Preparing for the maths section of the test requires lots of practice and memorization of some formulas, but it’s also important to know how to recognise trick questions, sift through unnecessary details, and remember simple tricks like reading the entire question through before starting to work on it.
Here are 15 maths problems from the SAT that people usually get wrong – with step-by-step explanations for how to solve them.
Many people misread this question about the original price of a laptop.
When people read this question in a rush, they assume that it’s asking about the cost of the laptop with the discount plus tax and pick “C,” says SAT blog Love The SAT. But look carefully, – it’s asking for the original price of the computer.
Alma is paying 8% sales tax, which can also be expressed as 108% of the price. There’s also a 20% discount, meaning she’s paying 80% of the price, or 0.8.
So if p is the total amount Alma paid to the cashier and x is the original price of the laptop, the equation reads as follows:
p = (1.08)(0.8)(x)
Now solve for x by dividing both sides by (1.08)(0.8).
p/(1.08)(0.8) = x
The correct answer is “D.”
This question requires you to write out all the steps, even though the maths itself isn’t too complicated.
You’re trying to figure out the price per pound of beef (b) when it was equal to the price per pound of chicken (c). In other words, when b = c, or 2.35 + 0.25x = 1.75 + 0.40x. So you need to find the value of x in order to plug it back into the “b” equation, writes Dora Seigel of PrepScholar.
Subtract 1.75 from each side:
2.35(−1.75) + 0.25x = 1.75(−1.75) + 0.40x
That leaves you with 0.6 + 0.25x = 0.40x. So subtract 0.25x from each side:
0.6 + 0.25x(−0.25x) = 0.40x(−0.25x)
0.60 = 0.15x
The last step is to reduce the equation:
0.60/0.15 = x
4 = x
Now that you know the value of x, you can put it into the equation for the price of beef:
b = 2.35 + 0.25x
b = 2.35 + 0.25(4)
b = 2.35 + 1
b = 3.35
The correct answer is “D,” $US3.35.
Here, people often solve the wrong part of the equation — a common mistake.
This question is tricky because it gives you lots of numbers and letters and it’s not entirely clear what you’re supposed to do with them. It’s crucial to figure out what the question is asking before you start doing pointless calculations that won’t get you any closer to the answer. PrepScholar suggests reading the entire question through, circling the important information, and determining what you’re being asked before doing any work.
In this case, you’re looking for the value of sinF.
Start with what you know: triangle ABC is a right triangle, and angle B is the right angle. That means that AC is the hypotenuse and BC is one of the sides.
You can use the Pythagorean theorum to figure out the length of the last remaining side:
A2 + B2 = C2
A2 + 162 = 202
A2 = 202 – 162
A = √(400)−(256)
A = √144 = 12
The problem told you triangle DEF is similar to triangle ABC. That means C and F are corresponding vertices: sinF =sinC.
If you know the acronym SOHCAHTOA, you’ll know that sin = opposite/hypotenuse.
sin F = sinC = 12/20 = 3/5 = 0.6
The answer is 3/5 or 0.6.
This question about absolute values is easy to slip up on if you miss one little detail.
Caroline C. of Chegg writes that there are a few possible correct answers here, but tread carefully. The question is asking for the absolute value of x, not the actual value of x.
You want the absolute value of x – 3 to be between six and seven, so multiple values of x work: -3.1, -3.2, etc. But the answer you would write is the absolute value of those numbers: 3.1, 3.2, etc, since that’s what they’re asking for.
SAT prep site PrepScholar ranked this question as one of the hardest SAT maths problems of 2016.
According to PrepScholar, eight and two are both powers of two, so you can simplify things before you begin:
8x/2y = (23)x/2y = 23x/2y
Because the numerator and denominator of the fraction are now the same, you can rewrite the equation as 2(3x-y). And how convenient! The problem told you that 3x – y = 12.
2(3x-y) = 2(12)
The answer is “A,” 2(12).
Sometimes, it’s simply the format of a question that throws people off.
A big chart can scare off test-takers who think it will take too long and they will return to it later if they have time. But PrepScholar says it’s just like any other maths question.
If x = left-handed female students and y = left-handed male students, this system of equations is true:
x + y = 18
5x + 9y = 122
Solve the system of equations with substitution.
x + y = 18
x = 18 – y
5 (18 – y) + 9y = 122
90y – 5y + 9y = 122
90y + 4y = 122
4y = 32
y = 8
If y = 8, then x = 10.
There are five times as many right-handed female students as left-handed female students: 5x = 5(10) = 50. The probability of a random right-handed student being female is 50/122, or 0.410.
The answer is “A.”
Pictures often confuse people.
The grain silo pictured is nothing more than a cylinder and two cones, says PrepScholar, both of which have formulas for calculating their volume:
Volume of a cone = 1/3 πr2h
Volume of a cylinder = πr2h
Volume of the silo = πr2h + 2(1/3 πr2h)
Just plug in the radius and height measurements from the picture.
π(52)(10) + (2)(1/3) π(52)(5) = (4/3)(250)π = 1047.2
The answer is “D,” 1047.2 cubic feet.
Quadratic functions sneak up on many people who take the SAT.
For starters, you can tell from the graph that the y-intercept is 2, which automatically eliminates “C” where the y-intercept is -2.
The vertex of the graph is at x = 0, meaning that the “b” in the quadratic equation ax2 + bx + c has to be 0. Otherwise, the graph would be shifted to the left or right. Therefore, you can also rule out “B” and “D” using the FOIL method. (PrepScholar offers a more detailed explanation of what the FOIL method is and how to apply it to this question.)
The answer is “A,” y = x2 + 2.
Some people forget to memorise formulas that aren’t provided.
As PrepScholar explains, it’s impossible to answer this question if you don’t know the formulas for the sine and cosine of an angle.
“If you were a formula whiz and knew the complementary angle relationship for sine and cosine, which is sin(x°)=cos(90°−x°), you’d know immediately that the answer is cos(90°−x°)= 4/5 or 0.8,” PrepScholar explains.
You can still solve this problem by drawing a diagram of the triangle, but speed is key on the maths portion of the SAT, where you should allot yourself one minute per question.
Problems with percentages can also be tricky.
Since this is a percentage question, SAT prep site Get800 recommends substituting numbers in for b and k and playing out all of the answers to see which one makes sense.
Let’s say b = 100 and k = 25. If there are 100 bricks and 25 of them have been stacked, that means 75 bricks have not yet been stacked, or 75% of the bricks.
Which of the multiple choice answers gives you 75% when you plug in those numbers?
A: 100/7500 = 0.0133%
B: 7500/100 = 75%
C: 10,000/25 = 400%
D: 2500/100 = 25%
The answer is “B.”
If the problem involves a circle, the key is likely understanding the radius.
If you know the length of one radius of a circle, you know them all.
Here, the problem tells you that sides AB and AO of a triangle are equal. AO is a radius of the circle, and so is BO. The radii of a circle are always equal, so AO and BO are also the same length. That means that triangle ABO is an equilateral triangle, and all of its angles measure 60 degrees.
The answer is “D,” 60 degrees.
Don’t let drawings fool you — this is a question about circles, not squiggles.
Speed is key on the SAT, and the quickest way to solve this problem is to imagine that RS is the diameter of a complete circle, says Prepscholar. You can do this because the picture shows two radii and two half-circles – put them together and you have one circle.
Circumference = πd, so the answer is “C,” 12π.
You can figure out theoretical maths questions with real numbers.
PrepScholar recommends plugging in real numbers to a theoretical maths question to figure out the correct answer.
Let’s say a = 3 and b = 2. Which of the options results in an odd number?
A: 3 x 2 = 6
B: 3 + 3 = 6
C: 2(2+3) = 10
D: 3 + 2(2) = 7
E: 2(3) + 2 = 8
The answer is “D,” a + 2b.
For single variable equations, isolate the variable and make sure you know what the question is asking.
This equation is cleverly disguised as a word problem. The word “is” means “equals,” and “5 more than 10” means 15.
A simpler way to write this is 10 + x = 15. Subtract 10 from each side of the equation and you get x = 5.
Don’t forget the last step! The question isn’t asking for the value of x, it’s asking for 2x.
2 x 5 = 10.
The answer is “C,” 10.
You don’t need multiple variables to solve this question about sandwiches. Keep everything in like terms for maximum efficiency.
Set this up as an equation with “a” representing the number of sandwiches Ali made, PrepScholar advises. Ben made three times as many as Ali, and Carla made twice as many as Ben.
Put Carla’s sandwiches in terms of Ali’s sandwiches so that you can combine like terms. She made twice as many as Ben: 2(3a) = 6a.
a + 3a + 6a = 20
10a = 20
a = 2
Plug a=2 back into the equation to make sure it works.
2 + (3×2) + (6×2) = 20
2 + 6 + 12 = 20
The answer is “A,” two.