ACT Math Tutor in Victorville: 4 Problems That Cost Students Points (Solved Step by Step)
Try this before you read anything else:
A jacket costs $40. The store raises the price by 25%, then puts it on sale for 20% off. What is the final price?
Most students answer $42, because "up 25, down 20" feels like "up 5%." The real answer is $40. Same price you started with. We will work it out below.
That is what the ACT math section is really testing. Not hard math. Careful math, fast. Below are four problems that cost High Desert students points every year, each one solved step by step.
How the ACT math section works
About 45 questions in about 50 minutes, so a little over one minute per question.
A calculator is allowed on the whole math section.
There is no penalty for a wrong answer, so never leave a question blank.
Topics run from pre-algebra and percents through algebra, geometry and basic trigonometry.
One minute per question means the student who sets the problem up right the first time wins. Here is what that looks like.
Problem 1: The percent trap
Back to the jacket. Work one change at a time.
Raise by 25%: 40 × 1.25 = 50
Take 20% off the new price: 50 × 0.80 = 40
Final price: $40
The habit: a percent always applies to the number in front of it right now, not the original price. Never add or subtract percents.
Problem 2: Slope, then the equation of the line
A line passes through (1, 2) and (4, 11). What is y when x = 10?
Slope = rise ÷ run = (11 − 2) ÷ (4 − 1) = 9 ÷ 3 = 3
Use y = mx + b with the point (1, 2): 2 = 3(1) + b, so b = −1
The line is y = 3x − 1
When x = 10: y = 3(10) − 1 = 29
The habit: find the slope first, every time. Students who guess at b lose this one.
Problem 3: The quadratic shortcut
What is the sum of the solutions of x² − 5x + 6 = 0?
The long way: factor to (x − 2)(x − 3) = 0, so x = 2 or x = 3, and the sum is 5.
The fast way: for x² + bx + c = 0, the solutions always add to −b. Here b = −5, so the sum is 5. Done in ten seconds.
The habit: read what the question asks for. It asked for the sum, not the solutions.
Problem 4: SOH-CAH-TOA without panic
In a right triangle, the hypotenuse is 13 and the side opposite angle θ is 5. What is cos θ?
Find the missing side: 5² + a² = 13², so 25 + a² = 169, a² = 144, a = 12
Cosine = adjacent ÷ hypotenuse
cos θ = 12/13
The habit: draw the triangle and label it before you touch SOH-CAH-TOA. Most trig mistakes are labeling mistakes.
The pattern behind all four
Not one of these problems needs advanced math. Every lost point comes from the same three places:
Rushing the setup instead of the arithmetic
Not reading what the question actually asks for
One old skill (percents, slope, the Pythagorean theorem) that was never fully fixed
That last one is the big one. When we sit down with a student, we usually find one or two gaps from earlier years. Fix those and the score moves.
Watch a test question solved
Here Mr. T works through a real SAT-style question step by step. SAT and ACT math test the same core skills, so the habits carry straight over.
More free lessons on our YouTube channel.
ACT math tutoring in Victorville and the High Desert
US Elite Mathematics Tutoring is the High Desert's math specialist. Mr. T is a certificated high school math teacher who works one-on-one with students on ACT, SAT, ASVAB and AP math.
In person in Victorville, Hesperia, Apple Valley and Oak Hills. We come to you: no driving, no waiting room.
Online anywhere in the US, if you are too far away or too busy.
By appointment, so sessions fit around school, sports and work.
Your first session is FREE. We find exactly where the points are being lost and give you a clear plan. Nothing to lose: you leave with the plan either way.
Frequently asked questions
Is the first session really free?
Yes. The first session is a free assessment. No commitment.
Should my student take the SAT or the ACT?
Many students do better on one than the other. In the free session we can look at where your student is strong and help you decide.
How early should we start ACT prep?
A few months before the test date is ideal, but even a few weeks of focused work on the biggest gaps can help. The sooner we find the gaps, the more time there is to fix them.
Do you only tutor in Victorville?
No. We tutor in person in Victorville, Hesperia, Apple Valley and Oak Hills, and online anywhere in the US.
Book your free ACT math session
Call or text: 909-780-9495
Did you get the jacket question right? Now you know how. Let's find the next point together.
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