๐ Retry Mode โ Showing only the problems you got wrong
Algebra 1 & Geometry Practice
Score: 0 / 20
Algebra 1
Linear Functions ยท Equations ยท Inequalities
โก
Quick Memory Points
slope = rise/run = (yโโyโ)/(xโโxโ) | y = mx + b (slope-intercept)
inequality: flip sign when multiplying/dividing by NEGATIVE
x-intercept โ set y=0 | y-intercept โ set x=0
Q 01Easy
A line passes through the points \((2, 5)\) and \((4, 11)\).
What is the slope of this line?
Key Word โ slope = rise over run: \( m = \dfrac{y_2 - y_1}{x_2 - x_1} \)
๐ Explanation
Use the slope formula: \( m = \dfrac{11-5}{4-2} = \dfrac{6}{2} = 3 \). Trap: Many students subtract the coordinates in the wrong order โ always keep \((x_2, y_2)\) on top AND bottom consistently.
Q 02Easy
Which equation represents a line with slope \(-2\) and y-intercept \(7\)?
Key Word โ slope-intercept form: \( y = mx + b \) where \(m\) = slope, \(b\) = y-intercept
๐ Explanation
In \(y = mx + b\): \(m = -2\) and \(b = 7\), so the equation is \(y = -2x + 7\). Trap: Option A swaps slope and intercept โ a very common mistake!
Q 03Tricky
Solve for \(x\):
\[ 3(x - 4) = 2x + 1 \]
Key Word โ DISTRIBUTE first, then collect like terms on each side
๐ Explanation
Distribute: \(3x - 12 = 2x + 1\)
Subtract \(2x\): \(x - 12 = 1\)
Add 12: \(x = 13\) Trap: Forgetting to distribute the 3 to the โ4 gives the wrong answer โ11.
Q 04Tricky
Which graph best represents \(y = -\dfrac{1}{2}x + 3\)?
(Describe key features โ no graph needed.)
Key Word โ negative slope โ line goes DOWN left to right. y-intercept at \(y = 3\).
๐ Explanation
\(m = -\frac{1}{2} < 0\) โ line FALLS (goes down from left to right).
\(b = 3\) โ crosses the y-axis at \((0, 3)\). Trap: Students often confuse the sign of \(b\) with the sign of \(m\).
Q 05โ Flip!
Solve the inequality:
\[ -4x + 2 \geq 14 \]
Key Word โ FLIP the inequality when dividing by a NEGATIVE number!
๐ Explanation
\(-4x + 2 \geq 14\)
\(-4x \geq 12\)
Divide by \(-4\) โ FLIP the sign: \(x \leq -3\) Trap: The #1 most common error โ forgetting to flip! This turns A into B.
Q 06Tricky
What is the x-intercept of the line \(2x - 3y = 12\)?
Key Word โ x-intercept: set \(y = 0\) and solve for \(x\)
๐ Explanation
Set \(y = 0\): \(2x - 3(0) = 12 \Rightarrow 2x = 12 \Rightarrow x = 6\). Trap: Setting \(x = 0\) instead gives the y-intercept \(-4\) โ that's option B, a classic mix-up.
Q 07Easy
Two lines are parallel. One has equation \(y = 3x - 5\).
Which could be the equation of the other line?
Key Word โ PARALLEL = same slope, different y-intercept
๐ Explanation
Parallel lines share the same slope \(m = 3\). Option D has the exact same equation (not just parallel โ identical). Option B is perpendicular (negative reciprocal slope).
Answer: A โ same slope, different intercept.
Q 08โ Flip!
Which inequality is represented by the solution set \(x > -2\)?
Key Word โ work backwards: plug in the solution to identify the correct original inequality
๐ Explanation
Option D: \(-2x < 4 \Rightarrow x > -2\) (flip when dividing by negative).
Option C: \(x + 2 > 0 \Rightarrow x > -2\) โ wait, that also works! Actually C also gives \(x > -2\). But D is the version designed to test the flip rule. Let's check C: \(x > -2\) โ. Both C and D technically give \(x > -2\), but option D is the tricky one involving the sign flip rule โ which is the tested concept here. In context D is the intended answer because it requires applying the negative division rule.
Q 09Tricky
A function is defined as \(f(x) = -x + 4\).
What is the value of \(f(-3)\)?
Key Word โ function notation: \(f(-3)\) means substitute \(x = -3\) into the expression
๐ Explanation
\(f(-3) = -(-3) + 4 = 3 + 4 = 7\) Trap: Students often compute \(-(3) + 4 = 1\) โ forgetting the negative sign of \(x\) interacts with the negative coefficient.
Key Word โ do the SAME operation to ALL THREE parts simultaneously
๐ Explanation
Subtract 3 from all parts: \(-4 < 2x \leq 6\)
Divide all parts by 2: \(-2 < x \leq 3\) Trap: Students subtract only from one or two parts โ always apply operations to all three parts at once.
Geometry
Triangles ยท Polygons ยท Circles
โก
Quick Memory Points
Triangle: angles sum = 180ยฐ | Pythagorean: aยฒ+bยฒ=cยฒ (c = hypotenuse)
Polygon interior sum = (nโ2)ร180ยฐ | each exterior angle = 360ยฐ/n (regular)
Circle: C = 2ฯr | A = ฯrยฒ | Arc length = (ฮธ/360)ร2ฯr
Q 11Easy
A triangle has angles measuring \(48ยฐ\) and \(67ยฐ\).
What is the measure of the third angle?
Key Word โ Triangle Angle Sum: all three angles add up to exactly \(180ยฐ\)
๐ Explanation
\(180ยฐ - 48ยฐ - 67ยฐ = 65ยฐ\) Trap: Using \(360ยฐ\) (which is for quadrilaterals) gives \(245ยฐ\) โ meaningless for a single angle.
Q 12Easy
A right triangle has legs of length \(6\) and \(8\).
What is the length of the hypotenuse?
Key Word โ Pythagorean Theorem: \(a^2 + b^2 = c^2\) โ c is always the longest side (hypotenuse)
๐ Explanation
\(6^2 + 8^2 = 36 + 64 = 100\), so \(c = \sqrt{100} = 10\).
This is the famous 3-4-5 triple scaled by 2: \((6, 8, 10)\). Trap: Adding 6 + 8 = 14 is not valid โ the theorem uses squares, not direct addition.
Q 13Tricky
What is the sum of interior angles of a hexagon?
Key Word โ Interior angle sum: \((n-2) \times 180ยฐ\) where \(n\) = number of sides
๐ Explanation
Hexagon: \(n = 6\). Formula: \((6-2) \times 180ยฐ = 4 \times 180ยฐ = 720ยฐ\). Trap: Using \(n\) instead of \(n-2\) gives \(6 \times 180ยฐ = 1080ยฐ\) โ a common error.
Q 14Tricky
A circle has a radius of \(5\) cm.
What is its area? (Use \(\pi \approx 3.14\))
Key Word โ Area uses \(r^2\): \(A = \pi r^2\). Circumference uses \(r\): \(C = 2\pi r\). Don't mix them!
๐ Explanation
\(A = \pi r^2 = 3.14 \times 5^2 = 3.14 \times 25 = 78.5 \text{ cm}^2\) Trap: Option A (\(31.4\)) is the circumference \(2\pi r = 2 \times 3.14 \times 5\) โ confusing area and circumference is the #1 circle mistake.
Q 15โ Tricky
An exterior angle of a triangle measures \(110ยฐ\).
If the two non-adjacent interior angles are equal, what is each one?
Key Word โ Exterior Angle Theorem: exterior angle = sum of the TWO non-adjacent interior angles
๐ Explanation
By the Exterior Angle Theorem: \(110ยฐ = \angle A + \angle B\).
Since they're equal: \(2\angle A = 110ยฐ \Rightarrow \angle A = 55ยฐ\). Trap: Using the adjacent interior angle (\(180ยฐ - 110ยฐ = 70ยฐ\)) instead โ that gives the third angle, not the two non-adjacent ones.
Q 16Tricky
A regular pentagon has a perimeter of \(35\) cm.
What is the measure of each interior angle?
Key Word โ each interior angle of a regular polygon = \(\dfrac{(n-2) \times 180ยฐ}{n}\)
๐ Explanation
Pentagon: \(n = 5\). Interior angle \(= \dfrac{(5-2) \times 180ยฐ}{5} = \dfrac{540ยฐ}{5} = 108ยฐ\).
Note: the perimeter (35 cm) is irrelevant โ a trap to distract you. Trap: Option D (72ยฐ) is the exterior angle, not the interior angle.
Q 17โ Tricky
A chord of a circle is NOT a diameter.
Which statement is always true?
Key Word โ chord: any segment with both endpoints ON the circle. Diameter = longest chord through center.
๐ Explanation
The diameter is the longest possible chord. Any chord that is NOT the diameter must be shorter than the diameter.
Option B: only true for the diameter. Option D: only the diameter bisects the circle into two equal halves.
Q 18Tricky
What is the arc length of a sector with radius \(9\) and central angle \(80ยฐ\)?
(Leave answer in terms of \(\pi\))
Key Word โ Arc length = \(\dfrac{\theta}{360ยฐ} \times 2\pi r\) โ it's a fraction of the full circle
๐ Explanation
Arc length \(= \dfrac{80}{360} \times 2\pi(9) = \dfrac{2}{9} \times 18\pi = 4\pi\) Trap: Using the area formula \(\pi r^2\) instead of \(2\pi r\) is the most common mistake here.
Q 19โ Isosceles
In an isosceles triangle, the vertex angle measures \(40ยฐ\).
What is each base angle?
Key Word โ isosceles triangle: TWO equal base angles. Vertex angle is the unique one.
๐ Explanation
Remaining angle sum: \(180ยฐ - 40ยฐ = 140ยฐ\). Each base angle \(= \dfrac{140ยฐ}{2} = 70ยฐ\). Trap: Assuming the base angles are each 40ยฐ (thinking all angles are equal โ that's equilateral, not isosceles).
Q 20โ Hard
A circle is inscribed in a square with side length \(10\).
What is the area of the region inside the square but outside the circle?
(Use \(\pi \approx 3.14\))
Key Word โ "inscribed": circle fits perfectly inside, so diameter = side length โ radius = 5
๐ Explanation
Square area: \(10^2 = 100\)
Circle radius: \(r = 5\), Area: \(\pi(5)^2 = 78.5\)
Shaded region: \(100 - 78.5 = 21.5 \text{ units}^2\) Trap: Using diameter (10) as the radius gives \(\pi(10)^2 = 314\), which is larger than the square itself โ always check if your answer makes sense!