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Math Practice
Worksheet

Algebra 1 & Geometry · Beginner Friendly
📐 Algebra 1 · 10Q
🔺 Geometry · 10Q
🌟 Easy Level
Name: Date:
ALGEBRA 1

Master the core skills · Watch the traps!

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Quick Memory Cards
ALGEBRA SURVIVAL KIT
GOLDEN RULE: What you do to one side, do to the other! LIKE TERMS: same variable, same exponent FOIL: First · Outer · Inner · Last
Isolate = move everything away from the variable!
1
SOLVING EQUATIONS MOST MISSED ★
🎯 Solve for x
Solve for x:
3x + 7 = 22
ISOLATE the variable: subtract 7 FIRST, then divide by 3. Order matters!
Don't divide by 3 first! Always undo addition/subtraction before multiplication/division (reverse PEMDAS)
2
COMBINING LIKE TERMS TRICKY
🧩 Simplify the Expression
Simplify:
5x + 3y − 2x + 8y
SORT by variable: group all x-terms together, then all y-terms together. Numbers must match the SAME letter!
5x and 3y are NOT like terms — you cannot add them together! They have different variables.
3
TWO-STEP EQUATION
⚖️ Balance Both Sides
Solve for x:
2x − 5 = 11

Then check: if x = 2, is the equation true?
STEP 1 → add 5 to both sides · STEP 2 → divide both sides by 2 · STEP 3 → plug back in to CHECK!
4
DISTRIBUTIVE PROPERTY MOST MISSED ★
📦 Distribute First!
Expand and simplify:
3(2x + 4) − 5 = 19
DISTRIBUTE: multiply 3 by EVERY term inside the parentheses: 3×2x AND 3×4
3(2x + 4) ≠ 6x + 4. The 3 must multiply BOTH terms. 3×4 = 12, not 4!
5
SLOPE CRITICAL
📈 Rise Over Run
Find the slope of the line that passes through:
A(2, 3)  and  B(6, 11)

Which graph matches? A line going UP or DOWN from left to right?
RUN RISE slope = rise/run
slope = (y₂−y₁) ÷ (x₂−x₁) · Always subtract in the SAME order (2nd point minus 1st point)
Don't mix up x and y! slope = Δy/Δx · POSITIVE slope goes up-right, NEGATIVE slope goes down-right
6
LINEAR EQUATIONS
📏 Slope-Intercept Form
A line has slope = 3 and y-intercept = −2.
Write the equation in y = mx + b form.
What is the value of y when x = 4?
y = mx + b → m is the SLOPE, b is where the line CROSSES the y-axis (x=0). Plug in values!
7
INEQUALITIES FLIP THE SIGN!
↔️ The Sign-Flip Rule
Solve and graph on a number line:
−4x + 2 > 18
-4 -3 -2 -1 0 →
Solve like a normal equation, BUT if you multiply or divide by a NEGATIVE number → FLIP THE > or < sign!
−4x > 16 ÷ by −4 → x < −4 (sign FLIPS!). This is the #1 most forgotten rule in inequalities!
8
WORD PROBLEM TRANSLATION SKILL
📝 English → Math
Sam has 3 times as many stickers as Alex.
Together they have 48 stickers total.
How many stickers does Alex have?
Let Alex = x → Sam = 3x → Together: x + 3x = 48. "3 times as many" = multiply by 3!
Don't answer with Sam's amount! The question asks for ALEX. Final answer: x, not 3x.
9
SYSTEMS OF EQUATIONS MOST MISSED ★
🔀 Two Equations, Two Unknowns
Solve the system using substitution:
y = 2x + 1
3x + y = 16
SUBSTITUTION: since y = 2x+1, swap y in the second equation with (2x+1). Now you have ONE equation with ONE variable!
10
EXPONENTS
🚀 Power Rules
Simplify each expression:
x³ · x⁴ = ?
x⁸ ÷ x² = ?
(x²)³ = ?
MULTIPLY → ADD exponents  |  DIVIDE → SUBTRACT exponents  |  POWER of POWER → MULTIPLY exponents
x³ · x⁴ ≠ x¹² (that's wrong!). You ADD the exponents: 3+4=7, so the answer is x⁷
✦ ✦ ✦ ✦ ✦
GEOMETRY

Shapes · Angles · Proof logic · Visual thinking!

🃏
Quick Memory Cards
GEOMETRY SURVIVAL KIT
TRIANGLE: angles always add to 180° STRAIGHT LINE: always 180° CIRCLE: always 360° PYTHAGOREAN: a² + b² = c²
COMPLEMENTARY = 90° (C for Corner!) · SUPPLEMENTARY = 180° (S for Straight!)
1
TRIANGLE ANGLES MOST MISSED ★
🔺 The 180° Rule
A triangle has angles of 55° and 72°.
What is the third angle?
?° 72° 55° 180° total!
ALL triangles: angle1 + angle2 + angle3 = 180° (ALWAYS). Subtract what you know!
Don't forget: this is only for TRIANGLES (3 sides). Quadrilaterals add up to 360°, not 180°!
2
PYTHAGOREAN THEOREM CRITICAL
📐 a² + b² = c²
A right triangle has legs a = 6 and b = 8.
Find the hypotenuse c.
a=6 b=8 c=? 6²+8²=c²
c² = a² + b² → c² = 36+64 = 100 → c = √100 · c is ALWAYS the HYPOTENUSE (longest side, opposite right angle)
The hypotenuse is ALWAYS c (the longest side). You can't put a leg as c! Also √100 = 10, not 50.
3
COMPLEMENTARY ANGLES
📐 Corner = 90°
Two angles are complementary.
One angle is 34°. What is the other angle?

Also: two angles are supplementary. One is 110°. Find the other.
COMPLEMENTARY = add to 90° (think: C = Corner of a room) · SUPPLEMENTARY = add to 180° (think: S = Straight line)
Easy to mix these up! C before S in the alphabet → 90° before 180°. Memory word: "C omes before S, 90° comes before 180°"
4
AREA OF SHAPES FORMULA CONFUSION
📏 Area Formulas
Find the area of each shape:
A) Rectangle: length = 12, width = 7
B) Triangle: base = 10, height = 6
C) Circle: radius = 5 (use π ≈ 3.14)
l × w ½ × b × h π × r²
Triangle = ½ × b × h (HALF because a triangle is half a rectangle!). Don't forget the ½!
Triangle area: you need the HEIGHT (perpendicular), not the slant side. b×h gives a rectangle area — divide by 2!
5
VERTICAL ANGLES LOOK-ALIKE TRAP
✖️ X Marks the Equal Angles
Two lines intersect. One angle is 65°.
Find all four angles at the intersection.
65° ?° ?° ?°
VERTICAL ANGLES are EQUAL (opposite each other in the X shape) · Adjacent angles are SUPPLEMENTARY (add to 180°)
There are only 2 different angle values — opposite angles match! So: 65°, 115°, 65°, 115°
6
PARALLEL LINES + TRANSVERSAL MOST MISSED ★
🛤️ The Angle Pairs
Two parallel lines are cut by a transversal. One angle is 120°.
Find the alternate interior angle and the co-interior (same-side) angle.
120° ALT INT? → →
ALTERNATE INTERIOR = EQUAL (Z-shape!) · CO-INTERIOR = add to 180° (C/U-shape!) · Arrows mean PARALLEL!
Co-interior angles are NOT equal! They add up to 180° (they look like they should be equal but they're not!)
7
PERIMETER
🔲 Around the Outside
Find the perimeter of a rectangle with length = 15 cm and width = 9 cm.

A square has perimeter = 48 cm. What is the side length?
PERIMETER = add up ALL sides · Rectangle has 2 lengths + 2 widths = 2(l+w) · Square: all 4 sides are EQUAL
Perimeter ≠ Area! Perimeter = distance AROUND the shape (like a fence). Area = space INSIDE (like a floor).
8
TYPES OF TRIANGLES CLASSIFICATION
🔺 Name That Triangle!
Classify each triangle by its angles AND its sides:
A) Angles: 60°, 60°, 60°
B) Angles: 90°, 45°, 45° — sides: 5, 5, 7.07
C) Angles: 30°, 60°, 90° — sides: 3, 4, 5
BY ANGLES: Acute (all <90°) | Right (one =90°) | Obtuse (one >90°) · BY SIDES: Equilateral (3 equal) | Isosceles (2 equal) | Scalene (none equal)
9
CONGRUENCE TRICKY
🔄 Are These Triangles the Same?
Two triangles have:
△ABC: AB=5, BC=7, ∠B=60°
△DEF: DE=5, EF=7, ∠E=60°

Which congruence rule applies: SSS, SAS, ASA, or AAS?
SAS = Side-Angle-Side (the angle is BETWEEN the two sides). Here: two sides AND the included angle are equal → SAS!
SSA (side-side-angle) is NOT a valid rule! The angle must be BETWEEN the two sides (SAS) to guarantee congruence.
10
COORDINATE GEOMETRY MOST MISSED ★
📍 Distance Between Points
Find the distance between points P(1, 2) and Q(5, 5).
d = √[(x₂−x₁)² + (y₂−y₁)²]

Also find the midpoint of PQ.
P(1,2) Q(5,5) mid
Distance: use Pythagorean theorem on the coordinate grid! Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) — average the x's, average the y's
Don't subtract the coordinates in the wrong order — (x₂−x₁)² = (x₁−x₂)² either way (squaring removes the negative). But be careful with midpoint: ADD then divide, don't subtract!

🔐 Answer Key

Try all problems first before looking! Flip the page! 📖
── ALGEBRA 1 ──
Q1 · Solving Eq
x = 5
3(5)+7=22 ✓
Q2 · Like Terms
3x + 11y
5x−2x=3x; 3y+8y=11y
Q3 · Two-Step
x = 8
x=2 makes it FALSE
Q4 · Distribute
x = 3
6x+12−5=19 → x=3
Q5 · Slope
slope = 2
(11−3)÷(6−2)=8÷4=2
Q6 · y=mx+b
y=3x−2; y=10
when x=4: y=12−2=10
Q7 · Inequality
x < −4
SIGN FLIPS when ÷−4
Q8 · Word Prob
Alex = 12
x+3x=48 → x=12
Q9 · Systems
x=3, y=7
3(3)+7=16 ✓
Q10 · Exponents
x⁷, x⁶, x⁶
Add, Subtract, Multiply
── GEOMETRY ──
G1 · Triangle∠
53°
180−55−72=53
G2 · Pythagoras
c = 10
√(36+64)=√100=10
G3 · Comp/Supp
56°; 70°
90−34=56; 180−110=70
G4 · Area
84; 30; 78.5
12×7; ½×10×6; 3.14×25
G5 · Vertical∠
65°,115°,65°,115°
Opposite angles equal
G6 · Parallel
Alt=120°; Co=60°
Z-shape equal; C adds 180°
G7 · Perimeter
48 cm; side=12
2(15+9)=48; 48÷4=12
G8 · Triangles
A:Equilateral·Acute B:Right·Isosceles C:Right·Scalene
By angles + sides
G9 · Congruence
SAS
Angle BETWEEN the sides
G10 · Distance
d=5; mid=(3,3.5)
√(16+9)=5; avg coordinates