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🇺🇸 PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) · flashcards
PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) Math: Algebra Flashcards
50 question-and-answer cards covering Math: Algebra as it is examined in PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test). 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Math: Algebra deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
How are the slopes of two perpendicular lines related?
They are negative reciprocals; their product is −1 (m₁ · m₂ = −1).
To graph a line from y = mx + b, what is the standard procedure?
Plot the y-intercept (0, b), then use the slope m = rise/run to find a second point, and draw the line through them.
How do you find the x-intercept of a line?
Set y = 0 and solve for x.
A line passes through (0, 4) with slope −2. Write its equation.
y = −2x + 4.
Write the equation of the line through points (1, 2) and (3, 8).
Slope = (8−2)/(3−1) = 3; y = 3x − 1.
What is a system of linear equations?
Two or more linear equations considered together; a solution is an ordered pair (x, y) that satisfies all equations simultaneously.
What does the solution to a system of two linear equations represent graphically?
The point of intersection of the two lines.
Describe the substitution method for solving a system.
Solve one equation for one variable, substitute that expression into the other equation, solve for the remaining variable, then back-substitute to find the first.
Describe the elimination method for solving a system.
Multiply equations as needed so one variable has opposite coefficients, add the equations to eliminate that variable, solve, then back-substitute.
When is substitution usually the easier method?
When one variable is already isolated or has a coefficient of 1 (or −1).
Solve by substitution: y = 2x and x + y = 9.
x + 2x = 9, so x = 3 and y = 6; solution (3, 6).
Solve by elimination: x + y = 10 and x − y = 4.
Adding gives 2x = 14, so x = 7 and y = 3; solution (7, 3).
How many solutions does a system have when the lines have different slopes?
Exactly one solution (the lines intersect at one point).
How many solutions does a system have when the lines have the same slope but different y-intercepts?
No solution (the lines are parallel and never intersect).
How many solutions does a system have when both equations represent the same line?
Infinitely many solutions.
While solving a system algebraically, you get 0 = 5. What does this mean?
The system has no solution (the lines are parallel).
While solving a system algebraically, you get 0 = 0. What does this mean?
The system has infinitely many solutions (the equations represent the same line).
For what value of k does the system y = 3x + 2 and y = kx − 5 have no solution?
k = 3 (equal slopes with different intercepts make the lines parallel).
Tickets cost $8 for adults and $5 for children. 200 tickets sold for $1,300. Write the system.
a + c = 200 and 8a + 5c = 1300, where a = adult and c = child tickets.
In a mixture or word-problem system, what two equations do you usually write?
One equation for the total quantity (counts/amounts) and one for the total value (cost, weight, or concentration).
What are the basic steps to solve a linear inequality in one variable?
Isolate the variable using inverse operations, just like an equation—but flip the inequality sign whenever you multiply or divide both sides by a negative number.
Solve: −2x + 3 ≤ 9.
−2x ≤ 6, divide by −2 and flip: x ≥ −3.
How do you graph the solution to a two-variable linear inequality?
Graph the boundary line (solid for ≤ or ≥, dashed for < or >), then shade the side that satisfies the inequality (test a point such as (0,0)).
What does the overlapping shaded region represent when graphing a system of inequalities, and how is 'at least'/'no more than' translated?
The overlap is the set of points satisfying all inequalities; 'at least' means ≥, 'at most'/'no more than' means ≤, and quantities are typically also restricted to x ≥ 0, y ≥ 0.
What this deck covers
The Math: Algebra deck follows the PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) Math: Algebra syllabus — 4 chapters and 12 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 12.5 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 82 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Math: Algebra flashcards FAQ
How many Math: Algebra flashcards are in this PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Math: Algebra cards cover?
They follow the PSAT/NMSQT (Preliminary SAT/National Merit Scholarship Qualifying Test) Math: Algebra syllabus — 4 chapters and 12 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.