SHSAT · Practice from the ASPIRE question bank, not an official form. No score is guaranteed.
Free SHSAT algebra systems practice questions
Free SHSAT algebra systems practice questions: free samples from the ASPIRE question bank, not an official SHSAT form. Take the free Explorer diagnostic with no credit card. One diagnostic and 50 practice questions a month are included.
The diagnostic is on the free Explorer plan. No credit card. One diagnostic and 50 practice questions a month are included.
← Free SHSAT practice questions
Sample questions
5 items from the ASPIRE practice bank. More are in the app.
If x + y = 10 and x - y = 4, what is x?
Show the answer
Answer: C. 7. Add both equations: (x + y) + (x - y) = 10 + 4. This gives 2x = 14, so x = 7. To verify, substitute: if x = 7, then y = 3 from x + y = 10. Check second equation: 7 - 3 = 4 ✓
If x + y = 12 and x − y = 4, what is the value of xy?
Show the answer
Answer: C. 32. Add the equations: 2x = 16, so x = 8. Then y = 12 − 8 = 4. So xy = 8 × 4 = 32. Tip: match coefficients before eliminating a variable. Plug your (x, y) back into both originals to verify.
If 2x + y = 7 and x - y = 2, what is y?
Show the answer
Answer: A. 1. From the second equation: x = y + 2. Substitute into the first: 2(y + 2) + y = 7. Expand: 2y + 4 + y = 7. Combine: 3y + 4 = 7. Subtract 4: 3y = 3. Divide: y = 1. Check: if y = 1, then x = 3. Verify both: 2(3) + 1 = 7 ✓ and 3 - 1 = 2 ✓
A store sells notebooks for $3 each and pens for $1.50 each. Maria buys a total of 10 items and spends $22.50. How many notebooks did she buy?
Show the answer
Answer: C. 5. Let n = notebooks, p = pens. n + p = 10 and 3n + 1.5p = 22.50. From first equation: p = 10 − n. Substitute: 3n + 1.5(10 − n) = 22.50 → 3n + 15 − 1.5n = 22.50 → 1.5n = 7.50 → n = 5.
Tickets cost $5 for adults and $3 for children. A group of 8 people paid $30 total. How many adults were there?
Show the answer
Answer: B. 3. Let a = adults, c = children. a + c = 8 and 5a + 3c = 30. From first: c = 8 − a. Substitute: 5a + 3(8 − a) = 30 → 5a + 24 − 3a = 30 → 2a = 6 → a = 3.