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Self-Study Workbook

Algebra 1 & Geometry 1

20 core problems — with memory keys, worked examples, and instant feedback

Algebra 1 · 10 Questions Geometry 1 · 10 Questions Multiple Choice
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Algebra 1

10 Questions · Core Topics
Q01 Linear Equations ⭐ Easy
🔑 Memory Key: ISOLATE x → move constants away from x
Example context: Solve for the unknown variable.
Solve for \(x\):
\(3x - 7 = 14\)
Q02 Slope of a Line ⭐ Easy
🔑 Memory Key: RISE over RUN = (y₂−y₁)/(x₂−x₁)
A very common test trap: make sure you subtract in the right order!
What is the slope of the line passing through \((2, 5)\) and \((6, 13)\)?
Q03 Systems of Equations ⭐⭐ Medium
🔑 Memory Key: SUBSTITUTE → replace one variable, then solve
Tricky trap: students often forget to solve for BOTH variables.
Solve the system:
\(y = 2x + 1\)
\(y = -x + 7\)
What is the value of \(x\)?
Q04 Factoring Quadratics ⭐⭐ Medium
🔑 Memory Key: PRODUCT × SUM → find two numbers that multiply to c, add to b
Classic mistake: wrong sign on the factors!
Factor completely:
\(x^2 - 5x + 6\)
Q05 Quadratic Formula ⭐⭐ Medium
🔑 Memory Key: x = (−b ± √(b²−4ac)) / 2a
Know the formula cold — it's always on the hardest questions.
Use the quadratic formula to find the solutions of:
\(x^2 - 4x - 5 = 0\)
Q06 Inequalities ⭐⭐ Medium
🔑 Memory Key: FLIP the sign when multiplying or dividing by NEGATIVE
Most missed rule in all of Algebra 1.
Solve the inequality:
\(-2x + 4 > 10\)
Q07 Exponent Rules ⭐ Easy
🔑 Memory Key: SAME BASE → ADD exponents when multiplying
Trap: students sometimes multiply the exponents instead of adding.
Simplify:
\(x^3 \cdot x^5\)
Q08 Functions & Domain ⭐⭐ Medium
🔑 Memory Key: f(x) = OUTPUT; plug x IN, get y OUT
Functions are machines: input → process → output.
If \(f(x) = 3x^2 - 2x + 1\), what is \(f(-1)\)?
Q09 Slope-Intercept Form ⭐ Easy
🔑 Memory Key: y = mx + b → m = SLOPE, b = y-INTERCEPT
Which part is m and which is b? Don't mix them up!
A line has slope \(m = -\dfrac{3}{2}\) and y-intercept \(b = 4\).
Which equation represents this line?
Q10 Distributive Property ⭐ Easy
🔑 Memory Key: DISTRIBUTE → multiply OUTSIDE to EVERY term inside
Big trap: forgetting to distribute to the second term!
Expand and simplify:
\(-3(2x - 5) + 4x\)

Geometry 1

10 Questions · Core Topics
Q11 Pythagorean Theorem ⭐ Easy
🔑 Memory Key: a² + b² = c² → c is always the LONGEST side (hypotenuse)
A right triangle has legs. The side opposite the right angle = hypotenuse.
A right triangle has legs of length 6 and 8.
What is the length of the hypotenuse?
Q12 Triangle Angle Sum ⭐ Easy
🔑 Memory Key: ALL triangles → angles always ADD to 180°
Trap: students forget this rule applies to ALL triangles.
A triangle has angles measuring \(48°\) and \(65°\).
What is the measure of the third angle?
Q13 Area of a Circle ⭐ Easy
🔑 Memory Key: Area = πr² → use RADIUS not diameter!
#1 mistake: using the diameter instead of the radius.
A circle has a diameter of \(10\) cm.
What is its area? (Leave answer in terms of \(\pi\))
Q14 Parallel Lines & Transversal ⭐⭐ Medium
🔑 Memory Key: ALTERNATE INTERIOR = EQUAL; CO-INTERIOR = 180°
Know the angle pair names — they appear constantly in Geometry.
Two parallel lines are cut by a transversal. One angle measures \(112°\).
What is the measure of its co-interior (same-side interior) angle?
Q15 Congruent Triangles (SAS) ⭐⭐ Medium
🔑 Memory Key: SSS, SAS, ASA, AAS, HL → these PROVE congruence
SAS means: Side–Angle–Side. The angle must be BETWEEN the two sides.
Two triangles have: two pairs of equal sides, and the included angle between them is also equal.
Which congruence postulate applies?
Q16 Volume of a Rectangular Prism ⭐ Easy
🔑 Memory Key: V = length × width × height → multiply ALL THREE
3D shapes: always confirm you're multiplying all three dimensions.
A box has length \(5\) cm, width \(4\) cm, and height \(3\) cm.
What is its volume?
Q17 Similar Triangles ⭐⭐ Medium
🔑 Memory Key: SIMILAR = same shape, different size → RATIOS are equal
Set up the proportion carefully — mismatching sides is the top error.
Two similar triangles have corresponding sides in ratio \(3:5\). The smaller triangle has a side of \(12\).
What is the corresponding side of the larger triangle?
Q18 Exterior Angle Theorem ⭐⭐ Medium
🔑 Memory Key: EXTERIOR ANGLE = sum of TWO non-adjacent interior angles
Trap: students subtract instead of add the two remote angles.
In a triangle, two interior angles are \(42°\) and \(73°\).
What is the measure of the exterior angle at the third vertex?
Q19 Midpoint Formula ⭐ Easy
🔑 Memory Key: MIDPOINT = average both x's, average both y's → ((x₁+x₂)/2, (y₁+y₂)/2)
Remember: midpoint is the AVERAGE of each coordinate pair.
Find the midpoint of the segment connecting \((-2, 4)\) and \((8, -6)\).
Q20 Angle Bisector ⭐⭐ Medium
🔑 Memory Key: BISECT = cut in HALF → each part = original ÷ 2
Bisector problems: always find the whole first, then halve.
An angle measures \(124°\). An angle bisector divides it into two equal parts.
What is the measure of each smaller angle?