44 SAT Maths Practice Questions with Answers & Explanations - Part 1

SAT Math MCQs – 44 Questions with Answers and Explanations

SAT Math MCQs – 44 Questions

Domains: Heart of Algebra, Problem Solving & Data Analysis, Passport to Advanced Math, Additional Topics. Correct options marked with ✅.

Heart of Algebra (Q1–Q11)

Q1. Solve for \(x\): \(2x + 5 = 15\).
A) 3 B) 5 ✅ C) 10 D) 15
2x = 10 → x = 5.
Q2. Solve: \(7x - 3 = 4x + 15\).
A) 4 B) 6 ✅ C) 9 D) 12
7x − 4x = 15 + 3 → 3x = 18 → x = 6.
Q3. If \(3(x-2)=2(x+5)\), find \(x\).
A) 16 ✅ B) 4 C) 2 D) 8
3x−6 = 2x+10 → x = 16.
Q4. Solve the system: \(\begin{cases} x+y=9\\ 2x-y=3 \end{cases}\).
A) (3,6) B) (4,5) ✅ C) (5,4) D) (6,3)
Add: 3x = 12 → x=4, then y=5.
Q5. Inequality solution set of \(5-2x \le 11\) is:
A) \(x \ge -3\) B) \(x \ge -3\) ✅ C) \(x \le -3\) D) \(x \le 8\)
−2x ≤ 6 → x ≥ −3.
Q6. Line with slope 3 through (1,2): point-slope form?
A) \(y-2=2(x-1)\) B) \(y-2=3(x-1) ✅\) C) \(y+2=3(x+1)\) D) \(y=3x+2\)
Point-slope: \(y-y_1=m(x-x_1)\) → \(y-2=3(x-1)\).
Q7. If \(f(x)=2x+1\), find \(f^{-1}(x)\).
A) \(\frac{x-1}{3}\) B) \(\frac{x-1}{2} ✅\) C) \(2x-1\) D) \(\frac{x+1}{2}\)
Swap y=x: y=2x+1 → x=(y−1)/2 → \(f^{-1}(x)=(x-1)/2\).
Q8. Solve: \(\frac{x-3}{4}=\frac{x+1}{6}\).
A) 7 B) 9 C) 11 ✅ D) 13
Cross-multiply: 6(x−3)=4(x+1) → 6x−18=4x+4 → 2x=22 → x=11.
Q9. Slope of line through (−2,5) and (4,−1)?
A) 1 B) −1 ✅ C) 2 D) −2
m = (−1−5)/(4−(−2)) = −6/6 = −1.
Q10. If \(ax+b=0\) and \(a\ne0\), solution is:
A) \(x=\frac{a}{b}\) B) \(x=-\frac{b}{a} ✅\) C) \(x=\frac{b}{a}\) D) \(x=-ab\)
ax = −b → \(x = -b/a\).
Q11. Intercept form of line with x-int 3, y-int −6:
A) \(\frac{x}{-3}+\frac{y}{6}=1\) B) \(\frac{x}{3}+\frac{y}{-6}=1 ✅\) C) \(3x-6y=1\) D) \(x+y=9\)
Intercept form: \(x/a + y/b = 1\) → \(x/3 + y/(-6) = 1\).

Problem Solving & Data Analysis (Q12–Q22)

Q12. A bag has 3 red and 5 blue balls. Probability of red?
A) \(1/8\) B) \(3/8 ✅\) C) \(5/8\) D) \(3/5\)
P(red)=3/8.
Q13. A price increases from 80 to 100. Percent increase?
A) 20% B) 25% ✅ C) 12.5% D) 30%
Increase 20 over 80 → 20/80=0.25 → 25%.
Q14. Mean of data: 3, 7, 10, 10?
A) 7 B) 7.5 ✅ C) 8 D) 10
Sum=30, n=4 → mean=7.5.
Q15. Median of 2, 5, 7, 12, 15?
A) 7 B) 7 ✅ C) 9.5 D) 12
Ordered middle value is 7.
Q16. A recipe uses 3 cups flour to 2 cups sugar. If flour=12, sugar=?
A) 6 B) 8 ✅ C) 10 D) 12
Ratio 3:2 → multiply by 4 → sugar=8.
Q17. 30% of x is 45. Find x.
A) 120 B) 150 ✅ C) 180 D) 200
0.3x=45 → x=150.
Q18. If event A has probability 0.4 and B has 0.3, P(A∪B) assuming independence and no overlap?
A) 0.7 B) 0.58 ✅ C) 0.12 D) 0.82
P(A∪B)=0.4+0.3−0.12=0.58 (independent).
Q19. A scatterplot shows positive linear trend. Correlation r likely is:
A) −0.8 B) +0.8 ✅ C) 0 D) −0.2
Positive, strong → r ≈ +0.8.
Q20. From a table, 18 of 60 students prefer math. What percent?
A) 20% B) 30% ✅ C) 25% D) 35%
18/60=0.3 → 30%.
Q21. Unit rate: 240 miles in 4 hours?
A) 50 mph B) 60 mph ✅ C) 70 mph D) 80 mph
240/4=60 mph.
Q22. If z-score of 72 is +1 for mean 60, SD=?
A) 6 B) 12 ✅ C) 18 D) 24
z=(72−60)/SD=1 → SD=12.

Passport to Advanced Math (Q23–Q33)

Q23. Solve \(x^2 - 5x + 6 = 0\).
A) x=1,6 B) x=2,3 ✅ C) x=−2,−3 D) x=0,6
(x−2)(x−3)=0 → x=2,3.
Q24. Vertex of \(y=(x-4)^2+3\).
A) (−4,3) B) (4,3) ✅ C) (3,4) D) (4,−3)
Vertex form → (h,k)=(4,3).
Q25. Solve \(3^{x}=27\).
A) 2 B) 3 ✅ C) 4 D) 5
27=3^3 → x=3.
Q26. Simplify \(\sqrt{50}\).
A) 5√2 B) \(5\sqrt{2} ✅\) C) \(10\sqrt{5}\) D) \(25\)
\(\sqrt{25\cdot2}=5\sqrt{2}\).
Q27. If \(f(x)=x^2-9\), solve \(f(x)=0\).
A) x=0 B) x=±3 ✅ C) x=±9 D) x=3
x^2=9 → x=±3.
Q28. Factor \(x^2-4x-12\).
A) (x−6)(x+2) B) (x−6)(x+2) ✅ C) (x+6)(x−2) D) (x+4)(x−3)
Products −12, sum −4 → −6, +2.
Q29. Solve \(\frac{x}{x-2} = 3\).
A) 1 B) 3 ✅ C) 4 D) 6
x = 3(x−2) → x=3x−6 → 2x=6 → x=3.
Q30. If \(g(x)=2(x-1)^2+5\), minimum value of g?
A) 3 B) 5 ✅ C) 7 D) 9
Square ≥0 → min at x=1 → g=5.
Q31. Solve \(x^2=16\).
A) 4 B) ±4 ✅ C) −4 D) 8
x=±4.
Q32. If \(h(x)=\frac{1}{x}\), what is \(h(−2)\)?
A) 2 B) −\(\frac{1}{2} ✅\) C) −2 D) \(\frac{1}{2}\)
h(−2)=−1/2.
Q33. Solve \(4^{x}=1\).
A) −1 B) 0 ✅ C) 1 D) 2
Any base^0 = 1 → x=0.

Additional Topics (Q34–Q44)

Q34. Circle area with \(r=7\): \(A=\pi r^2\).
A) \(14\pi\) B) \(49\pi ✅\) C) \(98\pi\) D) \(28\pi\)
\(A=\pi\cdot49=49\pi\).
Q35. Right triangle with legs 6 and 8. Hypotenuse?
A) 10 B) 10 ✅ C) 12 D) 14
\(\sqrt{6^2+8^2}=\sqrt{36+64}=10\).
Q36. If \(\sin\theta=3/5\) (right triangle), then \(\cos\theta=\)?
A) 3/4 B) 4/5 ✅ C) 5/3 D) 1/2
Opp=3, hyp=5 → adj=4 → cos=4/5.
Q37. Slope of line perpendicular to slope −2?
A) −1/2 B) 1/2 ✅ C) 2 D) −2
Perpendicular slope = negative reciprocal → 1/2.
Q38. Complex: \((3+2i)+(5-7i)=\)?
A) 8+9i B) 8−5i ✅ C) −2+9i D) −2−5i
Real 3+5=8, imag 2−7=−5.
Q39. Rectangle perimeter with \(l=9, w=4\).
A) 26 B) 26 ✅ C) 36 D) 13
P=2(l+w)=2(13)=26.
Q40. Triangle angles: two are 35° and 75°. Third angle?
A) 70° B) 70° ✅ C) 80° D) 65°
Sum 180 → 180−(35+75)=70.
Q41. Volume of a cube with edge 3.
A) 9 B) 27 ✅ C) 18 D) 36
V = \(3^3 = 27\).
Q42. Distance between points (−1,2) and (3,−2).
A) 4 B) \(\sqrt{32} ✅\) C) \(\sqrt{16}\) D) \(\sqrt{20}\)
\(\sqrt{(3+1)^2+(-2-2)^2}=\sqrt{16+16}=\sqrt{32}\).
Q43. If a circle has circumference \(C=2\pi r=20\pi\), find r.
A) 5 B) 10 ✅ C) 20 D) \(10\pi\)
2Ï€r=20Ï€ → r=10.
Q44. Standard position angle with slope 1 passes through origin. Its measure?
A) 0° B) 45° ✅ C) 90° D) 60°
Slope 1 line y=x makes 45° with x-axis.