ALEKS Math Exam Flashcards

Q: Is ALEKS Math a pass/fail exam?

No. ALEKS PPL is a placement assessment. Colleges and universities set their own score ranges for course placement, so students should check their institution's current placement policy.

Q: What should I review for ALEKS Math?

Focus on prerequisite math skills: arithmetic, fractions, linear and quadratic equations, functions, rational expressions, radicals, logarithms, geometry, and trigonometry if your placement target requires it.

Question 1

Subtracting a negative

Accepted Answer

Change subtraction of a negative into addition: a - (-b) = a + b. This sign rule is a common ALEKS arithmetic trap.

Question 2

Order of operations

Accepted Answer

Evaluate grouping symbols first, then exponents, then multiplication/division left to right, then addition/subtraction left to right.

Question 3

Fraction addition

Accepted Answer

Use a common denominator before adding or subtracting fractions. Only the numerators combine after the denominators match.

Question 4

Percent change

Accepted Answer

Percent change = (new - original) / original x 100%. Use the original value as the denominator.

Question 5

Ratio to proportion

Accepted Answer

A ratio comparison can be solved by cross-multiplying equivalent fractions, as long as the units line up consistently.

Question 6

Absolute value

Accepted Answer

Absolute value is distance from zero. |x| = a gives two cases when a > 0: x = a or x = -a.

Question 7

Solving a linear equation

Accepted Answer

Undo operations in reverse order and perform the same operation on both sides. Check by substituting the result back in.

Question 8

Distributive property

Accepted Answer

a(b + c) = ab + ac. Distribute the sign as well as the coefficient, especially when a is negative.

Question 9

Combining like terms

Accepted Answer

Only terms with the same variable part and exponent combine. 3x and 5x combine; 3x and 5x^2 do not.

Question 10

Inequality sign flip

Accepted Answer

When multiplying or dividing both sides of an inequality by a negative number, reverse the inequality symbol.

Question 11

Slope-intercept form

Accepted Answer

y = mx + b, where m is slope and b is the y-intercept. ALEKS often asks you to read both from a graph or equation.

Question 12

Slope formula

Accepted Answer

Slope between two points is (y2 - y1) / (x2 - x1). It measures vertical change divided by horizontal change.

Question 13

Parallel line slopes

Accepted Answer

Nonvertical parallel lines have equal slopes. Perpendicular nonvertical lines have slopes that are negative reciprocals.

Question 14

Function notation

Accepted Answer

f(a) means substitute a for x in the rule f(x). It is an output value, not multiplication by f.

Question 15

Domain of a function

Accepted Answer

The domain is the allowed input set. Exclude values that create division by zero or an even root of a negative number.

Question 16

Range of a function

Accepted Answer

The range is the set of possible output values. Use the graph, vertex, or restrictions to identify what y-values occur.

Question 17

x-intercept

Accepted Answer

An x-intercept occurs where y = 0. To find it algebraically, set the expression equal to zero and solve for x.

Question 18

y-intercept

Accepted Answer

A y-intercept occurs where x = 0. Substitute x = 0 into the equation or read where the graph crosses the y-axis.

Question 19

Quadratic standard form

Accepted Answer

A quadratic in standard form is ax^2 + bx + c. The graph is a parabola, and a determines whether it opens up or down.

Question 20

Factoring a common factor

Accepted Answer

Before using other factoring methods, pull out the greatest common factor from every term.

Question 21

Difference of squares

Accepted Answer

a^2 - b^2 factors as (a - b)(a + b). It applies only to subtraction of two square terms.

Question 22

Product rule for exponents

Accepted Answer

When multiplying like bases, add exponents: x^a x^b = x^(a+b). The base must be the same.

Question 23

Power rule for exponents

Accepted Answer

When raising a power to a power, multiply exponents: (x^a)^b = x^(ab).

Question 24

Negative exponent

Accepted Answer

A negative exponent means reciprocal: x^-a = 1/x^a for x not equal to zero.

Question 25

Zero exponent

Accepted Answer

Any nonzero base to the zero power equals 1. The expression 0^0 is not treated as a standard simplification.

Question 26

Polynomial degree

Accepted Answer

The degree of a polynomial is the greatest exponent on the variable after the expression is simplified.

Question 27

Rational expression restriction

Accepted Answer

Values that make the denominator zero are excluded, even if a factor later cancels.

Question 28

Simplifying rational expressions

Accepted Answer

Factor numerator and denominator, cancel common factors, and keep the original denominator restrictions.

Question 29

Adding rational expressions

Accepted Answer

Find a common denominator, rewrite each fraction, combine numerators, then factor and simplify if possible.

Question 30

Solving rational equations

Accepted Answer

Multiply by the least common denominator to clear fractions, then reject any solution that makes an original denominator zero.

Question 31

Square root principal value

Accepted Answer

The radical symbol gives the principal nonnegative square root. sqrt(25) = 5, not plus or minus 5.

Question 32

Radical domain

Accepted Answer

For real-valued even roots, the radicand must be greater than or equal to zero.

Question 33

Rational exponent

Accepted Answer

x^(m/n) means the nth root of x raised to the m power, when the expression is defined in the real numbers.

Question 34

Solving radical equations

Accepted Answer

Isolate the radical, raise both sides to the needed power, and check for extraneous solutions.

Question 35

Exponential growth form

Accepted Answer

A common model is y = a(1 + r)^t, where r is the growth rate per period. Decay uses 1 - r.

Question 36

Logarithm meaning

Accepted Answer

log_b(x) asks: what exponent on b gives x? It is equivalent to b^y = x.

Question 37

Log product rule

Accepted Answer

log_b(xy) = log_b(x) + log_b(y), for positive x and y and base b > 0, b not equal to 1.

Question 38

Log quotient rule

Accepted Answer

log_b(x/y) = log_b(x) - log_b(y), with positive arguments and a valid base.

Question 39

Log power rule

Accepted Answer

log_b(x^k) = k log_b(x). This is often used to solve exponential equations.

Question 40

Distance formula

Accepted Answer

Distance between (x1, y1) and (x2, y2) is sqrt((x2 - x1)^2 + (y2 - y1)^2).

Question 41

Midpoint formula

Accepted Answer

The midpoint is ((x1 + x2)/2, (y1 + y2)/2). Average the x-values and y-values separately.

Question 42

Pythagorean theorem

Accepted Answer

For a right triangle, a^2 + b^2 = c^2, where c is the hypotenuse.

Question 43

Circle area

Accepted Answer

Area of a circle is pi r^2. Circumference is 2 pi r or pi d.

Question 44

Triangle area

Accepted Answer

Area = 1/2(base)(height). The height must be perpendicular to the base.

Question 45

Slope of a vertical line

Accepted Answer

A vertical line has undefined slope because the change in x is zero.

Question 46

SOH-CAH-TOA

Accepted Answer

sin(theta) = opposite/hypotenuse, cos(theta) = adjacent/hypotenuse, tan(theta) = opposite/adjacent.

Question 47

Unit circle coordinates

Accepted Answer

On the unit circle, a point at angle theta has coordinates (cos theta, sin theta).

Question 48

Radians and degrees

Accepted Answer

180 degrees equals pi radians. Convert degrees to radians by multiplying by pi/180.

Question 49

Solving systems by substitution

Accepted Answer

Solve one equation for a variable, substitute into the other equation, then back-substitute to find the remaining variable.

Question 50

ALEKS open-response habit

Accepted Answer

Practice producing the answer, not just recognizing it. The real ALEKS placement assessment uses open-response adaptive questions.

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