Quick Memory Points — Algebra 1
ISOLATE → get the variable alone ·
INVERSE → undo each operation in reverse order ·
DISTRIBUTE → multiply outside × everything inside ·
COMBINE → only like terms (same variable & exponent) ·
FOIL → First · Outer · Inner · Last
A-01
Linear Equations
A school store sells notebooks for $3 each and pens for $1.50 each. Emma buys a total of 8 items and spends $18.00. How many notebooks did she buy?
A-02
Inequalities
⚠ Tricky
Solve the inequality and choose the correct solution set:
−3x + 7 > 16 Watch out: What happens to the inequality sign when you divide by a negative number?
−3x + 7 > 16 Watch out: What happens to the inequality sign when you divide by a negative number?
A-03
Slope & Lines
Two points are given: (2, 5) and (6, 13). What is the slope of the line passing through them?
m = y₂ − y₁x₂ − x₁
A-04
Distributive Property
⚠ Tricky
Simplify completely:
3(2x − 4) − 2(5 − x)
A-05
Word Problem
A car travels at 60 mph. Another car starts 30 minutes later and travels at 80 mph in the same direction. How many hours after the second car departs will it catch up to the first car?
A-06
Factoring
⚠ Tricky
Factor completely:
x² − 5x − 14
Hint: find two numbers that multiply to −14 and add to −5.
A-07
Functions
Given f(x) = 2x² − 3x + 1, evaluate f(−2).
A-08
Quadratic
⚠ Tricky
Using the quadratic formula, solve:
x² − 6x + 5 = 0
x = −b ± √(b² − 4ac)2a
A-09
Percent / Proportion
A shirt originally costs $48. It is on sale for 25% off. After applying the discount, a 10% sales tax is added. What is the final price?
A-10
Systems of Equations
⚠ Tricky
Solve the system by substitution:
y = 2x − 1
3x + y = 9
What is the value of x?
Quick Memory Points — Geometry
SUPPLEMENTARY → adds to 180° ·
COMPLEMENTARY → adds to 90° ·
PYTHAGOREAN → a² + b² = c² (c = hypotenuse) ·
SIMILAR → same shape, sides are proportional ·
INTERIOR ANGLES → triangle = 180°, quadrilateral = 360°
G-01
Angles
⚠ Tricky
Two angles are supplementary. One angle is 3x + 10° and the other is 5x − 2°. What is the value of the larger angle?
G-02
Pythagorean Theorem
A right triangle has legs of length 7 and 24. What is the length of the hypotenuse?
a² + b² = c²
G-03
Area & Perimeter
⚠ Tricky
A rectangle has a perimeter of 46 cm and a length of 14 cm. What is the area?
P = 2(l + w) · A = l × w
G-04
Similar Triangles
⚠ Tricky
Two similar triangles have corresponding sides. The smaller triangle has sides 4, 6, 8 and the larger triangle has a shortest side of 10. What is the longest side of the larger triangle?
G-05
Circle
A circle has a diameter of 18 cm. What is its area? Use π ≈ 3.14.
A = πr²
G-06
Triangle Angles
In a triangle, two angles measure 52° and 79°. What is the measure of the exterior angle at the third vertex?
G-07
Volume
⚠ Tricky
A cylinder has a radius of 5 cm and a height of 12 cm. A cone has the same base and height. What is the difference in their volumes? Use π ≈ 3.14.
Vcylinder = πr²h · Vcone = 13πr²h
G-08
Parallel Lines
⚠ Tricky
Two parallel lines are cut by a transversal. One angle measures 115°. Which of the following correctly identifies the co-interior (same-side interior) angle?
G-09
Coordinate Geometry
What is the distance between points (1, 2) and (4, 6)?
d = √[(x₂−x₁)² + (y₂−y₁)²]
G-10
Surface Area
⚠ Tricky
A rectangular box (rectangular prism) has dimensions 3 cm × 4 cm × 5 cm. What is its total surface area?
SA = 2(lw + lh + wh)