Popular problems, fully worked.

Original examples with complete workings, rules and reasoning. Free to read without an account.

Linear equations
$3 x - 4 y = 12$
Answer: $y = \frac{3}{4} x - 3$
Linear equations
$\frac{x}{3} + \frac{x}{2} = 5$
Answer: $x = 6$
Quadratic equations
$x^{2} + 8 x - 9 = 0$
Answer: $x = 1, x = - 9$
Radicals
$\frac{6}{3}$
Answer: $23$
Logarithms
$lo g_{3} 54 - lo g_{3} 2$
Answer: $3$
Trigonometry
$A = 3 0^{\circ}, B = 4 5^{\circ}, b = 10$
Answer: $a = 52 \approx 7.07$
Geometry
$b_{1} = 8 cm, b_{2} = 12 cm, h = 5 cm$
Answer: $50 cm^{2}$
Geometry
$s = 4 cm$
Answer: $d = 43 cm \approx 6.93 cm$
Derivatives
$\frac{d}{d x} e^{3 x^{2}}$
Answer: $6 x e^{3 x^{2}}$
Integrals
$\int_{0}^{π /2} cos x d x$
Answer: $1$
Statistics
$80 \cdot 0.4 + 90 \cdot 0.6$
Answer: $86$
Probability
$P (R_{1} \cap R_{2}), 3 red, 2 blue$
Answer: $\frac{3}{10} = 30%$
Combinatorics
$Arrange APPLES$
Answer: $360$
Word problems
$d = 300 mi, v_{1} = 60 mph, v_{2} = 40 mph$
Answer: $t = 3 hours$
Percentages
$Price: + 20% then - 10%$
Answer: $8% increase$
Quadratic equations
$x^{2} - 5 x + 6 = 0$
Answer: $x = 2, x = 3$
Quadratic equations
$x^{2} + 4 x - 5 = 0$
Answer: $x = - 5, x = 1$
Quadratic equations
$2 x^{2} + 3 x - 2 = 0$
Answer: $x = \frac{1}{2}, x = - 2$
Linear equations
$3 (x - 4) = 2 x + 7$
Answer: $x = 19$
Linear equations
$2 x + 5 = 13$
Answer: $x = 4$
Systems of equations
${2 x + y = 7 x - y = 2$
Answer: $x = 3, y = 1$
Factoring
$x^{2} - 9$
Answer: $(x - 3) (x + 3)$
Factoring
$x^{3} - 8$
Answer: $(x - 2) (x^{2} + 2 x + 4)$
Quadratic equations
$x^{2} + 6 x + 2$
Answer: $(x + 3)^{2} - 7$
Derivatives
$\frac{d}{d x} (x^{3} sin x)$
Answer: $3 x^{2} sin x + x^{3} cos x$
Derivatives
$\frac{d}{d x} x^{2}$
Answer: $2 x$
Derivatives
$\frac{d}{d x} ln x$
Answer: $\frac{1}{x}$
Derivatives
$\frac{d}{d x} sin (2 x)$
Answer: $2 cos (2 x)$
Integrals
$\int \frac{1}{x} d x$
Answer: $ln ∣ x ∣ + C$
Integrals
$\int_{0}^{1} (2 x + 1) d x$
Answer: $2$
Integrals
$\int x e^{x} d x$
Answer: $x e^{x} - e^{x} + C$
Limits
$lim_{x \to 0} \frac{s i n x}{x}$
Answer: $1$
Trigonometric equations
$sin x = \frac{1}{2}, 0 \leq x < 2 π$
Answer: $x = \frac{π}{6}, \frac{5 π}{6}$
Trigonometric identities
$sin^{2} x + cos^{2} x = 1$
Answer: $Identity proved$
Geometry
$c = 3^{2} + 4^{2}$
Answer: $5$
Geometry
$A = π (5)^{2}$
Answer: $25 π \approx 78.54$
Geometry
$V = \frac{4}{3} π (3)^{3}$
Answer: $36 π \approx 113.10$
Coordinate geometry
$m = \frac{11 - 2}{4 - 1}$
Answer: $3$
Percentages
$0.18 \times 240$
Answer: $43.2$
Percentages
$\frac{52 - 40}{40} \times 100%$
Answer: $30%$
Radicals
$72$
Answer: $62$
Logarithms
$lo g_{2} x = 5$
Answer: $x = 32$
Exponential equations
$2^{x} = 16$
Answer: $x = 4$
Statistics
$x ˉ = \frac{4 + 8 + 15 + 16 + 23 + 42}{6}$
Answer: $18$
Statistics
$σ = \frac{\sum ( x _{i} - μ ) ^{2}}{N}$
Answer: $2$
Probability
$P (sum = 7)$
Answer: $\frac{1}{6}$
Combinatorics
$^{5} C_{2}$
Answer: $10$
Word problems
$v ˉ = \frac{240 + 180}{3 + 2}$
Answer: $84 km/h$
Word problems
$A = 1000 (1.05)^{10}$
Answer: $$1628.89$