SAT Math — Practice Set 1

Algebra, advanced math, problem solving and data analysis, and geometry. Every solution gives the full method and the fast route, because on the SAT you have roughly 95 seconds per question and the full method is often not the one to use.

How to use this: time yourself. Accuracy without speed does not produce an SAT score. If a question takes you over two minutes, the point of reviewing it is to find the shortcut you missed.

Algebra

1. If $3x + 7 = 22$, what is the value of $6x + 5$?

Full method:   3x + 7 = 22  →  3x = 15  →  x = 5
               6x + 5 = 6(5) + 5 = 35

Fast route:    6x is exactly 2 × 3x.
               3x = 15, so 6x = 30, so 6x + 5 = 35

Answer: 35

The habit worth building: the SAT frequently asks for an expression, not for $x$. Check whether you can get there by scaling what you already have. It saves a step and a chance to slip.

2. A line passes through $(2, 5)$ and $(6, 13)$. What is its equation in slope-intercept form?

        y₂ - y₁     13 - 5     8
slope = -------- = -------- = --- = 2
        x₂ - x₁      6 - 2     4

y = 2x + b, substitute (2, 5):
5 = 2(2) + b  →  b = 1

y = 2x + 1

Answer: $y = 2x + 1$

3. If $2(x - 3) = 4x + 6$, what is $x$?

2x - 6 = 4x + 6
-6 - 6 = 4x - 2x
-12    = 2x
x      = -6

Answer: $-6$

Common mistake: dropping the negative when moving terms. Substituting back takes five seconds: $2(-6-3) = -18$ and $4(-6)+6 = -18$ ✓

Advanced Math

4. If $x^2 - 5x + 6 = 0$, what are the solutions?

Factor:  (x - 2)(x - 3) = 0
         x = 2  or  x = 3

Answer: $x = 2$ and $x = 3$

Fast route: find two numbers multiplying to $+6$ and adding to $-5$: that is $-2$ and $-3$. On the SAT, quadratics almost always factor over the integers — if yours does not, re-read the question before reaching for the formula.

5. The function $f(x) = 2x^2 - 3$. What is $f(-2)$?

f(-2) = 2(-2)² - 3
      = 2(4) - 3
      = 8 - 3
      = 5

Answer: 5

Common mistake: computing $2(-2)^2$ as $(-4)^2 = 16$. The exponent applies to $-2$ before the multiplication by 2. Order of operations decides this question.

6. If $\sqrt{x + 7} = 5$, what is $x$?

Square both sides:  x + 7 = 25
                    x     = 18

Answer: 18

Always check radical equations: $\sqrt{18 + 7} = \sqrt{25} = 5$ ✓. Squaring can introduce solutions that do not satisfy the original equation, and the SAT includes such traps.

Problem Solving and Data Analysis

7. A shirt costs \$40 after a 20% discount. What was the original price?

The sale price is 80% of the original:

0.80 × original = 40
original        = 40 ÷ 0.80
                = $50

Answer: \$50

Common mistake: adding 20% to \$40 to get \$48. Percentages are taken of the original, so you must divide, not add back. This is among the most-missed question types on the test.

8. In a survey of 250 students, 40% preferred online classes. How many preferred in-person?

Preferred online   = 0.40 × 250 = 100
Preferred in-person = 250 - 100  = 150

Answer: 150

Fast route: 60% of 250. Since 10% is 25, 60% is 150 — no long multiplication needed.

9. The mean of five numbers is 12. Four of them are 8, 10, 14 and 16. What is the fifth?

Sum of all five = 5 × 12 = 60
Sum of the four = 8 + 10 + 14 + 16 = 48
Fifth number    = 60 - 48 = 12

Answer: 12

The move to remember: when a question gives you a mean, immediately convert it to a total. Nearly every mean question on the SAT opens this way.

10. A car travels 180 miles in 3 hours. At the same rate, how far in 5 hours?

Rate     = 180 ÷ 3 = 60 mph
Distance = 60 × 5  = 300 miles

Answer: 300 miles

Fast route: 5 hours is $\frac{5}{3}$ of 3 hours, so the distance is $180 \times \frac{5}{3} = 300$.

Geometry and Trigonometry

11. A right triangle has legs 6 and 8. What is the hypotenuse?

c² = 6² + 8² = 36 + 64 = 100
c  = 10

Answer: 10

Worth memorising: the triples 3-4-5, 5-12-13, 8-15-17 and 7-24-25, plus their multiples. 6-8-10 is just 3-4-5 doubled — recognising it removes the arithmetic entirely.

12. A circle has area $36\pi$. What is its circumference?

πr² = 36π  →  r² = 36  →  r = 6
C   = 2πr  = 2π(6) = 12π

Answer: $12\pi$

13. In a right triangle, $\sin\theta = \frac{3}{5}$. What is $\cos\theta$?

sin θ = opposite/hypotenuse = 3/5
So opposite = 3, hypotenuse = 5.

adjacent = √(5² - 3²) = √16 = 4

cos θ = adjacent/hypotenuse = 4/5

Answer: $\frac{4}{5}$

Fast route: recognise the 3-4-5 triangle and read off the answer.

How to actually gain points on this section

1. Know when to skip. Every question is worth the same. Two minutes spent on a hard one costs you two easy ones you would have got right.
2. Substitute the answer choices. On multiple choice, testing options is often faster than solving — especially for quadratics and radicals.
3. Estimate first. Knowing the answer is "a bit under 50" eliminates most choices before you compute anything.
4. Use the reference sheet. The formulas are provided. Do not spend memory on them; spend it on recognising which one applies.
5. Answer everything. There is no penalty for a wrong answer, so a blank is strictly worse than a guess.

Where to go next

• GCSE Mathematics Practice Paper 1 — non-calculator algebra practice, which sharpens SAT speed
• KCSE Mathematics Practice Paper 1 — more work on showing method

Ask StudyAI for more questions on any topic here, timed to SAT pacing.