0 / 20 answered

Algebra 1
& Geometry

20 carefully selected problems — the ones students miss most. Work through each section at your own pace.

10Algebra Problems
10Geometry Problems
4Choices Each

Algebra 1 Linear Functions, Equations & Inequalities

Core skills: slope, intercepts, solving equations, graphing inequalities, systems of equations

01
Slope
What is the slope of the line passing through the points (2, 5) and (6, 13)?
⚡ SLOPE = RISE / RUN — m = (y₂ − y₁) / (x₂ − x₁)
A
m = 1
B
m = 2
C
m = 3
D
m = 4
02
Slope-Intercept
A line has equation 3x − 2y = 12. What are the slope and y-intercept?
⚡ REARRANGE to y = mx + b — isolate y first!
A
m = 3, b = −12
B
m = 3/2, b = 12
C
m = 3/2, b = −6
D
m = −3/2, b = 6
03
Solving Equations
Solve for x:  2(3x − 4) + 5 = 3x + 7
⚡ DISTRIBUTE → COMBINE → ISOLATE — always expand brackets first
A
x = 2
B
x = 3
C
x = 1
D
x = −2
04
Inequalities
Solve and graph: −4x + 3 ≤ 11. Which value of x is in the solution set?
⚡ FLIP THE SIGN when multiplying or dividing by a NEGATIVE number!
A
x = −3
B
x = −2
C
x = −4
D
x = 2
05
Systems
Solve the system:  y = 2x + 1  and  3x + y = 16
⚡ SUBSTITUTION — plug one equation into the other to eliminate a variable
A
(2, 5)
B
(3, 7)
C
(4, 9)
D
(1, 3)
06
Parallel Lines
Which equation represents a line parallel to y = −3x + 7 passing through (1, 2)?
⚡ PARALLEL = SAME SLOPE — only the y-intercept changes
A
y = 3x − 1
B
y = −3x + 7
C
y = −3x + 5
D
y = 1/3x + 2
07
Compound Inequality
Solve: −1 < 2x − 3 ≤ 5. Express as an interval.
⚡ DO THE SAME THING TO ALL THREE PARTS — add/subtract/multiply across all sections
A
1 < x ≤ 4
B
−2 < x ≤ 1
C
0 < x ≤ 4
D
1 ≤ x < 4
08
Function Notation
If f(x) = 3x2 − 2x + 1, find f(−2).
⚡ SUBSTITUTE carefully — negative numbers squared become POSITIVE: (−2)² = 4
A
9
B
5
C
17
D
17
09
Word Problem — Linear
A taxi charges $3.50 base fare plus $0.75 per mile. If the total cost is $12.50, how many miles was the ride?
⚡ SET UP: Total = Rate × x + Fixed → isolate x
A
10 miles
B
12 miles
C
9 miles
D
15 miles
10
Absolute Value
Solve: |2x − 6| = 10
⚡ SPLIT into TWO equations: one positive (+10) and one negative (−10)
A
x = 8 only
B
x = −2 only
C
x = 8 or x = −2
D
x = 2 or x = −8

Geometry Triangles, Polygons & Circles

Core skills: angle relationships, triangle congruence, area formulas, circle theorems, Pythagorean theorem

11
Triangle Angles
In triangle ABC, angle A = 47° and angle B = 63°. What is angle C?
⚡ TRIANGLE SUM = 180° — always, no exceptions
A
60°
B
70°
C
80°
D
110°
12
Pythagorean Theorem
A right triangle has legs of length 5 cm and 12 cm. What is the hypotenuse?
⚡ a² + b² = c² — c is always the LONGEST side (hypotenuse)
A
11 cm
B
17 cm
C
13 cm
D
14 cm
13
Circle — Arc
A circle has radius 8 cm. What is the length of an arc with a central angle of 135°? (Use π ≈ 3.14)
⚡ ARC LENGTH = (θ/360) × 2πr — fraction of the full circle
A
≈ 18.84 cm
B
≈ 22.5 cm
C
≈ 15.0 cm
D
≈ 30.14 cm
14
Polygon Interior Angles
What is the sum of the interior angles of a regular hexagon?
⚡ SUM = (n − 2) × 180° — n is the number of SIDES
A
540°
B
900°
C
1080°
D
720°
15
Circle — Chord Theorem
An inscribed angle intercepts an arc of 84°. What is the measure of the inscribed angle?
⚡ INSCRIBED ANGLE = ½ × (intercepted arc) — half the arc, always
A
84°
B
42°
C
168°
D
21°
16
Triangle Congruence
Two triangles share two equal sides and the included angle between them is equal. Which congruence rule applies?
⚡ SAS: Side-ANGLE-Side — the angle must be BETWEEN the two sides
A
SAS (Side-Angle-Side)
B
ASA (Angle-Side-Angle)
C
SSS (Side-Side-Side)
D
AAS (Angle-Angle-Side)
17
Area — Trapezoid
A trapezoid has parallel sides of 6 cm and 10 cm, and a height of 4 cm. What is the area?
⚡ A = ½(b₁ + b₂) × h — average of the two bases, times height
A
24 cm²
B
40 cm²
C
32 cm²
D
16 cm²
18
Exterior Angles
What is the measure of each exterior angle of a regular pentagon?
⚡ EXTERIOR ANGLE = 360° ÷ n — all exterior angles of any polygon sum to 360°
A
60°
B
72°
C
108°
D
45°
19
Circle — Tangent
A tangent segment from an external point P is 8 cm. The external segment of a secant from the same point is 4 cm and the whole secant is 16 cm. Are these consistent with the secant-tangent theorem?
⚡ tangent² = external × whole secant — power of a point
A
Yes — 8² = 4 × 16 ✓
B
No — the formula doesn't apply to tangents
C
Yes — but only for circles with radius 8
D
No — 8² ≠ 4 × 16
20
Similar Triangles
Triangle ABC is similar to triangle DEF. Side AB = 6, BC = 9. If DE = 10, what is EF?
⚡ CORRESPONDING SIDES are PROPORTIONAL — set up a ratio: AB/DE = BC/EF
A
12
B
13.5
C
16
D
15
—
—Correct
—Wrong
—Algebra Score
—Geometry Score