A teacher poses a problem with no obvious solution path. Which step in Polya's four-step problem-solving framework comes immediately after understanding the problem?
Problem Solving Reasoning
Question · Easy
Would you rather: marbles
Short
Which statement is the contrapositive of "If a number is divisible by 6, then it is divisible by 3"?
Question · Hard
Chapter 1: Exam Orientation & the Current Blueprint
1.1 Exam Facts, Format, Scoring & Calculator Policy
Study guide
A train travels 180 miles in 3 hours, then 220 miles in 4 hours. What is the train's average speed for the entire trip?
A student estimates that 48 x 52 is approximately 2,500. Which reasoning best justifies this estimate?
Which problem-solving strategy is most appropriate for finding the number of diagonals in a polygon with many sides?
Question · Medium
Stats test: find the median
If the pattern 2, 6, 12, 20, 30, ... continues, what is the rule for the nth term?
1.2 The Five-Competency Blueprint & How to Study It
A counterexample to the claim "all prime numbers are odd" is which number?
A recipe for 12 cookies uses 3/4 cup of sugar. How much sugar is needed for 30 cookies?
Number Sense Proportionality
Which of the following correctly orders these numbers from least to greatest: 0.7, 3/5, 0.65, 2/3?
Find x
A shirt originally priced at $40 is discounted 25%, then an additional 10% is taken off the sale price. What is the final price?
Chapter 2: Number Sense and Operations
2.1 Comparing and Converting Rational Numbers
What is the prime factorization of 360?
The ratio of boys to girls in a class is 3:5. If there are 32 students total, how many are girls?
Which expression is equivalent to -8 - (-3) + (-5)?
Factor it
A number is increased by 20% and the result is then decreased by 20%. Compared to the original number, the final value is:
2.2 Rational-Number Operations & Multi-Step Order of Operations
What is the least common multiple (LCM) of 12 and 18?
Solve for x: 3(x - 4) = 2x + 5.
Foundations Of Algebra
What is the slope of the line passing through the points (2, -3) and (6, 5)?
Which inequality represents the solution to -2x + 3 > 11?
2.3 Properties of Operations, Factors, GCF & LCM
Simplify the expression: 4(2x + 3) - 2(x - 5).
What is the equation of the line with slope -3 that passes through the point (0, 4)?
Simplify the square root of 72 to its simplest radical form.
Which property is illustrated by the statement 5(x + 7) = 5x + 35?
2.4 Estimating Irrational Numbers and Square Roots
If 2x - 3y = 12 and the line crosses the x-axis, what is the x-intercept?
A number line shows a solid dot at -2 with shading extending to the right. Which inequality does this represent?
What value of x makes the proportion x/8 = 15/24 true?
Two parallel lines have the same slope. If one line is y = 2x + 5, which equation represents a line parallel to it?
Chapter 3: Notation, Radicals & Proportional Reasoning
3.1 Scientific Notation & Significant Digits
Solve the equation: x/3 + 5 = 11.
Which expression represents "five less than three times a number n"?
What is the value of the expression 3x^2 - 2x + 1 when x = -2?
A line is perpendicular to y = 4x - 1. What is the slope of the perpendicular line?
3.2 Radicals, Rational Exponents & the Laws of Exponents
A function is defined by f(x) = 2x + 3. What is f(5)?
Algebraic Thinking
Which table represents a linear function?
Solve the system: y = x + 2 and y = 2x - 1. What is the solution point?
Factor the quadratic expression x^2 + 7x + 12.
3.3 Ratios, Rates, Proportions, Percents & Measurement Conversions
A graph of a parabola opens downward and has its vertex at (0, 4). Which equation could represent it?
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