1000\).
Explanation
\(12a+800-8a=1000\Rightarrow 4a=200\Rightarrow a=50\).
B
Advanced Math
Quadratics, exponentials, polynomials, and nonlinear functions
35 Questions
36.
Factor: \(x^2 - 9\)
A\((x-3)^2\)
B\((x-9)(x+1)\)
C\((x-3)(x+3)\)
D\((x-9)(x+9)\)
This is a difference of squares.
Explanation
\(x^2-9=(x-3)(x+3)\).
37.
Solve: \(x^2 = 49\)
A\(x=7\) only
B\(x=-7\) only
C\(x=7\) or \(x=-7\)
D\(x=49\)
Take the square root of both sides.
Explanation
\(x=\pm7\).
38.
Simplify: \(x^3 \cdot x^4\)
A\(x^7\)
B\(x^{12}\)
C\(x\)
D\(2x^7\)
Add exponents when multiplying same base.
Explanation
\(x^{3+4}=x^7\).
39.
Expand: \((x+4)^2\)
A\(x^2+16\)
B\(x^2+8x+16\)
C\(x^2+4x+16\)
D\(x^2+8x+8\)
Use \((a+b)^2=a^2+2ab+b^2\).
Explanation
\(x^2+8x+16\).
40.
Solve: \(x^2 - 5x + 6 = 0\)
A\(x=1,6\)
B\(x=2,3\)
C\(x=-2,-3\)
D\(x=2,-3\)
Factor into two binomials.
Explanation
\((x-2)(x-3)=0\Rightarrow x=2,3\).
41.
If \(f(x)=x^2+1\), what is \(f(3)\)?
A9
B10
C11
D12
Substitute \(x=3\).
Explanation
\(f(3)=9+1=10\).
42.
Simplify: \(\dfrac{x^6}{x^2}\)
A\(x^3\)
B\(x^4\)
C\(x^8\)
D\(x^{12}\)
Subtract exponents when dividing.
Explanation
\(x^{6-2}=x^4\).
43.
Solve: \(2x^2 = 32\)
A\(x=4\) only
B\(x=\pm4\)
C\(x=16\)
D\(x=\pm16\)
Divide by 2, then take the square root.
Explanation
\(x^2=16\Rightarrow x=\pm4\).
44.
Which is equivalent to \((2x^3)(3x^2)\)?
A\(5x^5\)
B\(6x^5\)
C\(6x^6\)
D\(5x^6\)
Multiply coefficients and add exponents.
Explanation
\(2\cdot3=6\), \(x^{3+2}=x^5\), giving \(6x^5\).
45.
What are the zeros of \(f(x) = x^2 - 4x\)?
A\(0, 4\)
B\(0, -4\)
C\(4\) only
D\(-4,4\)
Factor out \(x\) first.
Explanation
\(x(x-4)=0\Rightarrow x=0,4\).
46.
Simplify \(\sqrt{50}\)
A\(5\sqrt2\)
B\(2\sqrt5\)
C\(10\sqrt5\)
D\(25\sqrt2\)
Find the largest perfect-square factor of 50.
Explanation
\(\sqrt{50}=\sqrt{25\cdot2}=5\sqrt2\).
47.
If \(g(x) = 2^x\), what is \(g(4)\)?
A8
B12
C16
D32
Compute \(2\) raised to the 4th power.
Explanation
\(2^4=16\).
48.
Solve: \(x^2 + 6x + 9 = 0\)
A\(x=3\)
B\(x=-3\)
C\(x=\pm3\)
D\(x=9\)
This is a perfect square trinomial.
Explanation
\((x+3)^2=0\Rightarrow x=-3\).
49.
Which equation represents exponential decay?
A\(y=3(1.2)^x\)
B\(y=5(0.8)^x\)
C\(y=2x+3\)
D\(y=x^2\)
Decay has base between 0 and 1.
Explanation
\(0.8\) is between 0 and 1, so \(y=5(0.8)^x\) decays.
50.
Solve for \(x\): \(\sqrt{x+3} = 5\)
A19
B20
C21
D22
Square both sides.
Explanation
\(x+3=25\Rightarrow x=22\).
51.
What is the vertex of \(y = (x-2)^2 + 5\)?
A(2,5)
B(-2,5)
C(2,-5)
D(-2,-5)
Vertex form is \(y=a(x-h)^2+k\), vertex \((h,k)\).
Explanation
Here \(h=2,\,k=5\), so vertex is \((2,5)\).
52.
Use the quadratic formula to solve \(x^2 - 2x - 8 = 0\).
A\(x=4,-2\)
B\(x=2,-4\)
C\(x=4,2\)
D\(x=-4,-2\)
Factor: two numbers multiply to \(-8\), add to \(-2\).
Explanation
\((x-4)(x+2)=0\Rightarrow x=4,-2\).
53.
Simplify: \((3x^2y)(2xy^3)\)
A\(5x^3y^4\)
B\(6x^3y^4\)
C\(6x^2y^3\)
D\(5x^2y^3\)
Multiply coefficients, add exponents of like variables.
Explanation
\(3\cdot2=6\); \(x^{2+1}=x^3\); \(y^{1+3}=y^4\).
54.
If \(h(x) = \dfrac{1}{x-2}\), what is the domain restriction?
A\(x\neq0\)
B\(x\neq2\)
C\(x\neq-2\)
D\(x\neq1\)
The denominator cannot equal zero.
Explanation
\(x-2=0\Rightarrow x=2\) is excluded.
55.
Solve: \(x^2 - 3x - 10 = 0\)
A\(x=5,-2\)
B\(x=2,-5\)
C\(x=5,2\)
D\(x=-5,-2\)
Find factors of \(-10\) that sum to \(-3\).
Explanation
\((x-5)(x+2)=0\Rightarrow x=5,-2\).
56.
Which value of \(x\) is NOT in the domain of \(f(x)=\sqrt{x-4}\)?
A3
B4
C5
D9
The expression under the square root must be \(\ge0\).
Explanation
At \(x=3\): \(x-4=-1<0\), not allowed.
57.
If \(2^{x} = 32\), what is \(x\)?
A4
B5
C6
D16
Write 32 as a power of 2.
Explanation
\(32=2^5\), so \(x=5\).
58.
Solve for real \(x\): \(x^2 + 4 = 0\)
A\(x=2i,-2i\)
B\(x=2,-2\)
Cno real solution
D\(x=4\)
Isolate \(x^2\): it becomes negative.
Explanation
\(x^2=-4\) has no real solution.
59.
The graph of \(y = x^2 - 6x + 8\) crosses the \(x\)-axis at how many points?
A0
B1
C2
D3
Factor to find the roots.
Explanation
\((x-2)(x-4)=0\) gives two distinct roots, so two \(x\)-intercepts.
60.
Simplify: \(\dfrac{x^2-9}{x-3}\) (\(x\neq3\))
A\(x-3\)
B\(x+3\)
C\(x-9\)
D\(x+9\)
Factor the numerator as a difference of squares.
Explanation
\(\dfrac{(x-3)(x+3)}{x-3}=x+3\).
61.
If \(f(x) = x^2 - 2x + 1\), what is the minimum value of \(f\)?
A-1
B0
C1
D2
Rewrite as a perfect square.
Explanation
\(f(x)=(x-1)^2\), whose minimum value is \(0\).
62.
Solve: \(3x^2 - 12 = 0\)
A\(x=\pm2\)
B\(x=\pm4\)
C\(x=2\)
D\(x=4\)
Isolate \(x^2\) first.
Explanation
\(x^2=4\Rightarrow x=\pm2\).
63.
What is the sum of the roots of \(x^2 - 7x + 10 = 0\)?
A5
B6
C7
D10
For \(x^2-bx+c\), sum of roots \(=b\).
Explanation
Sum of roots \(=7\) (roots are 2 and 5).
64.
Solve for \(x\): \(\sqrt{2x - 1} = 3\)
A3
B4
C5
D6
Square both sides then isolate \(x\).
Explanation
\(2x-1=9\Rightarrow x=5\).
65.
If \(f(x)=(x-1)(x+5)\), what are the zeros of \(f\)?
A\(1,-5\)
B\(-1,5\)
C\(1,5\)
D\(-1,-5\)
Set each factor equal to zero.
Explanation
\(x=1\) or \(x=-5\).
66.
Which expression is equivalent to \(x^{-2}\)?
A\(-x^2\)
B\(\dfrac{1}{x^2}\)
C\(2x\)
D\(\dfrac{1}{2x}\)
A negative exponent means reciprocal.
Explanation
\(x^{-2}=1/x^2\).
67.
The function \(f(x) = -2(x-3)^2 + 7\) has a maximum value of what?
A-2
B3
C7
D-3
Vertex form: since \(a<0\), the vertex is a maximum, at \(k\).
Explanation
Maximum value is \(k=7\).
68.
Solve the system: \(y = x^2\) and \(y = 4x\). What are the \(x\)-values of the intersection points?
A\(0,4\)
B\(0,-4\)
C\(2,-2\)
D\(4,-4\)
Set \(x^2=4x\) and solve.
Explanation
\(x^2-4x=0\Rightarrow x(x-4)=0\Rightarrow x=0,4\).
69.
Simplify: \(\left(\dfrac{x^3}{y^2}\right)^2\)
A\(\dfrac{x^6}{y^4}\)
B\(\dfrac{x^5}{y^4}\)
C\(\dfrac{x^6}{y^2}\)
D\(\dfrac{x^9}{y^4}\)
Apply the exponent to both numerator and denominator.
Explanation
\(\dfrac{x^{3\cdot2}}{y^{2\cdot2}}=\dfrac{x^6}{y^4}\).
70.
If \(3x^2 + 5x - 2 = 0\), what are the solutions?
A\(x=\tfrac13,-2\)
B\(x=\tfrac13,2\)
C\(x=-\tfrac13,2\)
D\(x=-\tfrac13,-2\)
Factor: \((3x-1)(x+2)=0\).
Explanation
\(x=\tfrac13\) or \(x=-2\).
C
Problem-Solving and Data Analysis
Ratios, percentages, statistics, and data interpretation
15 Questions
71.
A recipe uses 2 cups of flour for every 3 cups of sugar. How many cups of flour are needed for 9 cups of sugar?
A4
B5
C6
D7
Set up a proportion: \(2/3 = x/9\).
Explanation
\(x = 2\cdot(9/3) = 6\).
72.
What is 30% of 150?
A30
B35
C45
D50
Multiply 150 by 0.30.
Explanation
\(0.30\times150=45\).
73.
A data set is: 4, 6, 6, 8, 10. What is the mean?
A6
B6.8
C7
D7.2
Sum the values and divide by 5.
Explanation
\((4+6+6+8+10)/5 = 34/5 = 6.8\).
74.
A data set is: 2, 5, 7, 9, 12. What is the median?
A5
B7
C9
D7.5
The median is the middle value when ordered.
Explanation
The middle (3rd of 5) value is \(7\).
75.
A car travels 240 miles using 8 gallons of gas. What is its fuel efficiency in miles per gallon?
A24
B28
C30
D32
Divide distance by gallons used.
Explanation
\(240/8=30\) mpg.
76.
In a survey of 200 students, 120 prefer tea. What percent prefer tea?
A50%
B55%
C60%
D65%
Divide 120 by 200 and convert to a percent.
Explanation
\(120/200=0.6=60\%\).
77.
A scatterplot shows a linear trend with equation \(y = 2.5x + 10\). What does the slope represent?
AThe starting value of y
BThe rate of change of y per unit x
CThe maximum value of y
DThe value of x when y=0
In a linear model, slope is the rate of change.
Explanation
The slope \(2.5\) is how much \(y\) increases per unit increase in \(x\).
78.
A jar has 5 red, 3 blue, and 2 green marbles. What is the probability of picking a blue marble at random?
A\(1/5\)
B\(3/10\)
C\(1/2\)
D\(3/5\)
Probability \(=\) favorable outcomes over total outcomes.
Explanation
\(3/(5+3+2) = 3/10\).
79.
The price of an item increases from \$40 to \$50. What is the percent increase?
A10%
B20%
C25%
D30%
Percent increase \(=\dfrac{ ext{change}}{ ext{original}} imes100\).
Explanation
\((50-40)/40 = 0.25 = 25\%\).
80.
A survey's margin of error is \(\pm3\%\) with a reported result of 47%. Which is most likely the true population percentage range?
A44% to 50%
B41% to 53%
C47% to 50%
D44% to 47%
Add and subtract the margin of error from the reported value.
Explanation
\(47\%\pm3\%\) gives \(44\%\) to \(50\%\).
81.
Data set A has a standard deviation of 2. Data set B has the same mean but is more spread out. Which is likely true of B's standard deviation?
ALess than 2
BEqual to 2
CGreater than 2
DCannot be determined
Standard deviation measures spread.
Explanation
More spread out data has a larger standard deviation, so B's is greater than 2.
82.
A company's revenue grew from \$2 million to \$2.6 million in one year. What was the percent growth?
A20%
B25%
C30%
D35%
Percent growth \(=\dfrac{ ext{increase}}{ ext{original}} imes100\).
Explanation
\((2.6-2)/2 = 0.3 = 30\%\).
83.
In a linear regression, the correlation coefficient is \(r = -0.9\). This indicates:
AA strong positive linear relationship
BA weak linear relationship
CA strong negative linear relationship
DNo linear relationship
The sign of \(r\) shows direction; magnitude shows strength.
Explanation
\(r=-0.9\) is close to \(-1\), indicating a strong negative linear relationship.
84.
A box contains 4 defective and 16 working bulbs. If one bulb is chosen at random, what is the probability it works?
A\(1/5\)
B\(4/5\)
C\(4/20\)
D\(16/4\)
Divide working bulbs by total bulbs.
Explanation
\(16/20 = 4/5\).
85.
Two variables have a scatterplot with points clustered tightly around a downward-sloping line. Which best describes the relationship?
AStrong positive linear
BWeak positive linear
CStrong negative linear
DNo relationship
A downward slope means negative association; tight clustering means strong.
Explanation
This describes a strong negative linear relationship.
D
Geometry and Trigonometry
Area, volume, triangles, and trigonometric ratios
15 Questions
86.
What is the area of a rectangle with length 8 and width 5?
A13
B26
C35
D40
Area \(=\) length \( imes\) width.
Explanation
\(8\times5=40\).
87.
A triangle has angles measuring \(50°\) and \(60°\). What is the third angle?
A60°
B70°
C80°
D90°
Angles in a triangle sum to \(180°\).
Explanation
\(180-50-60=70°\).
88.
What is the circumference of a circle with radius 7? (Use \(\pi \approx 3.14\))
A21.98
B43.96
C153.86
D44.00
Circumference \(=2\pi r\).
Explanation
\(2\times3.14\times7=43.96\).
89.
In a right triangle, the two legs are 6 and 8. What is the length of the hypotenuse?
A9
B10
C12
D14
Use the Pythagorean theorem.
Explanation
\(\sqrt{6^2+8^2}=\sqrt{100}=10\).
90.
What is the volume of a rectangular prism with dimensions 3, 4, and 5?
A12
B20
C60
D47
Volume \(=\) length \( imes\) width \( imes\) height.
Explanation
\(3\times4\times5=60\).
91.
Two triangles are similar with a scale factor of 2. If the smaller triangle has a side of length 5, what is the corresponding side in the larger triangle?
A5
B7
C10
D25
Multiply the side length by the scale factor.
Explanation
\(5\times2=10\).
92.
What is the area of a circle with radius 4? (Use \(\pi\approx 3.14\))
A12.56
B25.12
C50.24
D100.48
Area \(=\pi r^2\).
Explanation
\(3.14\times16=50.24\).
93.
In a right triangle, one acute angle is \(30°\). What is the other acute angle?
A30°
B45°
C60°
D90°
Acute angles in a right triangle sum to \(90°\).
Explanation
\(90-30=60°\).
94.
For an angle \(\theta\) in a right triangle, \(\sin\theta = \dfrac{3}{5}\). What is \(\cos\theta\) if the triangle is a 3-4-5 right triangle?
A\(3/5\)
B\(4/5\)
C\(5/4\)
D\(5/3\)
Cosine is adjacent over hypotenuse.
Explanation
With sides 3, 4, 5, adjacent \(=4\), so \(\cos\theta=4/5\).
95.
What is the measure, in radians, of a \(90°\) angle?
A\(\pi/6\)
B\(\pi/4\)
C\(\pi/2\)
D\(\pi\)
Use \( ext{radians} = ext{degrees} imes\dfrac{\pi}{180}\).
Explanation
\(90\times\pi/180=\pi/2\).
96.
A sector of a circle has a central angle of \(90°\) and radius 6. What is the area of the sector? (Use \(\pi\approx3.14\))
A9.42
B14.13
C28.26
D56.52
Sector area \(=\dfrac{ heta}{360} imes\pi r^2\).
Explanation
\(\dfrac{90}{360}\times3.14\times36=28.26\).
97.
Two similar triangles have a ratio of areas of \(9:1\). What is the ratio of their corresponding side lengths?
A9:1
B3:1
C81:1
D6:1
The ratio of areas is the square of the ratio of sides.
Explanation
\(\sqrt{9}=3\), so the side ratio is \(3:1\).
98.
For angle \(\theta\), \(\tan\theta = \dfrac{12}{5}\) in a right triangle with legs 5 and 12. What is the hypotenuse?
A13
B15
C17
D18
Use the Pythagorean theorem with legs 5 and 12.
Explanation
\(\sqrt{5^2+12^2}=\sqrt{169}=13\).
99.
A cylinder has radius 3 and height 10. What is its volume? (Use \(\pi\approx3.14\))
A188.4
B282.6
C301.4
D314.0
Volume \(=\pi r^2 h\).
Explanation
\(3.14\times3^2\times10=3.14\times9\times10=282.6\).
100.
In a unit circle, what is the value of \(\sin(90°)\)?
A0
B0.5
C1
Dundefined
At \(90°\), the point on the unit circle is \((0,1)\).
Explanation
\(\sin(90°)=1\).
Answer Key
Top EduPrep · SAT Math Full Practice Test · 100 Questions
1C
2B
3B
4C
5D
6B
7C
8B
9C
10D
11C
12B
13C
14C
15B
16C
17C
18B
19C
20C
21B
22B
23A
24A
25B
26C
27C
28C
29C
30C
31B
32C
33A
34A
35C
36C
37C
38A
39B
40B
41B
42B
43B
44B
45A
46A
47C
48B
49B
50D
51A
52A
53B
54B
55A
56A
57B
58C
59C
60B
61B
62A
63C
64C
65A
66B
67C
68A
69A
70A
71C
72C
73B
74B
75C
76C
77B
78B
79C
80A
81C
82C
83C
84B
85C
86D
87B
88B
89B
90C
91C
92C
93C
94B
95C
96C
97B
98A
99B
100C
Top EduPrep · Teacher Kim Min-ho (김민호선생님) · SAT Math Full Practice Test