Score: 0 / 20
Algebra 1 & Geometry

Interactive Practice
Worksheet

Linear functions, equations, inequalities · Triangles, polygons, circles

20Questions
2Subjects
6Units

Algebra 1

Linear Functions · Equations · Inequalities — 10 core problems

Algebra Progress0 / 10
🧠
⚡ Memory Keys — Linear Functions
Slope = RISE over RUN  |  y-intercept = where line CROSSES y-axis
slope = (y₂−y₁)/(x₂−x₁) y = mx + b rise/run b = y-intercept
1
Linear Functions · Slope
A line passes through the points (2, 5) and (6, 13).
What is the slope of this line?
📖 Example First
Find the slope of a line through (1, 3) and (4, 9):
m = (9 − 3) / (4 − 1) = 6 / 3 = 2 Slope = 2. Now try the problem above!
2
Linear Functions · y-intercept & Slope-Intercept Form
A line has the equation y = −3x + 7.
Which of the following is true?
📖 Key Form
In y = mx + b: m is slope, b is y-intercept.
Example: y = 4x − 2 → slope = 4, y-intercept = −2
3
Linear Functions · Writing Equations
A line passes through (0, 4) with slope −2.
What is the equation of this line?
Unit 2 · Linear Equations
🧠
⚡ Memory Keys — Linear Equations
ISOLATE the variable · do the SAME thing to BOTH sides · INVERSE operations undo each other
balance inverse isolate distribute first combine like terms
4
Equations · One-Step
Solve for x:
3x − 8 = 16
5
Equations · Distributive Property
Solve for x:
2(x + 5) = 18
📖 Example
Solve 3(x − 2) = 12
Distribute: 3x − 6 = 12
Add 6: 3x = 18 → x = 6
6
Equations · Variables on Both Sides
Solve for x:
5x − 3 = 2x + 9
Unit 3 · Inequalities
🧠
⚡ Memory Keys — Inequalities
FLIP the inequality sign when you multiply or divide by a NEGATIVE number!
flip when × or ÷ negative > = open circle ≥ = closed circle shade the solution
7
Inequalities · Solving & Flip Rule
Solve the inequality:
−4x + 2 > 10 What is the correct solution?
8
Inequalities · Word Problem
Tom wants to spend at most $40 on books. Each book costs $6.
He already has $4 in his wallet. Which inequality shows
the maximum number of books n he can buy?
9
Inequalities · Graphing on Number Line
The solution to an inequality is x ≥ 3.
Which description correctly represents this on a number line?
10
Linear Equations · Tricky Fractions
Solve for x:
(x/2) + 3 = 7 ⚠️ Watch out — many students divide before subtracting!

Geometry

Triangles · Polygons · Circles — 10 core problems

Geometry Progress0 / 10
🧠
⚡ Memory Keys — Triangles
All angles add up to 180° · Exterior angle = sum of the two NON-adjacent interior angles
angle sum = 180 exterior = 2 remote interiors Pythagorean: a²+b²=c² c = hypotenuse
11
Triangles · Angle Sum
A triangle has angles of 52° and 73°.
What is the measure of the third angle?
12
Triangles · Pythagorean Theorem
A right triangle has legs of length 6 and 8.
What is the length of the hypotenuse?
📖 Formula
a² + b² = c² The hypotenuse c is always the side OPPOSITE the right angle (the longest side).
13
Triangles · Exterior Angle Theorem
In a triangle, two interior angles are 40° and 65°.
What is the measure of the exterior angle adjacent to the third interior angle?
📖 Exterior Angle Theorem
Exterior angle = sum of the TWO remote interior angles
(not the angle next to it!)
Unit 5 · Polygons
🧠
⚡ Memory Keys — Polygons
Interior angle sum = (n − 2) × 180  |  Each interior angle (regular) = sum ÷ n
(n−2)×180 n = number of sides exterior angles always = 360° regular = all equal
14
Polygons · Interior Angle Sum
What is the sum of the interior angles of a hexagon (6 sides)?
15
Polygons · Regular Polygon Angles
Each interior angle of a regular octagon (8 sides) measures how many degrees?
16
Polygons · Area of Rectangle & Triangle
A rectangle has length 12 cm and width 5 cm.
A diagonal divides it into two triangles.
What is the area of one triangle?
Unit 6 · Circles
🧠
⚡ Memory Keys — Circles
Circumference = 2πr = πd  |  Area = πr²  |  r = radius, d = diameter = 2r
C = 2πr A = πr² diameter = 2 × radius π ≈ 3.14
17
Circles · Circumference
A circle has a diameter of 10 cm.
What is its circumference? (Use π ≈ 3.14)
📖 Example
Diameter = 10 → radius = 5
C = πd = 3.14 × 10 = 31.4 cm OR: C = 2πr = 2 × 3.14 × 5 = 31.4 cm
18
Circles · Area
A circle has a radius of 7 cm.
What is its area? (Use π ≈ 3.14)
⚠️ Tricky: many students use diameter instead of radius!
19
Circles · Central Angle & Arc Length
A circle has a circumference of 40π cm.
A central angle of 90° intercepts an arc.
What is the length of that arc?
📖 Arc Length Formula
Arc = (central angle / 360) × circumference
Arc = (90/360) × 40π = (1/4) × 40π = 10π
20
Circles · Inscribed Angle Theorem
An inscribed angle in a circle intercepts an arc of 120°.
What is the measure of the inscribed angle?
📖 Inscribed Angle Theorem
Inscribed angle = ½ × intercepted arc
(The central angle EQUALS the arc; the inscribed angle is HALF)