Try first, then read the solution
Set aside about 10 minutes. Write down your reasoning before opening each explanation. You can use a calculator, but first decide which quantity the question actually asks for. A correct intermediate result is not always the final answer.
These are original educational questions, not official College Board questions or a full SAT practice test. Five questions cannot provide a calibrated SAT score. Use this set to notice which methods need more practice.
Five questions, five useful methods
1. Linear equations
If 5x − 7 = 3x + 11, what is x? A) 6 B) 9 C) 12 D) 18
Show worked solution
- Subtract 3x from both sides: 2x − 7 = 11.
- Add 7, then divide by 2: 2x = 18, so x = 9.
- Check: both sides equal 38. Choosing 18 would stop one step too early.
Answer: B) 9
2. Systems: read the requested quantity
The lines y = 2x + 1 and y = −x + 10 intersect at (x, y). What is x + y? Enter a number.
Show worked solution
- At the intersection, both expressions equal y: 2x + 1 = −x + 10.
- Collect terms: 3x = 9, so x = 3. Substitute to get y = 2(3) + 1 = 7.
- The question asks for the sum, not either coordinate: x + y = 3 + 7 = 10.
Answer: 10
3. Zeros of a quadratic function
For f(x) = (x − 4)² − 9, what is the sum of the two zeros? A) −9 B) −4 C) 4 D) 8
Show worked solution
- A zero is an input where f(x) = 0. Set (x − 4)² = 9.
- Both 3 and −3 square to 9: x − 4 = 3 or x − 4 = −3.
- The zeros are 7 and 1, so their sum is 8. The vertex’s x-coordinate, 4, is their midpoint.
Answer: D) 8
4. Successive percentage changes
In a hypothetical shop, a 24,000 AMD backpack is discounted by 15%. A 5% tax is then added to the discounted price. What is the final price in AMD? Enter a number.
Show worked solution
- A 15% reduction leaves 85%: 24,000 × 0.85 = 20,400.
- Add 5% to this new amount: 20,400 × 1.05 = 21,420.
- Do not combine these into a 10% discount: the percentages apply to different starting amounts.
Answer: 21,420 AMD
5. Right triangles and sine
A right triangle has legs of lengths 6 and 8. Angle θ is opposite the leg of length 6. What is sin θ? A) 3/5 B) 3/4 C) 4/5 D) 5/3
Show worked solution
- The hypotenuse satisfies c² = 6² + 8² = 100, so c = 10.
- Sine is opposite leg divided by hypotenuse: sin θ = 6/10 = 3/5.
- The ratio 6/8 = 3/4 would be tan θ. Draw and label the triangle before choosing a ratio.
Answer: A) 3/5
Make the mistakes useful
For each missed question, record whether the cause was a missing concept, an arithmetic error, or answering the wrong quantity. Review that topic, solve the question again without looking, and later try a different question using the same method.